Subtracting mixed numbers

Subtract the wholes, then the fractions. If the top fraction is too small, borrow one whole and turn it into a fraction first.

Wholes, then fractions

  1. 5 3/4 − 2 1/4: subtract the wholes, 5 − 2 = 3.
  2. Subtract the fractions: 3/4 − 1/4 = 2/4.
  3. Put them together and simplify: 3 2/4 = 3 1/2.

When the first fraction is bigger than the second, it is that simple.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

5 1/4 = 4 5/4
5 1/4: borrow one whole to make 4 wholes and 5 quarters.
5 1/4 − 2 3/4 = 2 2/4
Take away 2 wholes and 3 quarters: 2 2/4 = 2 1/2 is left.
012345610/421/4
On a number line: from 2 3/4 up to 5 1/4 is 2 2/4.

When you need to borrow

5 1/4 − 2 3/4: you can’t take 3 quarters from 1 quarter. So borrow one of the 5 wholes and cut it into quarters:

  1. 5 1/4 = 4 + 1 + 1/4 = 4 + 4/4 + 1/4 = 4 5/4.
  2. Now subtract: 4 5/4 − 2 3/4.
  3. Wholes 4 − 2 = 2, fractions 5/4 − 3/4 = 2/4.
  4. Answer: 2 2/4 = 2 1/2.

This is the fraction version of borrowing a ten in column subtraction. The key line is “one whole is 4 quarters”, or 3 thirds, or 8 eighths: whatever the denominator is.

Different denominators

For 4 1/3 − 1 1/2, first give the fractions a common denominator: 1/3 = 2/6 and 1/2 = 3/6. Now it is 4 2/6 − 1 3/6, which needs borrowing: 3 8/6 − 1 3/6 = 2 5/6.

See finding a common denominator.

Subtract any two mixed numbers, step by step

The calculator uses improper fractions, so you can check your borrowing.

Subtracting from a whole number

6 − 2 3/8: there are no eighths to take from, so borrow straight away. 6 = 5 8/8. Then 5 8/8 − 2 3/8 = 3 5/8.

A quick alternative is to count up: from 2 3/8, add 5/8 to reach 3, then 3 more to reach 6. That is 3 5/8 in total. Counting up is great for mental maths and change from a whole.

Another method: improper fractions

Change both to improper fractions and subtract: 5 1/4 − 2 3/4 = 21/4 − 11/4 = 10/4 = 2 2/4 = 2 1/2. No borrowing needed, but the numbers get bigger. Children who struggle with borrowing often find this method more reliable. See improper fractions and mixed numbers.

Quiz: subtracting mixed numbers

Write a whole number and a fraction. The hint shows the borrowing.

Where this fits: fractions step by step

  1. Halves and quarters
  2. What are fractions
  3. Unit fractions
  4. Numerator and denominator
  5. Fractions on a number line
  6. Fractions of a set
  7. Equivalent fractions
  8. Simplifying fractions
  9. Comparing fractions
  10. Ordering fractions
  11. Improper fractions and mixed numbers
  12. Adding fractions
  13. Subtracting fractions
  14. Finding a common denominator
  15. Adding mixed numbers
  16. Subtracting mixed numbers (this page)
  17. Fraction of a number
  18. Fractions × whole numbers
  19. Multiplying fractions
  20. Fractions as division
  21. Dividing fractions by whole numbers
  22. Dividing fractions
  23. Fractions to decimals
  24. Fraction word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “We have 3 1/4 pizzas and eat 1 3/4. Can we take 3 quarters from 1 quarter?” (No.)
  2. “Let’s cut one whole pizza into quarters. How many quarters now?” (5.)
  3. “And how many whole pizzas left?” (2.) “So 3 1/4 is the same as 2 5/4.”
  4. “Now: 2 − 1 is 1, and 5/4 − 3/4 is 2/4.” (1 2/4, which is 1 1/2!)
  5. “Borrow a whole, just like borrowing a ten.”

More worked examples

Example 1: no borrowing

7 5/6 − 3 1/6 = 4 4/6 = 4 2/3.

Example 2: borrowing

4 1/5 − 1 3/5 = 3 6/5 − 1 3/5 = 2 3/5.

Example 3: from a whole

5 − 1 2/3 = 4 3/3 − 1 2/3 = 3 1/3.

Example 4: unlike denominators

3 1/2 − 1 1/4 = 3 2/4 − 1 1/4 = 2 1/4.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 4 3/5 − 1 1/5
  2. 6 7/8 − 2 3/8
  3. 3 1/4 − 1 3/4
  4. 5 1/3 − 2 2/3
  5. 4 − 1 1/4
  6. 7 − 3 5/6
  7. 2 1/2 − 1 1/3
  8. A rope is 6 1/4 m. 2 3/4 m is cut off. How much is left?
  9. Estimate 8 1/10 − 2 9/10
  10. Stretch: 5 1/6 − 2 3/4
Show the answers
  1. 3 2/5
  2. 4 4/8 = 4 1/2
  3. 1 2/4 = 1 1/2
  4. 2 2/3
  5. 2 3/4
  6. 3 1/6
  7. 1 1/6
  8. 3 2/4 = 3 1/2 m
  9. About 5
  10. 2 5/12

Common mistakes

Subtracting the smaller fraction from the biggerWrites 5 1/4 − 2 3/4 = 3 2/4.Fix: you can’t swap the fractions round. Borrow a whole: 4 5/4 − 2 3/4 = 2 2/4.
Borrowing 10 instead of a wholeWrites 5 1/4 as 4 11/4.Fix: one whole is 4/4, not 10: 4 5/4.
Forgetting to reduce the wholeWrites 5 5/4 after borrowing.Fix: taking one whole leaves 4 wholes: 4 5/4.

How to teach it at home

Pizza borrowing

Cut a paper whole into pieces to show borrowing.

Time left

How long is left of a 2 1/2 hour trip after 1 3/4 hours?

Count up

Practice counting up from the smaller number to the bigger one.

By grade

More for each grade: Grade 4 math and the CBSE class 4 maths guide; Grade 5 math and the CBSE class 5 maths guide.

Worksheets and practice

Adding and subtracting mixed numbers worksheet, page 1

Adding and subtracting mixed numbers worksheet: printable PDF with an answer key. · Make a fresh test

Fraction practice · fraction calculator · fraction wall · fractions quiz · fraction levels · fraction games · fractions for kids

Last reviewed

Questions parents ask

How do you subtract mixed numbers?

Subtract the whole numbers, then the fractions. If the first fraction is smaller than the second, borrow one whole first.

How do you borrow when subtracting mixed numbers?

Take 1 from the whole number and write it as a fraction with the same denominator (1 = 4/4), then add it to the fraction part: 5 1/4 = 4 5/4.

How do you subtract a mixed number from a whole number?

Borrow 1 straight away: 6 − 2 3/8 = 5 8/8 − 2 3/8 = 3 5/8. Or count up from the smaller number.

Can I use improper fractions instead?

Yes. Change both to improper fractions, subtract, then change back. It avoids borrowing.

What grade learns subtracting mixed numbers?

Grade 4 with like denominators and grade 5 with unlike denominators.