How to Simplify a Ratio

Step-by-step solution

1. Find the greatest common factor of 18 and 24.

   $$\gcd(18, 24) = 6$$

   Why: Dividing by the largest shared factor simplifies the ratio in one step.

2. Divide both parts by 6.

   $$18 \div 6 = 3,\quad 24 \div 6 = 4$$

   Why: Both parts must change together so the ratio keeps its value.

3. Write the simplified ratio.

   $$3 : 4$$

   Why: 3 and 4 share no factor larger than 1, so the ratio is in lowest terms.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $15 : 25$

   Show answer

   $3 : 5$

2. 2

   $16 : 24$

   Show answer

   $2 : 3$

3. 3

   $27 : 36$

   Show answer

   $3 : 4$

4. 4

   $35 : 42$

   Show answer

   $5 : 6$

5. 5

   $44 : 66$

   Show answer

   $2 : 3$