Practice · Grade 6 Fractions
Simplify Fractions — Practice Problems
Training problems for simplifying fractions with the greatest common divisor, in rising difficulty. A hint and full solution for every question. Free.
Q1 of 7
0 correct
Reduce the fraction to lowest terms: 18/24.
18/24
Quick answer
How should I practice simplifying fractions?
For each problem, first find the greatest common divisor (GCD) of the numerator and denominator and divide both by it — that reduces the fraction to lowest terms in a single step. Find the GCD by prime factorisation or by testing the small divisors 2, 3 and 5. Always check at the end that the numerator and denominator are coprime, otherwise keep going. Work in rising difficulty and never hesitate to use a hint.
HowTo
A 4-step strategy
This order works for any fraction — proper, improper or with a minus sign.
- 1Step 1 of 4
Look at the numerator and denominator
Write the fraction and check for obvious common factors — both even, both ending in 0 or 5, both divisible by 3 (digit sum).
- 2Step 2 of 4
Find the greatest common divisor (GCD)
Break both numbers into prime factors and take the shared ones. Example: 24 = 2·2·2·3 and 36 = 2·2·3·3, shared is 2·2·3 = 12. The GCD is 12.
- 3Step 3 of 4
Divide both by the GCD
Always divide both by the same number, or the value changes. 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 24/36 = 2/3.
- 4Step 4 of 4
Check for coprime
Do the numerator and denominator now share only 1? For 2/3 yes — done. If not, your divisor was not the GCD: reduce again.
Examples
Worked practice examples
Four typical problems from grade 5–6 tests. Try each yourself first, then compare with the solution.
Easy
Reduce: 18/24
18 = 2·3·3, 24 = 2·2·2·3
GCD(18, 24) = 2·3 = 6
18 ÷ 6 = 3, 24 ÷ 6 = 4
Check: 3 and 4 are coprime ✓
Standard case: find the GCD, divide both, done in one step.
Medium
Reduce: 16/40
16 = 2·2·2·2, 40 = 2·2·2·5
GCD(16, 40) = 2·2·2 = 8
16 ÷ 8 = 2, 40 ÷ 8 = 5
Check: 2 and 5 are coprime ✓
Both even — here the GCD is a pure power of two.
Medium
Reduce: 100/35
100 = 2·2·5·5, 35 = 5·7
GCD(100, 35) = 5
100 ÷ 5 = 20, 35 ÷ 5 = 7
Check: 20/7 = 2 6/7 as a mixed number ✓
Improper fraction — reducing works the same way, the result stays above 1.
Hard
Boss: reduce 81/108
81 = 3·3·3·3, 108 = 2·2·3·3·3
GCD(81, 108) = 3·3·3 = 27
81 ÷ 27 = 3, 108 ÷ 27 = 4
Check: 3 and 4 are coprime ✓
Large GCD (27). Dividing only by 3 or 9 lands on 27/36 or 9/12 and is not finished yet.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up again and again when reducing.
Dividing only the numerator or only the denominator
Both must be divided by the same number. 18/24 becomes 3/4, not 3/24 — otherwise the value of the fraction changes.
Not fully reduced
12/16 divided by 2 gives 6/8 — that still reduces. Using the GCD (4) lands directly on 3/4. Always check for coprime at the end.
Cancelling across a plus sign
In (a + b)/c you can’t just cancel a and c. You cancel factors, never terms in a sum.
Confusing GCD with LCM
Reducing needs the greatest common divisor. The least common multiple is for adding fractions.
Trying to reduce coprime fractions
9/28 has GCD 1 — the numbers are coprime, so the fraction is already in simplest form. Not every fraction can be reduced.
Study
Practice with a plan — three quick tips
15 minutes at a time, not 90 in one go
Three short sessions over three days stick better than one long session the night before a test. The magic word is spaced repetition.
Know the divisibility rules by heart
Even number → divisible by 2. Ends in 0 or 5 → divisible by 5. Digit sum divisible by 3 → divisible by 3. This finds the GCD far faster than guessing.
For every wrong answer: why?
Was the fraction only half-reduced? Wrong GCD? Note the cause — and next time you will spot the mistake right away.
FAQ
Frequently asked questions about practising
Glossary
Each term in one sentence
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Simplify (reduce)
- Divide the numerator and denominator by the same number without changing the fraction’s value.
- Greatest common divisor (GCD)
- The largest number that divides two numbers with no remainder — the key to reducing in one step.
- Coprime
- Two numbers sharing no common factor other than 1, e.g. 3 and 4.
- Lowest terms
- A fraction whose numerator and denominator are coprime and that cannot be reduced further.
- Improper fraction
- A fraction whose numerator is larger than its denominator, e.g. 20/7.
- Boss question
- The last and hardest problem in a practice set.