Key takeaways
- a/b − c/d = (a×d − b×c) / (b×d).
- Order matters: a/b − c/d is not the same as c/d − a/b.
- A negative result means the second fraction was bigger than the first.
- Always simplify the final answer using the HCF, if possible.
In this guide
What is fraction subtraction?
When you subtract one fraction from another, you're finding the difference between two amounts of a whole, such as how much liquid is left after pouring some out of a jug.
Why does subtracting fractions matter?
Leftover ingredients, remaining budget, and unfinished parts of a project are often expressed as fractions. Subtracting them correctly tells you exactly how much is left.
Unlike whole numbers, subtracting fractions the wrong way around doesn't just flip the sign of a simple number — it can give you a completely different fraction unless you keep the order straight.
The formula
| Symbol | What it means | Example |
|---|---|---|
| a | First fraction's numerator (top) | 5 |
| b | First fraction's denominator (bottom) | 6 |
| c | Second fraction's numerator | 1 |
| d | Second fraction's denominator | 3 |
How to subtract fractions step by step
- 1Cross-multiply the first pair. Multiply the first numerator (a) by the second denominator (d):
5 × 3 = 15. - 2Cross-multiply the second pair. Multiply the second numerator (c) by the first denominator (b):
1 × 6 = 6. - 3Subtract the second result from the first to get your new numerator:
15 − 6 = 9. - 4Multiply the two denominators (b × d) for your new denominator:
6 × 3 = 18. Simplify with the HCF if possible.
Enter your own two fractions in the calculator below to see the full working.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Subtracting numerators and denominators straight across without a common size. The pieces must be the same size before you compare them.
- Ending with a fraction that isn't fully reduced. Always check if the top and bottom share a common factor, and simplify with the fraction simplifier if they do.
- Panicking at a negative numerator. It just means the fraction you subtracted was bigger — flip the problem to double-check.
Tips and tricks
- Estimate first. If both fractions are close to a simple value like 1/2 or 1, you can predict roughly what the answer should look like.
- Double-check by adding your answer back to the fraction you subtracted — you should get the first fraction again.
- See also adding fractions for the reverse operation, which uses the exact same cross-multiplication idea.
Where you'll use it in real life
- Cooking: working out leftover ingredients after using part of a recipe.
- Budgeting: figuring out how much of a budget or task remains.
- Measuring: comparing two lengths or amounts given as fractions.
- DIY projects: tracking how much material is left after cutting a fractional piece.
Quick summary
To subtract two fractions, cross-multiply to get matching denominators, subtract the numerators in the correct order, and simplify. Keep track of which fraction comes first — the order changes the answer. Try the calculator above with your own two fractions.
Worked example
A jug was 5/6 full of juice. You poured out 1/3 of a jug to make a smoothie. What fraction of the jug is left?
- 01a/b - c/d = (ad - bc) / bd
- 025/6 - 1/3 = (5×3 - 6×1) / (6×3)
- 03= (15 - 6) / 18
- 04= 9/18
- 05Simplified = 1/2
- 06As a decimal = 0.5
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do you subtract fractions with different denominators?
Cross-multiply each numerator with the other denominator, subtract the results in the right order, and put that over the product of both denominators. Then simplify.
What if the answer comes out negative?
It means the fraction you subtracted was bigger than the one you started with. Double-check which fraction should come first in your problem.
How do you subtract fractions with the same denominator?
Just subtract the numerators and keep the denominator the same. For example, 5/6 − 1/6 = 4/6, which simplifies to 2/3.
How do I check a fraction subtraction is correct?
Add your answer back to the fraction you subtracted (c/d). If you get the first fraction (a/b) back, your subtraction was correct.
