addition and subtraction of fraction problem solving

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Fraction Word Problems: Addition, Subtraction, and Mixed Numbers

In today’s post, we’re going to see how to solve some of the problems that we’ve introduced in Smartick: fraction word problems. They appear during the word problems section at the end of the daily session.

We’re going to look at how to solve problems involving addition and subtraction of fractions, including mixed fractions (the ones that are made up of a whole number and a fraction).

Try and solve the fraction word problems by yourself first, before you look for the solutions and their respective explanations below.

Fraction Word Problems

Problem nº 1.

Problem nº 2

Problem nº 3

Solution to Problem nº 1

This is an example of a problem involving the addition of a whole number and a fraction.

The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 5 / 6 biscuits.

Solution to Problem nº 2

In this example, we have to subtract two fractions with the same denominator.

To calculate how full the gas tank is, we have to subtract both fractions. Since we are given fractions, the best way to present the solution is in the form of a fraction. Additionally, we’re dealing with two fractions with the same denominator, so we just have to subtract the numerators of both fractions to get the result. 8 / 10 – 4 / 10 = 4 / 10

Solution to Problem nº 3

This problem requires us to subtract a mixed number and a fraction.

To solve this problem, we need to subtract the number of episodes that were downloaded this morning from the total number of episodes that are now downloaded.

To do this, we need to change the mixed number into a fraction: the 5 becomes 60 / 12 (5 x 12 = 60) and we add it to the fraction 60 / 12 + 8 / 12 = 68 / 12 .

We’ve converted the mixed number 5 8 / 12 to 68 / 12 . Now we just have to subtract the number of episodes that were downloaded yesterday ( 7 / 12 ),   68 / 12 – 7 / 12 = 61 / 12 .

Hopefully, you didn’t need the explanations and were able to solve them yourself without any help!

Fraction Video Tutorials

In the following video tutorials, you can learn a bit more about fractions. And if you would like to learn more math concepts, check out Smartick’s Youtube channel !

Simplifying Fractions

Simplification Using the GCD

Equivalent Fractions

If you would like to practice more fraction word problems like these and others, log in to Smartick and enjoy learning math.

Learn More:

• Word Problems with Fractions
• What Is a Fraction? Learn Everything There Is to Know!
• Using Mixed Numbers to Represent Improper Fractions
• Learning How to Subtract Fractions
• Learn How to Subtract Fractions
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Fractions  - Adding and Subtracting Fractions

Fractions  -, adding and subtracting fractions, fractions adding and subtracting fractions.

Fractions: Adding and Subtracting Fractions

Lesson 3: adding and subtracting fractions.

/en/fractions/comparing-and-reducing-fractions/content/

Adding and subtracting fractions

In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.

In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.

Click through the slideshow to learn how to set up addition and subtraction problems with fractions.

Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.

You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.

When you add fractions, you just add the top numbers, or numerators .

That's because the bottom numbers, or denominators , show how many parts would make a whole.

We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.

So we only need to add the numerators of our fractions.

We can stack the fractions so the numerators are lined up. This will make it easier to add them.

And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.

We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.

If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.

Just like when we added, we'll stack our fractions to keep the numerators lined up.

This is because we want to subtract 1 part from 3 parts.

Now that our example is set up, we're ready to subtract!

Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!

You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.

You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.

Your gas tank is 2/5 full, and you put in another 2/5 of a tank.

Solving addition problems with fractions

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.

Click through the slideshow to learn how to add fractions.

Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Remember, when we add fractions, we don't add the denominators.

This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .

3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.

The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.

3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.

Let's try another example: 7/10 plus 2/10 .

Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .

7 plus 2 equals 9 , so we'll write that to the right of the numerators.

Just like in our earlier example, the denominator stays the same.

So 7/10 plus 2/10 equals 9/10 .

Try solving some of the addition problems below.

Solving subtraction problems with fractions

Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!

Click through the slideshow to learn how to subtract fractions.

Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.

Just like in addition, we're not going to change the denominators.

We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.

We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.

Just like when we added, the denominator of our answer will be the same as the other denominators.

So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.

Let's try solving another problem: 5/6 minus 3/6 .

We'll start by subtracting the numerators.

5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.

As usual, the denominator stays the same.

So 5/6 minus 3/6 equals 2/6 .

Try solving some of the subtraction problems below.

After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .

Adding fractions with different denominators

On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.

In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .

We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.

Click through the slideshow to learn how to add fractions with different denominators.

Let's add 1/4 and 1/3 .

Before we can add these fractions, we'll need to change them so they have the same denominator .

To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .

It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .

Since 12 is the LCD, it will be the new denominator for our fractions.

Now we'll change the numerators of the fractions, just like we changed the denominators.

First, let's look at the fraction on the left: 1/4 .

To change 4 into 12 , we multiplied it by 3 .

Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .

1 times 3 equals 3 .

1/4 is equal to 3/12 .

Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.

Our old denominator was 3 . We multiplied it by 4 to get 12.

We'll also multiply the numerator by 4 . 1 times 4 equals 4 .

So 1/3 is equal to 4/12 .

Now that our fractions have the same denominator, we can add them like we normally do.

3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .

Try solving the addition problems below.

Subtracting fractions with different denominators

We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.

Click through the slideshow to learn how to subtract fractions with different denominators.

