Factors and Fractions

Simplifying Fractions to Lowest Terms

Reduce a fraction to lowest terms by dividing numerator and denominator by their GCF.

Example

Divide numerator and denominator by the GCF.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

2436\frac{24}{36}
24/36 means 24 shaded parts out of 36 equal parts.24 shaded / 36 total24 shaded parts out of 36 total partsNext, look for a common group size.

Step 2 — Find GCF

The greatest common factor is 12.

gcd⁡(24,36)=12\gcd( 24 , 36 )= \hl{12}
The common factor 12 groups both 24 and 36 evenly.12121224 shaded / 36 total24 = 2 groups of 12; 36 = 3 groups of 12Dividing top and bottom by the same common factor keeps the fraction value.

Step 3 — Divide numerator

Divide the numerator: 24 ÷ 12 = 2.

24÷12=224 \div 12 = \hl{2}
Divide the numerator by the same common factor 12.121224 div 12 = 22 equal groups remain for the numerator.

Step 4 — Divide denominator

Divide the denominator: 36 ÷ 12 = 3.

36÷12=336 \div 12 = \hl{3}
Divide the denominator by the same common factor 12.12121236 div 12 = 33 equal groups remain for the denominator.

Step 5 — Result

Read the final result.

2436=23\frac{24}{36} = \hlmath{\frac{2}{3}}
After dividing both parts by 12, the fraction is 2/3.24/36 = (24 div 12)/(36 div 12) = 2/3The shaded amount stays the same; only the group size changed.
simplify-fraction-to-lowest To simplify a fraction: - Find the GCF of numerator and denominator. - Divide both by the GCF.