Arithmetic & Numbers · Grades 4–7
How to Simplify Fractions to Lowest Terms
What “lowest terms” means
A fraction is in lowest terms when its numerator and denominator share no common factor except 1. Simplifying never changes the value — you are only writing the same amount with smaller numbers.
Method 1: divide by common factors
Spot a common factor, divide both numbers by it, and repeat until none is left. 18/24 can go to 9/12 (÷2) and then to 3/4 (÷3) — or in one step by the GCF 6, giving 3/4.
18/24
- Decimal: 0.75
- Check: 3 × 6 = 18 and 4 × 6 = 24
Step-by-step working 3 steps
- 1Write the fraction
18/24
- 2Find the greatest common factor (Euclid’s algorithm)
18 = 0 × 24 + 18 24 = 1 × 18 + 6 18 = 3 × 6 + 0
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 6.
- 3Divide top and bottom by the GCF
18 ÷ 6 = 3 24 ÷ 6 = 4 → 3/4
Method 2: Euclid’s algorithm for big numbers
When the numbers are large, find the GCF by repeated division with remainders. For 84/126 the result is 2/3.
84/126 with Euclid’s algorithm
- Decimal: 0.666667
- Check: 2 × 42 = 84 and 3 × 42 = 126
Step-by-step working 3 steps
- 1Write the fraction
84/126
- 2Find the greatest common factor (Euclid’s algorithm)
84 = 0 × 126 + 84 126 = 1 × 84 + 42 84 = 2 × 42 + 0
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 42.
- 3Divide top and bottom by the GCF
84 ÷ 42 = 2 126 ÷ 42 = 3 → 2/3
Fractions that are already simplified
If the GCF is 1 the fraction cannot be reduced: 7/13 stays 7/13.
Common mistakes
Dividing only the top
Whatever you divide the numerator by, divide the denominator by too.
Stopping too early
9/12 is correct but unfinished; keep going until the GCF is 1.
Cancelling across addition
You can cancel common factors, not common terms: (2+3)/(2+5) does not reduce to 3/5.
Frequently asked questions
Does simplifying change the value?
No. 18/24 and 3/4 are the same number written differently.
Should I simplify before or after multiplying fractions?
Either. Cancelling common factors first keeps the numbers small.
