skill 1-6

Ratio Problems

1. Write each of the following ratios in its simplest form:

[1] 48 : 16

\(\frac{48}{16} = \frac{3}{1}\) or 3:1

[2] 14 to 35

\(\frac{14}{35} = \frac{2}{5}\) or 2:5

[3] \(\frac{84}{40}\)

\(\frac{84 \div 4}{40 \div 4} = \frac{21}{10}\) or 21:10

[4] 50 : 75

\(\frac{50 \div 25}{75 \div 25} = \frac{2}{3}\) or 2:3

2. In one of the training sessions, Ahmed scored 8 goals out of 10 attempts. While Akram scored 3 goals out of 5 attempts. Are the two ratios equivalent?

\[ \small \begin{aligned} &\text{Ahmed's ratio} = \frac{8}{10} = \frac{4}{5} \\ &\text{Akram's ratio} = \frac{3}{5} \\ &\frac{4}{5} \neq \frac{3}{5} \Rightarrow \text{Not equivalent} \end{aligned} \]

3. Choose all the equivalent ratios to 18 : 8

\[ \small \frac{18}{8} = \frac{9}{4} \Rightarrow \text{Equivalent to: } \frac{54}{24}, \frac{90}{40} \]

4. Choose: If \(\frac{3}{4} = \frac{x}{28}\), what is the value of \(x\)?

\[ \small 4x = 3 \times 28 \Rightarrow x = 21 \]

5. Choose: If the ratio of boys to girls is 3 : 5, what is the ratio of girls to the total number of children?

\[ \small \text{Total} = 3 + 5 = 8 \Rightarrow \frac{5}{8} \ \]

6. Write the following rate as a unit rate: Reading 45 pages in 3 hours.

\[ \small \frac{45 \text{ pages}}{3 \text{ hours}} = 15 \text{ pages/hour} \]