Let's try subtracting 1/3 from 3/5 .

First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .

It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.

Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .

5 times 3 equals 15 . So our fraction is now 9/15 .

Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .

Now that our fractions have the same denominator, we can subtract like we normally do.

9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .

Try solving the subtraction problems below.

Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.

5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.

Let's add these two mixed numbers: 2 3/5 and 1 3/5 .

We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .

As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .

2 times 5 equals 10 .

Now, let's add 10 to the numerator, 3 .

10 + 3 equals 13 .

Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .

Now we'll need to convert our second mixed number: 1 3/5 .

First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .

Next, we'll add 5 to the numerators. 5 + 3 = 8 .

Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .

Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .

Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .

The answer, 4, will become our whole number.

And the remainder , 1, will become the numerator of the fraction.

So 2 3/5 + 1 3/5 = 4 1/5 .

/en/fractions/multiplying-and-dividing-fractions/content/

Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs

What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.

Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:

• Addition and subtraction of like fractions (fractions with same denominators)
• Addition and subtraction of unlike fractions (fractions with different denominators)

A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.

Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.

Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators. 

When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.

Related Worksheets

Addition and Subtraction of Like Fractions

The rules for adding fractions with the same denominator are really simple and straightforward. 

Let’s learn with the help of examples and visual bar models.

Addition of Like Fractions

Here are the steps to add fractions with the same denominator:

Step 1: Add the numerators of the given fractions. 

Step 2: Keep the denominator the same. 

Step 3: Simplify.          

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$  …$c \neq 0$

Example 1: Find $\frac{1}{4} + \frac{2}{4}$ .

$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$

We can visualize this addition using a bar model:

Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$

Subtraction of Like Fractions

Here are the steps to subtract fractions with the same denominator:

Step 1: Subtract the numerators of the given fractions. 

Step 3: Simplify. 

$\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$

Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$.

$\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$

Addition and Subtraction of Unlike Fractions

Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!

Addition of Unlike Fractions

We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator. 

Example: $\frac{3}{5} + \frac{3}{2}$

Step 1: Find the LCM (Least Common Multiple) of the two denominators.

The LCM of 5 and 2 is 10.

Step 2: Convert both the fractions into like fractions by making the denominators same.  

$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$  

$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$

Step 3: Add the numerators. The denominator stays the same.

$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$

Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1. 

In this case, GCF (21,10) $= 1$

The fraction $\frac{21}{10}$ is already in its simplest form. 

Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$

Subtraction of Unlike Fractions

Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.

Example: $\frac{5}{6} \;-\; \frac{2}{9}$

Step 1: Find the LCM of the two denominators.

LCM of 6 and $9 = 18$

Step 2: Convert both the fractions into like fractions by making the denominators same.

$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$   

$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$

Step 3: Subtract the numerators. The denominator stays the same.

$\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$

In this case, the GCF (11,18) $= 1$

So, it is already in its simplest form. 

Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$

A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa. 

Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .

Addition and Subtraction of Mixed Fractions with Same Denominators

The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.

Step 1: Convert the given mixed fractions to improper fractions.

Step 2: Add/Subtract the like fractions obtained in step 1.

Step 3: Reduce the fraction to its simplest form.

Step 4: Convert the resulting fraction into a mixed number.

Example 1: $2\frac{1}{5} + 1\frac{3}{5}$

$2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$

$1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$

Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$

Converting $\frac{19}{5}$ into a mixed number, we get

$\frac{19}{5} = 3\frac{4}{5}$

Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$

Addition and Subtraction of Mixed Fractions with Unlike Denominators

Step 2: Convert both the fractions into like fractions by finding the least common denominator.

Step 3: Add the fractions. (or subtract the fractions.)

Step 4: Reduce the fraction if possible or convert back to a mixed number 

Let us understand the addition of mixed numbers with unlike denominators with the help of an example.

Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$.

Convert the given mixed fractions to improper fractions.

$1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$

Step 2: Convert both the fractions into like fractions by making the denominators the same.

Here, LCM of 5 and 2 is 10.

Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$

Step 3: Add the fractions by adding the numerators.

$\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$

Step 4: Convert back into a mixed number. 

Thus, $\frac{41}{10}$ will become  $4\frac{1}{10}$

Therefore, $1\frac{3}{5} + 2\frac{1}{2} =  4\frac{1}{10}$

Here’s an example for subtraction. It follows the same steps.

Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$

Step 1: Convert the mixed numbers into improper fractions.

     $6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$

Step 2: Make the denominators equal.

LCM of 2 and 4 is 4. 

   $\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$ 

Step 3: Subtract the fractions.

        $\frac{26}{4} \;-\;  \frac{7}{4} = \frac{19}{4}$

Step 4: Convert the fraction as a mixed number.

            $\frac{19}{4}  = 4\frac{3}{4}$  

Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4}  =   4\frac{3}{4}$  

Facts about Addition and Subtraction of Fractions

• We cannot add or subtract fractions without converting them into like fractions.
• Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators.
• Equivalent fractions are two different fractions that represent the same value.
• The LCD (least common denominator) of two fractions is the LCM of the denominators.

In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.

• Solve: $\frac{2}{4} + \frac{1}{4}$ .

Solution: 

Here, the denominators are the same.

Thus, we add the numerators by keeping the denominators as it is.

$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$ 

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.

$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.

The LCM of 2 and 5 is 10.

