Ratio, Proportion & Percentage G7 worksheet - Free Printable

Let's solve each problem step by step.

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Problem 1: Ratios of Red Squares to Green Circles

#### (a)
- Red squares: 2
- Green circles: 4
- Ratio: \( \frac{2}{4} = \frac{1}{2} \)

Answer: \( 1:2 \)

#### (b)
- Red squares: 6
- Green circles: 2
- Ratio: \( \frac{6}{2} = \frac{3}{1} \)

Answer: \( 3:1 \)

#### (c)
- Red squares: 5
- Green circles: 8
- Ratio: \( \frac{5}{8} \) (already in simplest form)

Answer: \( 5:8 \)

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Problem 2: Ratio of Male Fans to Female Fans

- Men: 3000
- Women: 1800
- Ratio: \( \frac{3000}{1800} \)

Simplify the ratio:
\[ \frac{3000}{1800} = \frac{30}{18} = \frac{5}{3} \]

Answer: \( 5:3 \)

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Problem 3: Ratio of Ages

- Aidan: 12 years old
- Bill: 9 years old
- Cara: 3 years old

Write the ratio of their ages:
\[ \text{Ratio} = 12 : 9 : 3 \]

Simplify the ratio:
\[ \frac{12}{3} : \frac{9}{3} : \frac{3}{3} = 4 : 3 : 1 \]

Answer: \( 4:3:1 \)

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Problem 4: Socks in the Drawer

#### (a) Number of Black Socks
- The ratio of white socks to black socks is \( 1:3 \).
- There are 12 white socks.
- Let the number of black socks be \( x \).

From the ratio:
\[ \frac{\text{White socks}}{\text{Black socks}} = \frac{1}{3} \]
\[ \frac{12}{x} = \frac{1}{3} \]

Cross-multiply:
\[ 12 \times 3 = 1 \times x \]
\[ x = 36 \]

Answer: \( 36 \)

#### (b) Total Number of Socks
- White socks: 12
- Black socks: 36
- Total socks: \( 12 + 36 = 48 \)

Answer: \( 48 \)

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Problem 5: Apples and Oranges

- The ratio of apples to oranges is \( 2:5 \).
- James has 15 oranges.

Let the number of apples be \( a \) and the number of oranges be \( o \). From the ratio:
\[ \frac{a}{o} = \frac{2}{5} \]

Given \( o = 15 \):
\[ \frac{a}{15} = \frac{2}{5} \]

Cross-multiply:
\[ 5a = 2 \times 15 \]
\[ 5a = 30 \]
\[ a = \frac{30}{5} \]
\[ a = 6 \]

Answer: \( 6 \)

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Final Answers

1. (a) \( 1:2 \), (b) \( 3:1 \), (c) \( 5:8 \)
2. \( 5:3 \)
3. \( 4:3:1 \)
4. (a) \( 36 \), (b) \( 48 \)
5. \( 6 \)

\[
\boxed{1:2, 3:1, 5:8, 5:3, 4:3:1, 36, 48, 6}
\]