Simplify Fractions Calculator: Lowest Terms With Steps

How to use the simplify fractions calculator

Type the fraction as top/bottom.
The calculator runs Euclid’s algorithm to find the GCF.
Both parts are divided by that GCF.
Check the answer using the multiply-back line shown below the result.

Lowest terms

a/b = (a ÷ g) / (b ÷ g),  where g = GCF(a, b)
Euclid: GCF(a, b) = GCF(b, a mod b), until the remainder is 0

A fraction is in lowest terms exactly when GCF(numerator, denominator) = 1.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

18/24

Answer3/4

Decimal: 0.75
Check: 3 × 6 = 18 and 4 × 6 = 24

Step-by-step working 3 steps

1
Write the fraction
```
18/24
```
2
Find 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.
3
Divide top and bottom by the GCF
```
18 ÷ 6 = 3
24 ÷ 6 = 4
→ 3/4
```

84/126

Answer2/3

Decimal: 0.666667
Check: 2 × 42 = 84 and 3 × 42 = 126

Step-by-step working 3 steps

1
Write the fraction
```
84/126
```
2
Find 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.
3
Divide top and bottom by the GCF
```
84 ÷ 42 = 2
126 ÷ 42 = 3
→ 2/3
```

7/13

Answer7/13

Decimal: 0.538462

Step-by-step working 3 steps

1
Write the fraction
```
7/13
```
2
Find the greatest common factor (Euclid’s algorithm)
```
7 = 0 × 13 + 7
13 = 1 × 7 + 6
7 = 1 × 6 + 1
6 = 6 × 1 + 0
```
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 1.
3
Result
The GCF is 1, so 7/13 is already in lowest terms.

2 6/8

Answer11/4

Mixed number: 2 3/4
Decimal: 2.75
Check: 11 × 2 = 22 and 4 × 2 = 8

Step-by-step working 3 steps

1
Write the fraction
```
22/8
```
Mixed number converted to an improper fraction: 2 6/8 = 22/8.
2
Find the greatest common factor (Euclid’s algorithm)
```
22 = 2 × 8 + 6
8 = 1 × 6 + 2
6 = 3 × 2 + 0
```
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 2.
3
Divide top and bottom by the GCF
```
22 ÷ 2 = 11
8 ÷ 2 = 4
→ 11/4
```

Common mistakes to avoid

Dividing by a common factor that is not the largest

Dividing 18/24 by 2 gives 9/12, which is correct but not finished. Keep going or use the GCF straight away.

Changing only the numerator

Whatever you divide the top by, you must divide the bottom by too — otherwise the value changes.

Cancelling across a sum

You can cancel factors, not terms: (2 + 3)/(2 + 5) does not reduce by crossing out the 2s.

Frequently asked questions

Why Euclid’s algorithm instead of listing factors?

It finds the GCF of very large numbers in a handful of divisions, and it is the method taught in most curricula once the numbers are too big to factor by eye.

What if the numerator is larger than the denominator?

The fraction is simplified the same way, and a mixed-number form is shown as well.