Thus, we can write

$\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$

$= \frac{6}{10} + \frac{25}{10}$

            $= \frac{6}{10} + \frac{25}{10}$

            $= \frac{31}{10}$

Thus, $\frac{3}{5} + \frac{5}{2} =  \frac{31}{10}$

3. Find $\frac{4}{16} + \frac{5}{8}$.

Solution:  

To add two fractions with different denominators, we first need to find the LCM of the denominators.

The LCM of 16 and 8 is 16.

$\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$ 

            $= \frac{10}{16} + \frac{4}{16}$ 

            $= \frac{14}{16}$

$= \frac{7}{8}$

4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope.

Total length of the rope $= 12\frac{1}{2}$ ft.

Length of the rope that was cut off $= 7 \frac{6}{8}$ ft. 

The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$

$12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$

         $= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$

         $= \frac{100}{8} \;-\; \frac{62}{8}$

         $= \frac{38}{8}$

         $= \frac{19}{4}$

Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.

Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.

Attend this quiz & Test your knowledge.

Find $\frac{2}{4} + \frac{2}{4}$.

$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.

How do we add and subtract negative fractions?

Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.

How can we convert an improper fraction into a mixed number?

To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.

Example: $\frac{14}{3} = 4\; \text{R}\; 2$

Quotient $= 4$

Remainder $= 2$

$\frac{14}{3} = 4\frac{2}{3}$

How do we divide two fractions?

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.

$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$

For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$

What are the rules of adding and subtracting fractions?

• Before adding or subtracting, we check if the fractions have the same denominator.
• If the denominators are equal, then we add/subtract the numerators keeping the common denominator.
• If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is.

How do we add and subtract fractions with whole numbers?

• Convert the whole number to a fraction. To do this, give the whole number a denominator of 1.
• Convert to fractions of like denominators. 
• Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem.

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Adding & subtracting fractions word problems

Word problem worksheets: addition & subtraction of fractions.

Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers.  All fractions have like denominators.  Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.  These worksheets are pdf files .

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Fraction Word Problems (Grade 5)

These lessons, with videos, examples and solutions help Grade 5 students learn to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Related Pages Common Core for Grade 5 More Lessons for Grade 5

For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Common Core: 5.NF.2

Suggested Learning Targets

• I can solve addition and subtraction word problems with fractions.
• I can estimate fractions to make sense of my answer.

Solve Fraction Word Problems with Visual Bar Models

Example: Kayla weighed her Halloween treats. She counted 1/4 of a pound of lollipops and 2/7 of a pound of gobstoppers. She also counted 1/3 of a pound of mints. How many pounds of candy did Kayla have altogether?

Add mixed numbers word problems

Example: While gardening, Jan spend 1 3/4 hours planting and 2 1/8 hours trimming. What was the total hours worked by Jan in her garden?

Solve word problems involving addition of fractions - unlike denominators

Example: Matthew ran 1/6 of a mile then took a break before running another 3/4 of a mile. How far did Matthew run in all?

Subtracting Fractions From Whole Numbers Solve a word problem using bar models.

Example: A craft store has a 9-yard spool of ribbon. In the morning, a customer buys 1/5 yard of ribbon from the spool. In the afternoon, another customer buys 7/10 yard of ribbon from the spool. How much ribbon is left?

Adding and subtracting unlike fractions word problems

• Drew and Maddy were filling the class raised garden bed with soil. Drew shoveled in 1/3 of a cubic yard, and Maddy shoveled in 1/2 of a cubic yard. How much soil did they put into the garden bed altogether?
• Caden invited Owen over to his house. Caden shared his chocolate stash from last Halloween. He still had 4/5 of a pound of chocolate. Caden asked Owen how much chocolate he would like. Owen said that he would like 1/3 of a pound of chocolate. How much chocolate does Caden have left?

Adding and subtracting mixed numbers word problems

• Jaida went gold panning and found 1 1/5 pounds of gold. The next day she found 3 1/4 pound more. How much total gold did Jaida find?
• Jonathan collected 4 1/2 kilograms of filberts. He gave 2 3/4 kilograms to his friend. How many kilograms of filberts does Jonathan have now?

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• Math Article
• Addition And Subtraction Of Fractions

Introduction To Addition And Subtraction Of Fractions

A fraction is defined as a part of a whole or, more commonly, any number of equal parts. Sometimes we want to add or subtract two fractions to find out the total number. This activity is called Addition and Subtraction of Fractions . For example, Malini ate 1 ½ bread for lunch and 2 ½ bread for dinner. What is the total number of bread Malini ate? In the above example, it is necessary to add the fractions. How do add or subtract fractions? What are the steps involved to add or subtract fractions? Let us take an overview of the Addition and Subtraction of Fractions.

Addition and Subtraction of Fraction Methods

All fractions cannot be added or subtracted easily. The following methods are available to add or subtract fractions.

• Add or subtract fractions with the same denominator
• Add or subtract fractions with different denominators
• Add or subtract mixed number fraction

Addition or Subtraction of Fractions with the Same Denominator

In this method, the addition or subtraction of a fraction is very easy. Because the denominators of the two fractions are the same.

Example: 2 / 4 + 3 / 4 = ?

In the above fractions, the denominators are the same.

