How to subtract mixed numbers

This comprehensive guide provides step-by-step instructions to solve different types of mixed number subtraction problems.

Katie Wickliff headshot

Author
Katie Wickliff

Published
January 19, 2024

How to subtract mixed numbers

This comprehensive guide provides step-by-step instructions to solve different types of mixed number subtraction problems.

Katie Wickliff headshot

Author
Katie Wickliff

Published
Jan 19, 2024

How to subtract mixed numbers

This comprehensive guide provides step-by-step instructions to solve different types of mixed number subtraction problems.

Katie Wickliff headshot

Author
Katie Wickliff

Published
Jan 19, 2024

Key takeaways

  • Mixed numbers consist of a whole number and a fractional part, such as 4 ⅓
  • Finding the least common denominator is a key part of subtracting mixed numbers with unlike denominators
  • Some mixed number subtraction problems require students to regroup, or “borrow”

When your child is learning how to subtract mixed numbers, remembering the steps to the process may seem a little challenging at first. However, with quality instruction and a solid practice routine, your student will soon be able to subtract several types of mixed numbers. This article provides a complete overview of how to subtract mixed numbers with the same and different denominators. 

What are mixed numbers?

Before subtracting mixed numbers, students need to understand that a mixed number is comprised of a whole number and part of a number, which is also called a fraction. Students should be able to identify each component and recognise both the numerator and the denominator of the fraction, like this:

example of a mixed number

Subtracting mixed numbers step by step

When learning to subtract mixed numbers, reviewing the process one step at a time can help students recognise each part of the mixed number and determine how to solve for that particular problem.

Subtracting mixed numbers with like denominators

To subtract mixed numbers with like denominators, follow the steps below. 

Let’s use 6 ⅔ – 2 ⅓ as an example. 

First, subtract the whole numbers.

6-2=4

Next, subtract the fractions.

⅔-⅓=⅓ 

Finally, write the mixed number answer.           

4 ⅓ 

Subtracting mixed numbers with unlike denominators

To subtract mixed numbers with unlike–or unequal–denominators, let’s use the example problem of 5 ¾- 2 ⅛ 

First, we need to look at the fractions and find the least common denominator. 

¾ and ⅛ have a least common denominator of 8. 

What is the least common denominator?

The least common denominator, also known as the lowest common denominator, is the smallest number the denominators can be divided into. 

Example: 

The denominator in ¾ is 4. 

4 can be divided into 1,2, and 4. 

The denominator in ⅛ is 8. 8 can be divided into 1,2,4,8. 

The smallest number the denominators both have in common is 4. 

4 is the least common denominator. 

Next, we need to rename the fraction using the least common denominator. 

To do this, we multiply both the bottom and top of the fraction.

5 (3×2/4×2) = 5 6/8

Subtracting mixed numbers with unequal denominators

Now that the two fractions have equal denominators, we subtract the mixed numbers using the process above. 

5 6/8- 2 ⅛= 

5-2= 3

6/8- ⅛= ⅝

3 ⅝ 

Subtracting mixed numbers with regrouping

Let’s look at the example problem of 7 ⅓- 4 ⅚ 

First, we need to find the least common denominator. 

⅓ and ⅚ have a least common denominator of 6. 

Next, we need to rename the fraction using the least common denominator. 

To do this, we multiply both the bottom and top of the fraction.

subtracting mixed numbers with regrouping step 1

Now we can rewrite the problem as:

7 2/6- 4 ⅚

Even though our mixed numbers now have the same denominator, we can’t subtract 2/6 from ⅚ because we’d get a negative number. 

Similar to a whole number subtraction problem, we need to borrow one whole from the place to the left and add it to the right — but in fractional form. 

subtracting mixed numbers with regrouping step 2

Now, we have 7 8/6 and can easily subtract the like denominators.

7 8/6- 4 ⅚ = 3 3/6 or 3 ½

Practice problems

3 ⅚- 2 ⅙=?

3-2 = 1

⅚-⅙= 4/6

Answer: 4 4/6

6 8/9-5 ⅔=?

Find the least common multiple of 3 and 9, which is 9.

5 (2×3/3×3)= 5 6/9

6 8/9- 5 6/9= 

Answer: 1 2/9

9 ⅞- 5 ⅛=?

9-5= 4

⅞- ⅛= 6/8

Answer: 4 6/8

2 12/9- 1 5/9= 1 7/9

Find the least common multiple of 3 and 6, which is 6.

4 (1×2/3×2)= 4 2/6

4 2/6- 1 ⅙=

Answer: 3 1/6

FAQs about subtracting mixed numbers

To subtract mixed numbers, you must first find the least common denominator of each. Then you can subtract or regroup in order to subtract.

In order to subtract a whole number from a mixed number, you need to first convert the whole number into a fraction. Then, you need to change the mixed number into an improper fraction. Finally, find the common denominator of the two fractions in order to subtract.

Group 208

Lesson credits

Katie Wickliff headshot

Katie Wickliff

Katie holds a master’s degree in Education and a bachelor’s degree in both Journalism and English. She has over 15 years of experience as a teacher and is also a certified tutor. Most importantly, Katie is the mother of an 8 and 11-year-old. She's passionate about education and firmly believes that the right tools and support can help every child reach their full potential.

Katie Wickliff headshot

Katie Wickliff

Katie holds a master’s degree in Education and a bachelor’s degree in both Journalism and English. She has over 15 years of experience as a teacher and is also a certified tutor. Most importantly, Katie is the mother of an 8 and 11-year-old. She's passionate about education and firmly believes that the right tools and support can help every child reach their full potential.

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