See the idea
Before you start
Recognise equivalent fractions and recall small multiplication facts. Being able to list factors helps; the greatest common factor is useful but not essential at the first step.
Words used in this guide
- Factor
- A whole number that divides another whole number exactly.
- Common factor
- A factor shared by two numbers.
- Simplest form
- For a positive fraction, a form in which numerator and denominator have no common factor greater than 1.
Why the method works
Think of 8/12 as eight selected objects from twelve, bundled into groups of four. There are two selected bundles out of three total bundles: 2/3. Both the selected count and the total count must be bundled equally. You are renaming the same proportion. Simplifying does not mean making the amount smaller, and it does not always mean the final fraction is less than one.
Regroup equal pieces
Six eighths can be grouped into three pairs of eighths. Each pair is one quarter, so 6/8 = 3/4. This works because the total number of pieces is regrouped in the same way as the shaded pieces.
Use a common factor
For 18/24, both numbers are divisible by 6. Dividing gives (18 ÷ 6)/(24 ÷ 6) = 3/4. You can also divide in smaller steps, provided the same factor divides both numbers at every step.
Know when to stop
A fraction is in simplest form when its numerator and denominator have no common factor greater than 1. You cannot simplify 3/4 further using whole-number numerator and denominator. Do not subtract the same amount from each number.
Worked examples, step by step
Example 1: Simplify 12/18.
- The greatest common factor of 12 and 18 is 6.
- 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3.
Example 2: Simplify 24/36 in one step.
- Factors of 24 include 1, 2, 3, 4, 6, 8, 12 and 24. The largest one that also divides 36 is 12.
- Divide numerator and denominator by 12: 24/36 = 2/3.
- Check by multiplying both parts of 2/3 by 12. You return to 24/36.
Example 3: Simplify 42/70 without finding the greatest factor first.
- Both numbers are even, so divide by 2 to obtain 21/35.
- Both are now divisible by 7: 21/35 = 3/5. No common factor greater than 1 remains.
- Dividing by 2 and then 7 has the same effect as dividing by 14 at once.
Example 4: Of 30 seedlings, 18 sprout. What fraction sprout?
- The whole is all 30 seedlings, not the 12 that did not sprout. Write 18/30.
- Divide both numbers by 6 to get 3/5.
- The count is still 18 seedlings. The simplified fraction describes the share, not a new count of three seedlings.
Common mistakes and how to repair them
“I can cancel the digit 2 in 12/20.”
Digits are not factors. Dividing both numbers by 4 gives 3/5; deleting a digit would give 1/0 and is invalid.
“An odd numerator means the fraction is simplest.”
15/21 has two odd numbers, but both are divisible by 3. It simplifies to 5/7.
Check your understanding
Choose an answer for each question. You can check again after reading the explanation.
Worked answers
What is 10/15 in simplest form? 2/3. Divide both numbers by 5.
Which fraction is already in simplest form? 5/8. 5 and 8 have no common factor greater than 1.
Practise independently
Work these out on paper. Include a diagram or a sentence where the question asks you to explain. Open each solution after making an attempt.
3. Simplify 16/28.
Show the reasoning
4/7, after dividing both numbers by 4.
4. Simplify 45/60 in two steps.
Show the reasoning
One route is 45/60 = 9/12 = 3/4, dividing first by 5 and then by 3.
5. Is 14/25 already in simplest form?
Show the reasoning
Yes. Their prime factors are 2 × 7 and 5 × 5, with none in common.
6. Simplify 27/18 and express it as a mixed number.
Show the reasoning
27/18 = 3/2 = 1 1/2. An improper fraction can still be in simplest form.
If a method still feels uncertain, revisit the closest worked example, then try a fresh problem. A correct answer copied from a solution tells you less than an explanation you can give independently.
Learn it → Try it → Explain it
Put the idea into play
Build and compare fractions with pictures you can change.
Start with “Same amount” to strengthen fraction equivalence before returning to this guide. Simplifying and operations modes require sign-in.
Try Fraction Visuals →Free guest play has question, level and time limits. Sign in to continue or save progress. A game score is not a mastery assessment.
Questions students and parents ask
Do I always need the greatest common factor?
No. Any common factor greater than 1 makes progress. Repeat until no such factor remains.
Are HCF and GCF different?
Highest common factor and greatest common factor are different names for the same number.
Can zero be simplified?
With a non-zero denominator, 0/8 equals 0. A denominator of zero is never allowed.
Help at home: Bundle counters
Set out 12 counters, eight of one kind and four of another. Make equal groups of four, keeping the kinds separate. Ask how many selected groups there are out of all the groups.
Listen for “two out of three groups” and a link back to eight out of twelve counters. If the child subtracts, physically show that subtraction removes objects while regrouping does not.
Offer 10 out of 15 next. Ask them to choose a group size and explain why it divides both counts.
Keep the conversation focused on the reasoning you can hear or see. One short activity cannot establish lasting mastery or diagnose a learning difficulty.
How do I help my child simplify fractions without guessing?
Draw a bar with ten equal parts and shade six. Group adjacent parts in pairs. You now have five larger equal groups, with three groups shaded: 6/10 = 3/5. The shaded amount stayed the same even though both numbers became smaller.
Connect that picture to 6 ÷ 2 = 3 and 10 ÷ 2 = 5. If your child divides only the numerator, the fraction changes value. If finding the greatest common factor is difficult, smaller common factors are fine; divide both numbers each time and continue until there is no common factor greater than one.
Try 8/12. Dividing both numbers by two gives 4/6, which is equivalent but can simplify again to 2/3. Ask “could we group the pieces again?” instead of marking the first step wrong.
Helping your child with fractions? Start with this parent guide →
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