  3 / 4   =

In the above fractions, the box is divided into four parts. For 2 / 4  and 3 / 4 ,  take numerator parts respectively out of 4 equal parts.

The steps involved in adding fractions with the same denominators are given below:

Step 1: In the given fraction, check if the denominators are the same.

Step 2: If denominator s are the same, t ake the numerators of two fractions and add or subtract them .

Step 3: Give a final answer with a denominator.

Example 1: 5 / 8 + 2 / 8 = ?

Step 1: Denominators are the same.

Step 2: Take the numerators 5 and 2 respectively and add them.

  = (5+2) / 8

Step 3: Give the final answer.

Example 2: 5 / 8 – 2 / 8 =?

Step 2: Take the numerators 5 and 2 respectively and subtract the smaller from the bigger numerator.

  = (5-2) / 8

Addition or Subtraction of Fractions with the Different Denominator

In this method, the denominators are not the same in two fractions. Thus, the numerators and denominators are different in the two fractions. So we need to make the denominators equal. 

Let us add two fractions, 3 / 8 and 5 / 12 .

In the above fractions, numerators and denominators are different. Let’s have a look at the stepwise solution for the addition of two fractions 3/8 and 5/12.

Step 1: Take Least Common Multiple for denominators of the above fractions. i.e. 8 and 12 respectively.

(LCM is the smallest number which is used as a common multiple of two numbers)

24 is a common multiple for 8 and 12.

Step 2: Convert denominators 8 and 12 into 24.

For 3 / 8 , multiply the numerator and denominator by 3 = 3 / 8 x 3 / 3 = 9 / 24

For 5 / 12 , multiply the numerator and denominator by 2 = 5 / 12 x 2 / 2 = 10 / 24

Step 3: Now, the denominators of the two fractions are the same.

9 / 24 , 10 / 24

Step 4: Take the numerators 9 and 10 respectively and add them.

= (9+10) / 24

Step 5: Give a final answer

A similar procedure can be followed to subtract the fractions with different denominators.

Example: 3/8 – 5/12 =?

Step 1: Denominators are different. So, take the Least Common Multiple (LCM).

24 is a common multiple of 8 and 12.

Step 2: Make the denominators equal by multiplying 3/3 with ⅜ and multiplying 2/2 with 5/12.

3/8 => 3/8 x3/3 = 9/24

5/12 => 5/12x 2/2 = 10/24

Step 3: Take the numerators and subtract.

3/8 – 5/12  = 9/24 – 10/24

= (9-10)/24 (subtract the smaller numerator from the bigger)

Step 4:   Answer   = -1 / 24

Addition and Subtraction of Mixed Fractions

A  mixed fraction  is defined as a fraction and a whole number combined into one “ mixed ”  number .

Depending on the denominator, two following methods are available for adding or subtracting a mixed fraction.

• If the same denominators are present in the mixed fraction.
• If different denominators are present in the mixed fraction.

Click here to learn more about mixed fractions .

Addition or Subtraction of Mixed Fractions with the Same Denominator

In this method, the mixed fraction consists of the same denominators. The following steps are involved to add or subtract the mixed fraction.

Step 1: Add the whole number of two fractions separately.

Step 2: Add the fractions separately.

Step 3: Combine the whole number and the fraction both

Step 3: Convert the improper fraction into a mixed fraction.

Example:  3 2 / 5 + 1 4 / 5 = ?

Step 1: Add the whole number of two fraction separately

= 3+1 = 4 — (1)

Step 2: Add the fractions separately

= 2 / 5 + 4 / 5 = 6 / 5 —– (2)

Step 3: Combine the both equation (1) and (2)

= 4 6 / 5 —— (3)

In 4 6 / 5 , 6 / 5 is an improper fraction. So, convert it into a properly mixed fraction.

Equation (2) —–> 6 / 5 = 1 1 / 5 —– (3)

Step 4: Now, add equation (1) and (3)

4 + 1 1 / 5 = 5 1 / 5

Answer = 5 1 / 5

Alternative Method:

In this method, the step is to convert the given mixed fraction into an improper fraction and then we can perform the addition or subtraction.

Click here to convert the mixed fraction to improper fraction online.

The steps involved in this method are:

• Convert the mixed fractions to improper fractions.
• Check if the denominators are the same.
• Now, take the denominator as common and add or subtract (as per the given) the numerators.
• Finally, simplify the answer.

Thus, the above example can be solved as:

3 2 / 5 + 1 4 / 5 = ?

Now, 3 2 / 5 + 1 4 / 5 = 17/5 + 9/5

= (17 + 9)/5

Addition or Subtraction of Mixed Fractions with the Different Denominator

In this method, the mixed fraction consists of different denominators. The following steps are involved to add or subtract the mixed fraction.

Example: 6 3 / 4 + 3 5 / 8 = ?

Solution: In the above-mixed fractions, the denominators are different.  So we need to make the denominators the same.

Step 1: Take LCM for denominators of the above fractions. i.e. 4 and 8 respectively.

8 is a common multiple for 4 and 8.

Step 2: Convert denominators 4 and 8 into 8.

