Ratio

Ratios

A ratio is a comparison between two quantities measured in the same units.

Example 1

A class has 45 girls and 40 boys. Find the ratio of boys to girls in simplest form.

Step 1: Write the ratio as a fraction: $\frac{40}{45}$

Step 2: Find the GCD of 40 and 45, which is 5

Step 3: Divide both numerator and denominator by 5: $\frac{40 \div 5}{45 \div 5} = \frac{8}{9}$

Final Answer: $8:9$

Example 2

A football ground is 100 m long and 50 m wide. Find the ratio of length to width.

Step 1: Write the ratio as a fraction: $\frac{100}{50}$

Step 2: Simplify the fraction: $\frac{100 \div 50}{50 \div 50} = \frac{2}{1}$

Final Answer: $2:1$

Example 3

Question: Express the ratio 6:4 in lowest terms.

Step 1: Write as a fraction: $\frac{6}{4}$

Step 2: Simplify: $\frac{6 \div 2}{4 \div 2} = \frac{3}{2}$

Final Answer: $3:2$

Example 4

Joha received 15,000 shillings and Siwenza got 25,000 shillings. Find the ratio of Joha's to Siwenza's amount.

Step 1: Write the ratio: $\frac{15000}{25000}$

Step 2: Simplify by dividing both by 5,000: $\frac{15000 \div 5000}{25000 \div 5000} = \frac{3}{5}$

Final Answer: $3:5$

Example 5

Express 120:90 in simplest form.

Step 1: Write the ratio as a fraction: $\frac{120}{90}$

Step 2: Divide numerator and denominator by 30: $\frac{120 \div 30}{90 \div 30} = \frac{4}{3}$

Final Answer: $4:3$

Example 6

Find the ratio of 2 hours to 90 minutes.

Step 1: Convert 2 hours to minutes: $2 \times 60 = 120$ minutes

Step 2: Write the ratio: $\frac{120}{90}$

Step 3: Simplify the ratio by dividing by 30: $\frac{120 \div 30}{90 \div 30} = \frac{4}{3}$

Final Answer: $4:3$