Learn fraction operations
Fractions represent parts of a whole. Each operation has a reliable procedure, and final answers should be reduced to simplest form.
You will choose the correct rule for adding, subtracting, multiplying, or dividing fractions.
The idea in plain English
A fraction names parts of a whole. The bottom number says the size of the parts; the top says how many parts you have.
Adding needs matching part sizes. Multiplying and dividing do not need common denominators.
How to recognise this kind of question
- Two or more fractions are joined by an operation sign.
- The requested answer may need to be simplified.
- Mixed numbers may need conversion before calculating.
Quick decision: Add or subtract: common denominator. Multiply: straight across. Divide: multiply by the reciprocal.
The method
- For addition or subtraction, rewrite both fractions with a common denominator.
- For multiplication, multiply numerators and denominators.
- For division, multiply by the reciprocal of the second fraction, then simplify.
Worked examples
Answer:
Answer:
Your turn—with help
Need a hint?
Find a denominator both 3 and 4 divide into.
Show the answer and steps
- The common denominator is 12.
Answer:
Watch out for this mistake
Incorrect:
Why it fails: Adding denominators changes the size of the pieces and does not create an equivalent sum.
Do this instead: Use sixths: 3/6 + 2/6 = 5/6.
Quick check
Try these without looking. Then open each answer to check your thinking.
Need a hint?
Use denominator 6.
Show the answer and steps
Answer:
Need a hint?
Multiply straight across, then simplify.
Show the answer and steps
Answer:
Need a hint?
Flip the second fraction.
Show the answer and steps
Answer: 2
Common mistakes
- Adding denominators when adding fractions.
- Using a reciprocal during multiplication instead of division.
- Stopping before reducing the result.
Practice tips
- Estimate whether the result should be less than or greater than one.
- Reduce before multiplying when factors cancel cleanly.