In 3 / 4 , multiply the numerator and denominator by 2 = 3 / 4 x 2 / 2 = 6 / 8

In 5 / 8 , multiply the numerator and denominator by 1 = 5 / 8 x 1 / 1 = 5 / 8

(Note: We must do to the numerator what we do to the denominator)

Now, denominat ors are the same in t he mixed fraction

6 3 / 4 + 3 5 / 8   = 6 6 / 8 + 3 5 / 8

Step 3: Add the whole number of two fractions separately

= 6+3 = 9 ———— (1)

Step 4: Add the fractions separately

= 6 / 8 + 5 / 8 = 11 / 8 —– (2)

11 / 8 is an improper fraction. So, convert it into a properly mixed fraction.

11 / 8 = 1 3 / 8 ————(3)

Step 5: Combine both equation (1) and (3)

9+ 1 3 / 8 = 10 3 / 8

Answer: 10 3 / 8

• Check the denominators whether they are equal if not make them equal.

6 ¾ + 3 ⅝  = ?

The LCM of 4 and 8 is 8.

Now, make the denominators equal.

(27/4) × (2/2) = 54/8

29/8 × (1/1) = 29/8 

6 ¾ + 3 ⅝  = (54/8) + (29/8)

= (54 + 29)/8

Similarly, we can subtract the mixed fractions.

Suppose 6 ¾  –  3 ⅝  = (54/8) – (29/8) = (54 – 29)/8 = 25/8 = 3 1/8.

Video Lesson on Fractions

Practice Problems on Addition and Subtraction of Fractions

• Find the sum of 3/7 and 5/8.
• Subtract 5 ¼ from 6 2/7.
• Add 6/9, 2/9 and 11/9.
• Subtract 26/49 from 16/42.

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Adding and Subtracting Fraction Word Problems

Subject: Mathematics

Age range: 7-11

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Last updated

16 June 2015

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Fraction Addition Word Problems Worksheets

Let children work on our printable adding fractions word problems worksheets hammer and tongs! Whether it's sharing a meal with your friends or measuring the ingredients for a recipe, adding fractions is at the heart of it all, hence our worksheets. A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!

Adding Fractions with Whole Numbers

Dazzle 3rd grade kids with a gift of lifelike story problems! If you're a novice up against fraction addition, don't miss our pdf adding fractions word problems worksheets using whole numbers and fractions!

• Download the set

Adding Like Fractions Word Problems

Gerald ate 5/9 of an apple, and Garry ate 4/9 of it. How many apples did they eat in all? Good going! They both ate one whole apple. Simply combine the numerators and solve the like fraction word problems here!

Adding Unlike Fractions

A potpourri of word problems that involve adding unlike fractions, these pdfs mean that 4th grade and 5th grade students will breeze through addition of fractions with different denominators in their day-to-day lives.

Adding Mixed Numbers | Same Denominators

See in your mind's eye adding mixed numbers with same denominators riding on the several real-life scenarios in our printable worksheets! Convert the mixed numbers to fractions, and add them as usual.

Adding Mixed Numbers | Different Denominators

Steal a march on your 5th grade and 6th grade peers by getting your act together to power through the real-world situations featured in this set of printable adding mixed numbers word problems worksheets.

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Add and Subtract Fractions Online practice for grades 3-7

On this page, you can practice addition and subtraction of fractions. Each practice set will automatically include both addition and subtraction problems.

The options are:

• You can limit the fractions in the problems to like fractions (fractions with the same denominator), for example: 1/6 + 4/6.
• You can limit the script to use only proper fractions—fractions that are less than 1. With this option, the script will make problems such as 1/4 + 2/5, but will not make problems such as 8/5 − 4/5.
• When you choose problems that use simplified fractions, the script will only include fractions in the problems that are in lowest terms. For example, you could get a problem such as 5/6 + 3/5, but you would not see 2/4 + 6/8.
• The last option, when chose, allows or accepts answers to not be in lowest terms. In other words, the script will accept an answer such as 8/10.

Note: ALL answers have to be given as mixed numbers, when possible. In other words, your answer cannot be left as an improper fraction.

You may use the space below to write the intermediate step. Your work in this area will not be checked.

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How to Add and Subtract Fractions

Last Updated: April 6, 2024 Fact Checked

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 158,935 times.

Adding and subtracting fractions is an essential skill to have. Fractions show up in daily life all the time, especially in math classes, from elementary school through college. Just follow these steps to learn how to add and subtract them, whether they're like fractions, unlike fractions, mixed, or improper fractions. Once you know one way, the rest is pretty easy!

Adding and Subtracting Fractions with the Same Denominator

• In other words, 1/5 and 2/5 does not need to be written as 1/5 + 2/5 = ? It can be written as 1+2/5 = ? . The denominator is the same, so it can be written only once. Both numerators then go on top.

• Whether you have it written 1/5 + 2/5 or 1+2/5, you answer should be the same: 3! After all, 1 + 2 = 3.

• So, using the same example, our denominator is 5. That's it! That's the bottom number of our fraction. That's half the answer already!

• What was your numerator? 3. The denominator? 5. Therefore, 1/5 + 2/5, or 1+2/5, equals 3/5 .

Adding and Subtracting Fractions with Different Denominators

• Write out the multiples . The multiples of 3 are 3, 6, 9, 12, 15, 18...and so on. The multiples of 4? 4, 8, 12, 16, 20, etc. What's the lowest number seen in both of the sets? 12! That's your lowest common denominator, or LCD.
• Multiply the numbers together for small numbers. In some cases, like this one, you could just multiply the numbers together – 3 x 4 = 12. However, if your denominators are big, don't do this! You don't want to multiply 56 x 44 and have to work with 2,464 as your answer!

