What does it mean?
The denominator names the size of each fractional unit. You cannot directly remove a count of sixths from a count of fourths without first using a common unit. Renaming both quantities as twelfths changes their notation, not the amounts being subtracted.
To subtract unlike fractions, first rename them with a common denominator. Subtract the counts of equal-sized parts and keep their denominator. For 3/4 − 1/6, use twelfths: 9/12 − 2/12 = 7/12.
Learning goal: Subtract unlike fractions. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Adding fractions: match the parts first if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Choose a common multiple of the denominators. Multiply numerator and denominator together to rename each fraction. Subtract the numerators and retain the common denominator. Finally simplify if possible. In 7/10 − 2/5, fifths can be renamed as tenths, so 7/10 − 4/10 = 3/10.
Notation: common denominator first
Key rule and when to use it
Rename fractions with a common denominator, subtract the numerators and simplify. The common denominator names the size of every piece.
Worked examples, step by step
Example 1: Calculate 3/4 − 1/6.
- Use twelfths.
- 3/4 = 9/12 and 1/6 = 2/12.
- Subtract 2 from 9.
Answer: 7/12
Example 2: Calculate 5/6 − 1/4.
- Use twelfths.
- 5/6 = 10/12 and 1/4 = 3/12.
- Subtract the numerators.
Answer: 7/12
Example 3: Calculate 5/8 − 1/4 and check the result.
- Rename 1/4 as 2/8.
- Subtract: 5/8 − 2/8 = 3/8.
- Check by addition: 3/8 + 1/4 = 3/8 + 2/8 = 5/8.
Common mistakes and important boundaries
The fractions must refer to the same whole. Half of a small pizza cannot automatically be subtracted from a quarter of a much larger pizza as though the pieces had a shared reference. In a story, distinguish “1/3 of the whole pizza” from “1/3 of what remains”. Those are different amounts.
A point to explain
Subtract only after both fractions name equal-sized parts.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Subtracting Fractions with Different Denominators — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
3/4 − 1/3 = ?
Answer and a way to check
5/12
Rename both fractions, then subtract the numerators.
2/3 − 1/4 = ?
Answer and a way to check
5/12
Rename both fractions, then subtract the numerators.
7/8 − 1/3 = ?
Answer and a way to check
13/24
Rename both fractions, then subtract the numerators.
7/10 − 2/5 = ?
Answer and a way to check
3/10
Rename both fractions, then subtract the numerators.
A pizza had 5/6 left. Then 1/3 of the whole pizza was eaten. What part is left?
Answer and a way to check
1/2
Rename both fractions, then subtract the numerators.
Calculate 4/5 − 1/2.
Answer and a way to check
3/10
Use tenths: 8/10 − 5/10 = 3/10.
Calculate 5/6 − 2/3.
Answer and a way to check
1/6
Rename 2/3 as 4/6. Then 5/6 − 4/6 = 1/6.
Calculate 3/4 − 6/8.
Answer and a way to check
0
3/4 equals 6/8. Subtracting the same amount leaves zero.
Subtracting Fractions with Different Denominators — answer key
5/12 Rename both fractions, then subtract the numerators.
5/12 Rename both fractions, then subtract the numerators.
13/24 Rename both fractions, then subtract the numerators.
3/10 Rename both fractions, then subtract the numerators.
1/2 Rename both fractions, then subtract the numerators.
3/10 Use tenths: 8/10 − 5/10 = 3/10.
1/6 Rename 2/3 as 4/6. Then 5/6 − 4/6 = 1/6.
0 3/4 equals 6/8. Subtracting the same amount leaves zero.
Questions students and parents ask
Can the answer be negative?
Yes. 1/4 − 1/2 = −1/4. This guide starts with non-negative examples; a negative result means the amount removed is greater than the starting amount.
Must I always use the lowest common denominator?
No. Any common denominator works, but the lowest common multiple usually keeps the arithmetic smaller. An equivalent simplified answer should agree.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Adding fractions: match the parts first. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Ask what each denominator names. If your child subtracts both top and bottom, return to same-sized paper strips and describe which pieces are removed.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Subtract unlike fractions”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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