Fractions

Simplify a Fraction

Reduce 18/24 to lowest terms. First find GCD(18, 24) = 6, then divide both numerator and denominator by 6. The result, 3/4, cannot be reduced further because GCD(3, 4) = 1.

Example

Simplify 18/24 by dividing numerator and denominator by their GCD.

highlighted = computed this step

Step 1 — Set up

Set up the fraction expression.

1824\frac{18}{24}
Start with 18/24: 18 shaded pieces out of 2418/24The whole is still split into 24 equal pieces.

Step 2 — Find GCD

The GCD of 18 and 24 is 6.

gcd⁡(18,24)=6\gcd( 18 , 24 )= \hl{6}
Group pieces by the GCF 618/246666Each outlined group holds 6 equal pieces.

Step 3 — Divide numerator

Divide the numerator: 18 ÷ 6 = 3.

1824→324\frac{18}{24} \rightarrow \hlmath{\frac{3}{24}}
18 shaded pieces make 3 groups of 618/246666Counting shaded groups gives the new numerator 3.

Step 4 — Divide denominator

Divide the denominator: 24 ÷ 6 = 4.

324→34\frac{3}{24} \rightarrow \hlmath{\frac{3}{4}}
24 total pieces make 4 groups of 618/246666Counting all groups gives the new denominator 4.

Step 5 — Result

Read the final result.

1824=34\frac{18}{24} = \frac{3}{4}
18/24 simplifies to 3/418/246666The shaded amount did not change: 18/24 = 3/4.3/418 / 6 = 3 and 24 / 6 = 4
lowest-terms A fraction is in lowest terms when its numerator and denominator share no common factor greater than 1. Dividing both by their GCD does this in one step. Always check: if GCD = 1, you are done.