• You'll notice that the denominators, in this instance, are multiplied by each other. This works in this situation, but not all situations. Sometimes, instead of multiplying the two denominators together, you can multiply both denominators by different numbers to get one small number.
• And then in other cases, sometimes you only have to multiply one denominator to make it equal to the denominator of the other fraction in the equation.

• We had 2/3x4 and 3/4x3 as our first step – to add the second step, it's really 2 x 4/3 x 4 and 3 x 3/4 x 3. That means our new numbers are 8/12 and 9/12. Perfect!

• For this example, (8+9)/12 = 17/12. To turn this into a mixed fraction, simply subtract the denominator from the numerator and see what's left over. In this case, 17/12 = 1 5/12

Adding and Subtracting Mixed and Improper Fractions

• For the example for this section, let's work with 13/12 and 17/8.

• Let's figure out the multiples of our example, 12 and 8. What's the smallest number these two go into? 24. 8, 16, 24 and 12, 24 – bingo!

• So 13 x 2/12 x 2 = 26/24. And 17 x 3/8 x 3 = 51/24. We're well on our way to solving the problem!

• 26/24 + 51/24 = 77/24. There's your one fraction! That top number is mighty big, though....

• For this example, 24 goes into 77 three times. That is, 24 x 3 = 72. But there's 5 leftover! So what's your final answer? 3 5/24. That's it!

Adding and Subtracting Fractions without looking for the LCD

• e.g. ½ + ¾ + ⅝

• Multiply ¹ to the denominator/s of the other fractions.
• Multiply 1 to 4 and 8. [32]

• Multiply 3 with 2 and 8. [48]
• Lastly, multiply 5 with 4 and 2. [40]

• 32+48+40=120

• 120/64 = 1 56/64 = 1 ⅞

Joseph Meyer

To simplify fractions, you can divide both the numerator and denominator by a common factor. This creates a new, easier-to-use fraction with smaller components, but it represents the same value. For instance, if you divide both the numerator and denominator of 6/12 by 2, you get 3/6, which is equal to 1/2.

Calculator, Practice Problems, and Answers

Community Q&A

• This method might lead you to multiplying large numbers.
• This might require you a calculator.

You Might Also Like

• ↑ https://www.chilimath.com/lessons/introductory-algebra/adding-and-subtracting-fractions-with-same-or-like-denominator/
• ↑ https://www.mathsisfun.com/fractions_subtraction.html
• ↑ https://edu.gcfglobal.org/en/fractions/adding-and-subtracting-fractions/1/
• ↑ https://www.mathsisfun.com/least-common-denominator.html
• ↑ https://www.coolmath4kids.com/math-help/fractions/adding-and-subtracting-fractions-different-denominators
• ↑ https://www.bbc.co.uk/bitesize/topics/zhdwxnb/articles/z9n4k7h
• ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Mixed_Numbers_and_Improper_Fractions.pdf
• ↑ https://www.mathsisfun.com/numbers/fractions-mixed-addition.html
• ↑ https://www.chilimath.com/lessons/introductory-algebra/adding-and-subtracting-fractions-with-different-denominators/

About This Article

To add and subtract fractions with the same denominator, or bottom number, place the 2 fractions side by side. Add or subtract the numerators, or the top numbers, and write the result in a new fraction on the top. The bottom number of the answer will be the same as the denominator of the original fractions. To learn how to add and subtract fractions with different denominators, keep reading! Did this summary help you? Yes No

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Addition and Subtraction of Fractions

Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers to improper fraction. (ii) Find the L.C.M of the denominators of the fractions and place the L.C.M below a horizontal bar. (iii) The L.C.M is then divided by each denominator and the quotient is multiplied to the corresponding numerator. The results obtained are placed above the horizontal bar with proper sign (+) or (-) to obtain a single fraction. (iv) Reduce the fraction obtained to simplest form and then convert it into mixed form if needed.

In order to add or subtract like fractions, we add or subtract their numerators and retain the common denominator. 

Examples on addition or subtraction with like fractions; (i) 5/8 + 2/8 = (5 + 2)/8 = 7/8 (ii) 11/5 – 7/15 = (11 – 7)/15 = 4/15 (iii) 16/5 – 3/5 + 2/5 – 9/5 = (16 – 3 + 2 - 9)/5 = (18 – 12)/5 = 6/5 (iv) 4²/₃ + 1/3 – 4¹/₃ = (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3 = 14/3 + 1/3 – 13/3 = (14 + 1 - 13)/3 = (15 - 13)/3 = 2/3

In order to add and subtract unlike fractions, we follow the following steps: STEP I: Obtain the fractions and their denominators. STEP II: Find the LCM of the denominators. STEP III: Convert each of the fraction into an equivalent fraction having its denominator equal to the Least Common Multiple (LCM) obtained in step II. STEP IV: Add or subtract like fractions obtained in step III .

