# Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice!

Content Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice!
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Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice!
CCSS.MATH.CONTENT.4.NF.B.3.C CCSS.MATH.CONTENT.4.NF.B.3.D

## Adding and Subtracting Mixed Numbers with Common Denominators – Introduction

We're diving into the world of adding and subtracting mixed numbers with common denominators. These problems require us to work with both whole numbers and fractions. As we embark on this mathematical journey, remember that solving these problems is like unraveling a mystery, and you're the detective!

## What Are Mixed Numbers?

Mixed numbers are numbers that contain both a whole number and a fraction. When adding or subtracting mixed numbers, we need to handle the whole numbers and fractions separately. First, we gather clues by reading the problem carefully. Then, we use mathematical operations as our tools to solve the mystery.

Here are the steps to tackle adding and subtracting mixed numbers with common denominators:

Step # Action
1 Read the problem and determine what you are asked to find.
2 Identify the whole numbers and fractions.
3 Add or subtract the whole numbers.
4 Add or subtract the fractions.
5 Simplify the fraction if necessary.
6 Combine the whole number and fraction to get the final answer.
7 Check your answer to ensure it makes sense with the problem.

Let's practice understanding mixed number problems with a couple of exercises.

## Solving Mixed Number Problems – Example

Example 1:

Problem: Solve $2\frac{3}{7}+4\frac{2}{7}$

Steps to Solve the Problem:

Step # Action Equation
1 Write an equation for the problem. $2\frac{3}{7} + 4 \frac{2}{7}$
2 Add the whole numbers. $2 + 4 = 6$
3 Add the fractions. $\frac{3}{7}$ + $\frac{2}{7}$ = $\frac{5}{7}$
4 Combine the whole number and fraction. $6\frac{5}{7}$

Solution: The sum is $6\frac{5}{7}$.

Example 2:

Problem: Solve $5\frac{8}{10} - 1\frac{3}{10}$.

Steps to Solve the Problem:

Step # Action Equation
1 Write an equation for the problem. $5\frac{8}{10} - 1\frac{3}{10}$
2 Subtract the whole numbers. $5 - 1 = 4$
3 Subtract the fractions. $\frac{8}{10}$ - $\frac{3}{10}$ = $\frac{5}{10}$
4 Simplify the fraction if necessary. $\frac{5}{10}$ = $\frac{1}{2}$
5 Combine the whole number and fraction. $4\frac{1}{2}$

Solution: The difference is $4\frac{1}{2}$.

Example 3:

Problem: Solve $3\frac{1}{2} + 3\frac{1}{2} + 4$.

Steps to Solve the Problem:

Step # Action Equation
1 Write an equation for the problem. $3\frac{1}{2} + 3\frac{1}{2} + 4$
2 Add the whole numbers. $3 + 3 + 4 = 10$
3 Add the fractions. $\frac{1}{2}$ + $\frac{1}{2}$ = $\frac{2}{2}$
4 Simplify the fraction if necessary. $\frac{2}{2} = 1$
5 Combine the whole number and fraction. $10 + 1 = 11$

Solution: The sum is $11$.

## Solving Mixed Number Problems – Practice

Now, let's put your skills to the test. Solve these problems on your own, and check the solutions when you're ready!

Solve $2 \frac{1}{4} + 3 \frac{2}{4}$.
Solve $4\frac{5}{8} - 1\frac{3}{8}$.
Solve $1\frac{2}{3} + 2 \frac{1}{3}$.
Solve $5\frac{6}{10} - 2\frac{2}{10}$.
Solve $3\frac{3}{5} + 4\frac{2}{5}$.

## Solving Mixed Number Problems – Summary

Key Learnings from this Text:

• Solving problems with mixed numbers can be achieved by following these steps:
Step # Action
1 Read the problem and determine what you are asked to find.
2 Identify the whole numbers and fractions.
3 Add or subtract the whole numbers.
4 Add or subtract the fractions.
5 Simplify the fraction if necessary.
6 Combine the whole number and fraction to get the final answer.
7 Check your answer to ensure it makes sense with the problem.
• Mastering mixed number addition and subtraction is an important skill in mathematics.

Keep practicing these steps, and you'll become a pro at solving mixed number problems! Check out more fun math challenges and exercises on our website to continue sharpening your skills.

## Solving Mixed Number Problems – Frequently Asked Questions

Why do we need to convert fractions to have common denominators?
Can I simplify fractions before adding or subtracting mixed numbers?
What if my answer is an improper fraction?
Can I use these steps for subtracting mixed numbers?
How can I get better at adding and subtracting mixed numbers?

## Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice! exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice!.
• ### Workout the fraction problems using addition or subtraction.

Hints

First we need to add the whole number.

Next we add across our numerators.

Lastly, as the denominators (bottom number) are the same, our answer should have the same too. Remember sometimes our answers can be simplified

Use the images to help you. You can count the whole cakes and the slices.

In this example $\frac{1}{4}$ + $\frac{1}{4}$ = $\frac{2}{4}$

$\frac{2}{4}$ can be simplified. Both the numerator and denominator can be divided by 2, so our answer would be simplified from $\frac{2}{4}$ to $\frac{1}{2}$

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

Solution

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

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

2 $\frac{1}{2}$ + 2$\frac{1}{2}$ = 5

1 $\frac{2}{6}$ + 1 $\frac{1}{6}$ = 2 $\frac{1}{2}$

• ### Solve the addition and subtraction fraction problems

Hints

First, we add or subtract the whole numbers.

Next we add or subtract the numerators top numbers.

When the denominators bottom number are the same in the question, they will also be the same for the answer.

Solution

2 $\frac{2}{6}$ + 2 $\frac{3}{6}$ = 4$\frac{5}{6}$

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

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

1 $\frac{2}{3}$ - 1 $\frac{1}{3}$ = $\frac{1}{3}$

Hints

Firstly we need to add or subtract the whole numbers. How many whole cakes are there?

Next we need to add or subtract the numerator. The numerator refers to the parts we have (slices of cake)

The denominator bottom number is how many parts the cake has been split into.

Solution

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

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

1 $\frac{2}{6}$ + 2 $\frac{3}{6}$ = 3 $\frac{5}{6}$

2 $\frac{4}{5}$ - 2$\frac{3}{5}$ = $\frac{1}{5}$

• ### Solve the fraction problems.

Hints

First look to see what you need to do. Is it an addition or a subtraction question?

When you have done this, you can then add or subtract the whole numbers.

Then look at the numerators and either add or subtract these.

Finally look at the denominator bottom number. This will be the same for the answer. So we can write this in the blank denominator space.

Solution

2 $\frac{1}{5}$ + 3 $\frac{2}{5}$ = 5 $\frac{3}{5}$

3 $\frac{5}{7}$ - 1 $\frac{4}{7}$ = 2 $\frac{1}{7}$

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

1 $\frac{2}{5}$ + 1$\frac{3}{5}$ = 3

• ### Solve the equation to create a new fraction.

Hints

First we need to add the whole numbers, these are also shown as the whole pizzas. Then add this to the whole number box.

Next, we can add the parts of the fraction, these are the slices of pizza. Put your answer in the numerator top number box.

How many slices has the pizza been split into? This is our denominator bottom number.

Solution

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

• ### Work out the missing numbers.

Hints

Look at the questions. If the denominator (bottom number) is blank, we can look at the denominators in the question as they will all be the same.

If the numerator (top number) is blank we can use the inverse to help work it out. Look at this example.

Solution

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

2 $\frac{5}{7}$ - 1 $\frac{2}{7}$ = 1 $\frac{3}{7}$

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

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