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Maths Quiz - Level 3-4 Numbers - Fractions - Simplification (Questions)

Simplify fractions in KS3. Cancel common factors, write in lowest terms, and spot equivalent fractions to make calculations quicker and clearer.

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Fascinating Fact:

A fraction where the numerator is smaller than the denominator is called a proper fraction, and it can still be simplified.

In KS3 Maths, simplification means writing a fraction in its lowest terms. Divide the numerator and denominator by the same non-zero number, often their highest common factor, to get an equivalent fraction.

Key Terms

  • Numerator: The top number of a fraction that shows how many parts are taken.
  • Denominator: The bottom number that shows how many equal parts make a whole.
  • Highest Common Factor (HCF): The greatest number that divides both numerator and denominator exactly.

Frequently Asked Questions (Click to see answers)

How do I simplify a fraction step by step?

Find a common factor of the numerator and denominator, divide both, and repeat until no common factors remain. Example: 18/24 → divide by 6 → 3/4.

What is the difference between proper and improper fractions?

A proper fraction has a smaller numerator than denominator, like 3/5. An improper fraction has a numerator at least as big as the denominator, like 9/5.

How do I know a fraction is in simplest form?

It is simplest when the numerator and denominator share no common factor greater than 1. In other words, their HCF is 1.

Try These Related Quizzes

1. What is 30/40 as a fraction in its simplest form?
[ ] 1/2
[ ] 3/4
[ ] 30/40
[ ] 300/400
2. What is the biggest number you can divide into both the numerator and denominator of 30/40?
[ ] 3
[ ] 4
[ ] 10
[ ] There isn't one
3. How would you write 10/100 in its simplest form?
[ ] 1/10
[ ] 1/100
[ ] 100/10
[ ] 10/1
4. How would you write 33/66 in its simplest form?
[ ] 33/66
[ ] 3/6
[ ] 1/2
[ ] 3/4
5. What is the biggest number you can divide into both the numerator and denominator of 33/66?
[ ] 3
[ ] 6
[ ] 11
[ ] 33
6. What is the biggest number you can divide into both the numerator and denominator of 71/92?
[ ] 1/9
[ ] 7/9
[ ] 7/2
[ ] It's not possible
7. How would you write 9/81 in its lowest terms?
[ ] 1/9
[ ] 9/1
[ ] 9/8
[ ] It's not possible
8. What is the biggest number you can divide into both the numerator and denominator of 12/18?
[ ] 3
[ ] 6
[ ] 9
[ ] 12
9. How would you write 12/18 in its simplest form?
[ ] 1/3
[ ] 2/3
[ ] 3/4
[ ] 5/10
10. What is the simplest way of writing 1/2?
[ ] 1/4
[ ] 1/3
[ ] 1/2
[ ] 1/5

You can find more about this topic by visiting BBC Bitesize - How to simplify fractions

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Maths Quiz - Level 3-4 Numbers - Fractions - Simplification (Answers)
1. What is 30/40 as a fraction in its simplest form?
[ ] 1/2
[x] 3/4
[ ] 30/40
[ ] 300/400
The highest common factor of 30 and 40 is 10
2. What is the biggest number you can divide into both the numerator and denominator of 30/40?
[ ] 3
[ ] 4
[x] 10
[ ] There isn't one
Dividing 30 (the numerator) and 40 (the denominator) by 10 gives us 3/4
3. How would you write 10/100 in its simplest form?
[x] 1/10
[ ] 1/100
[ ] 100/10
[ ] 10/1
The common factor is 10
4. How would you write 33/66 in its simplest form?
[ ] 33/66
[ ] 3/6
[x] 1/2
[ ] 3/4
'Simplest form' is also known as 'lowest terms'
5. What is the biggest number you can divide into both the numerator and denominator of 33/66?
[ ] 3
[ ] 6
[ ] 11
[x] 33
Although both numbers are divisible by 11, it isn't the HIGHEST common factor
6. What is the biggest number you can divide into both the numerator and denominator of 71/92?
[ ] 1/9
[ ] 7/9
[ ] 7/2
[x] It's not possible
There is no common factor!
7. How would you write 9/81 in its lowest terms?
[x] 1/9
[ ] 9/1
[ ] 9/8
[ ] It's not possible
Both numbers are divisible by 9
8. What is the biggest number you can divide into both the numerator and denominator of 12/18?
[ ] 3
[x] 6
[ ] 9
[ ] 12
12 and 18 share a few factors - 1, 2, 3, 6 - but 6 is the highest
9. How would you write 12/18 in its simplest form?
[ ] 1/3
[x] 2/3
[ ] 3/4
[ ] 5/10
Divide 12 and 18 by 6 to find the answer
10. What is the simplest way of writing 1/2?
[ ] 1/4
[ ] 1/3
[x] 1/2
[ ] 1/5
1/2 is in its simplest form already!
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