Examples on addition or subtraction with unlike fractions; 1. Add: (i) 7/10 + 2/15 (ii) 2²/₃ + 3¹/₂ Solution: (i) 7/10 + 2/15

LCM of 10 and 15 is (5 × 2 × 3) = 30. So, we convert the given fractions into equivalent fractions with denominator 30. 7/10 = (7× 3)/(10 × 3) = 21/30 , and 2/15 = (2 × 2)/(15 × 2) = 4/30 Therefore, 7/10 + 2/15 = 21/30 + 4/30 = (21 + 4)/30 =

= (29 × 4)/(6 × 4) – (19 × 3)/(8 × 3) + (43 × 2)/(12 × 2) [Since, LCM of 6, 8, 12 is 2 × 3 × 2 × 2 = 24] = 116/24 – 57/24 + 86/24 = (116 – 57 + 86)/24 = (202 – 57)/24 = 145/24 4. Simplify the fraction: (i) 2 – 3/5      (ii) 4 + 7/8      (iii) 9/11 – 4/15      (iv) 8(1/2) – 3(5/8) (i) 2 – 3/5 Solution: 2 – 3/5 = 2/1 – 3/5          [Since, 2 = 2/1] = (2 × 5)/(1 × 5) – (3 × 1)/(5 × 1)           [Since, LCM of 1 and 5 is 5] = 10/5 - 3/5 = (10 - 3)/5 = 7/5 (ii) 4 + 7/8 Solution: 4 + 7/8 = 4/1 + 7/8           [Since, 4 = 4/1] = (4 × 8)/(1 × 8) + (7 × 1)/(8 × 1)           [Since, LCM of 1 and 8 is 8] = 32/8 + 7/8 = (32 + 7)/8 = 39/8 (iii) 9/11 – 4/15 Solution: 9/11 – 4/15 LCM of 11 and 15 is 11 × 15 = 165. = 9/11 - 4/15 = (9 × 15)/(11 × 15) = (4 × 11)/(15 × 11) = 135/165 – 44/165 = (135 – 44)/165 = 91/165 (iv) 8¹/₂ – 3⁵/₈ Solution: 8¹/₂ – 3⁵/₈ = 17/2 – 29/8 = (17 × 4)/(2 × 4) –(29 × 1)/(8 × 1) [Since, LCM of 2 and 8 is 8] = 68/8 – 29/8 = (68 – 29)/8 = 39/8 = 4⁷/₈ 5. Simplify: 4²/₃ – 3¹/₄ + 2¹/₆. Solution: 4²/₃ – 3¹/₄ + 2¹/₆. = 14/3 – 13/4 + 13/6 = (14 × 4)/(3 × 4) – (13 × 3)/(14 × 3) + (13 × 2)/(6 × 2) [Since, LCM of 3, 4 and 6 is 12, so we convert each fraction into an equivalent fraction with denominator 12] = 56/12 – 39/12 + 26/12 = (56 – 39 + 26)/12 = (82 – 39)/12 = 43/12 = 3⁷/₁₂

Word Problems on Addition and subtraction of fractions: 1. Ron solved 2/7 part of an exercise while Shelly solved 4/5 of it. Who solved less? Solution: In order to know who solved less part of the exercise, we will compare 2/7 and 4/5 LCM of denominators (i.e., 7 and 5) = 7 × 5 = 35 Converting each fraction in to an equivalent fraction having 35 as its denominator, we have 2/7 = (2 × 5 )/(7 × 5) = 10/35 and 4/5 = (4 × 7)/(5 × 7) = 28/35 Since, 10 < 28 Therefore, 10/35 < 28/35 => 2/7 < 4/5 Hence, Ron solved lesser part than Shelly.

2. Jack finished coloring a picture in 7/12 hour. Victor finished coloring the same picture in 3/4hour. Who worked longer? By what fraction was it longer? Solution: In order to know who worked longer, we will compare fractions 7/12 and 3/4. LCM of 12 and 4 = 12 Converting each fraction into an equivalent fraction with 12 as denominator 7/12 = (7 × 1)/(12 × 1) = 7/12 and 3/4 = (3 × 3)/(4 × 3) = 9/12 Since, 7 < 9 Therefore, 7/12 < 9/12 => 7/12 < 3/4 Thus, Victor finished coloring in longer time. Now, 3/4 - 7/12 = 9/12 – 7/12 = (9 – 7)/ 12 = 2/12 = 1/6 Hence, Victor finished coloring in 1/6 hour more time than Jack.

3. Sarah purchased 3¹/₂kg apples and 4³/₄ kg oranges. What is the total weight of fruits purchased by her? Solution: Total weight of the fruits purchased by Sarah is 3¹/₂ + 4³/₄ kg. Now, 3¹/₂ + 4³/₄ = 7/2 + 19/4 = (7 × 2)/(2 × 2) + (19 × 1)/(4 × 1) = 14/4 + 19/4 = (14 + 19)/4 = 33/4 = 8¹/₄ Hence, total weight is 8 1/4 kg. 4. Rachel ate 3/5 part of an apple and the remaining apple was eaten by her brother Shyla. How much part of the apple did Shyla eat? Who had the larger share? By how much? Solution: We have, Part of an apple eaten by Rachel = 3/5 Therefore, part of an apple eaten by Shyla = 1 - 3/5 = 5/5 – 3/5 = (5 - 3)/5 = 2/5 Clearly, 3/5 > 2/5 So, Rachel had the larger share. Now, 3/5 – 2/5 = (3 - 2)/5 = 1/5 Therefore, Rachel had 1/5 part more than Shyla. 5. Sam wants to put a picture in a frame. The picture is 7³/₅ cm wide. To fit in the frame the picture cannot be more than 7³/₁₀ cm wide. How much the picture should be trimmed? Solution: Actual width of the picture = 7³/₅ cm = 38/5cm Required width of the picture = 7³/₁₀ cm = 73/10 cm Therefore, extra width = (38/5 – 73/10) cm = (38 × 2)/(5 × 2) – (73 × 1)/( 10 × 1) cm = 76/10 – 73/10 cm = (76 – 73)/10 cm = 3/10 cm Hence, 3/10 cm width of the picture should be trimmed.

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How to Solve Word Problems With Addition and Subtraction of Fractions

Grandma Coco has two jars of jam. The first jar is 2/8 full. The second jar is 5/8 full. How much jam does Grandma Coco have in total?

Grandma Coco has 7/8 jar of jam.

A Bag of Soil

Robert has 5/6 bag of soil for gardening. He gave 3/6 bag to his neighbor Bill. How much soil does Robert have now?

Robert now has 2/6 of a bag of soil. ✅

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Fraction Addition and Subtraction: Problems with Solutions

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MATH NUMBERLESS WORD PROBLEMS for ADDITION and SUBTRACTION within 20

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Teaching math word problems becomes a breeze with these numberless word problems for adding and subtracting within 20. They are guaranteed to melt teacher anxiety away and transform your students into Rock Star problem solvers .

You see, when numbers are initially removed from a math problem, students are forced to slow down and truly focus on what, exactly, the question is asking.

By the time the numbers are revealed, students are ready to effectively tackle the problem head-on.

This strategy has propelled our students' abilities to think critically about math problem-solving to the next level.

========================================================================

This resource comes in two versions - a NO PREP Digital Version and a Printable Version . Whatever you need, we've got you covered!

==============================================================================

WHAT'S INCLUDED:

• 88 NUMBERLESS STORY PROBLEMS TO WORK THROUGH TOGETHER AS A CLASS
• 88 WORD PROBLEMS (NUMBERS INCLUDED) FOR INDEPENDENT PRACTICE
• FOR EASY DIFFERENTIATION, WE'VE ALSO INCLUDED A SET OF BLANK WORD PROBLEMS - JUST WRITE IN THE NUMBERS YOU WANT TO USE

=======================================================================

MORE ABOUT THIS RESOURCE:

The Word Problems are organized by word problem type so you can easily pick and choose exactly what you need.

• Joining Start Unknown
• Joining Change Unknown
• Joining Result Unknown
• Separating Start Unknown
• Separating Change Unknown
• Separating Result Unknown
• Part-Part-Whole Part Unknown
• Part-Part-Whole Result Unknown
• Compare Difference Unknown
• Compare Quantity Unknown
• Compare Referent Unknown

BENEFITS of NUMBERLESS WORD PROBLEMS:

Numberless word problems require students to process what the problem is and what is needed to solve it . Students will no longer absentmindedly add or subtract numbers they see, because there aren't any numbers there - at first, anyway.

For example:

There were students on the bus.

More students got on the bus.

How many more students got on the bus?

Give time for students to process and truly understand what is really going on in this situation.

After students THINK about and PROCESS the problem, they are presented with snippets of needed information, a little at a time. By presenting a word problem in a numberless manner first, students are truly focusing on what the problem is asking.

This strategy not only works but it cultivates deep mathematical thinking and obliviates absentmindedly guessing.

WHAT TEACHERS LIKE YOU ARE SAYING:

"I love, love, love this! It gets students thinking about what the problems are telling them and what they are not. My students are thinking rather than writing the first 2 numbers they see and adding them together."

"These are A-mazing !! These have helped my students understand what information is needed to solve different types of problems and to think about what they are solving for. The process used to think about a problem encouraged my students to engage in productive student discourse about math ."

"I just loved using this product this year with my students. I particularly love how student-friendly it is. I believe this teaching strategy is one of the best ones for teaching problem-solving. Your product made it very easy to use the strategy in my classroom!"

" I love this unit . Using numberless word problems has been a great boost to teaching word problems. The conversation is so much better. My kids get it. Thank you, thank you, thank you !"

"Our primary-grade teachers just were bemoaning how students always just want to add, whenever they see two numbers! This is brilliant ...one of those "why didn't I think of that?" moments when you realize you can begin without numbers. Thanks so much! I'm going to purchase extra licenses for my colleagues!"

For years we introduced and taught students how to solve math word problems teaching them strategies to use such as underlining the question, circling important information, and looking for keywords.

Some of our students had success, but many students struggled, especially when the unknown was not the end result. They didn't truly understand the situation or how to tackle it.

Luckily, we stumbled upon the idea of using numberless word problems to truly help students focus on the problem situation. It increased student discourse and understanding GREATLY.

With repeated exposure, discussion, and practice, students began approaching math word problems with understanding and success.

THIS RESOURCE IS HELPFUL FOR:

-Kindergarten, First Grade, and Second Grade Teachers

-Special Education Teachers

-Whole Group Math Instruction

-Small-Group Math Instruction

-Math Intervention

You may also like:

Number Talks - A Yearlong Program for First Grade

Number Talks - A Yearlong Program for Second Grade

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Becky & Cindy

Team Primary Bliss Teaching

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