Grade VIII math worksheet focusing on percentage applications, including conversions and real-world problems.

Let's solve each problem step by step with clear explanations.

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1. Express each of the following as a fraction.

a. 54%
To convert percentage to a fraction:
$$
54\% = \frac{54}{100} = \frac{27}{50} \quad \text{(simplified by dividing numerator and denominator by 2)}
$$

✔ Answer: $ \frac{27}{50} $

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b. 200%
$$
200\% = \frac{200}{100} = 2
$$
As a fraction: $ \frac{2}{1} $

✔ Answer: $ \frac{2}{1} $ or simply $ 2 $

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c. 4.5%
First, write as a fraction:
$$
4.5\% = \frac{4.5}{100}
$$
Multiply numerator and denominator by 10 to eliminate decimal:
$$
= \frac{45}{1000} = \frac{9}{200} \quad \text{(simplified by dividing by 5)}
$$

✔ Answer: $ \frac{9}{200} $

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2. Express each of the following as a decimal.

a. 4%
$$
4\% = \frac{4}{100} = 0.04
$$

✔ Answer: $ 0.04 $

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b. 72%
$$
72\% = \frac{72}{100} = 0.72
$$

✔ Answer: $ 0.72 $

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c. 350%
$$
350\% = \frac{350}{100} = 3.5
$$

✔ Answer: $ 3.5 $

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3. Convert each of the following as a percentage.

a. $ \frac{7}{25} $
Multiply by 100:
$$
\frac{7}{25} \times 100 = 28\%
$$

✔ Answer: $ 28\% $

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b. $ \frac{3}{125} $
$$
\frac{3}{125} \times 100 = \frac{300}{125} = 2.4\%
$$

✔ Answer: $ 2.4\% $

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4. Convert 5 : 6 to percentage.

This is a ratio. To express it as a percentage, consider it as a fraction:
$$
\frac{5}{6} \times 100 = \frac{500}{6} \approx 83.33\%
$$

✔ Answer: $ 83.33\% $

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5. Express 150% as a ratio.

$$
150\% = \frac{150}{100} = \frac{3}{2}
$$

So, the ratio is $ 3:2 $

✔ Answer: $ 3:2 $

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6. Which is largest in $ 2\frac{1}{3}\% $, 1.15?

First, convert $ 2\frac{1}{3}\% $ to decimal:

$$
2\frac{1}{3} = \frac{7}{3}, \quad \text{so } \frac{7}{3}\% = \frac{7}{3} \times \frac{1}{100} = \frac{7}{300} \approx 0.0233
$$

Now compare:
- $ 2\frac{1}{3}\% \approx 0.0233 $
- $ 1.15 $ (this is already a decimal)

Clearly, $ 1.15 > 0.0233 $

✔ Answer: $ 1.15 $ is larger.

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7. 40% of ? = 400

Let the unknown number be $ x $.
Then:
$$
40\% \times x = 400 \\
\Rightarrow \frac{40}{100} \times x = 400 \\
\Rightarrow 0.4x = 400 \\
\Rightarrow x = \frac{400}{0.4} = 1000
$$

✔ Answer: $ 1000 $

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8. What per cent of 90 is 120?

Let the percentage be $ x $. Then:
$$
\frac{x}{100} \times 90 = 120 \\
\Rightarrow \frac{90x}{100} = 120 \\
\Rightarrow 0.9x = 120 \\
\Rightarrow x = \frac{120}{0.9} = 133.\overline{3} \approx 133.33\%
$$

✔ Answer: $ 133.33\% $

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9. The population of a town increases by 6% annually. If it is 53,000 in the year 2018, what was its population in 2017?

Let the population in 2017 be $ x $.
It increased by 6% to become 53,000 in 2018.

So:
$$
x + 6\% \text{ of } x = 53000 \\
\Rightarrow x(1 + 0.06) = 53000 \\
\Rightarrow 1.06x = 53000 \\
\Rightarrow x = \frac{53000}{1.06} \approx 50000
$$

✔ Answer: $ 50,000 $

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10. A man saves 8% of his salary every month. If he saves ₹2880 every month, what is his monthly salary?

Let salary be $ x $.
Then:
$$
8\% \text{ of } x = 2880 \\
\Rightarrow \frac{8}{100} \times x = 2880 \\
\Rightarrow 0.08x = 2880 \\
\Rightarrow x = \frac{2880}{0.08} = 36000
$$

✔ Answer: ₹36,000

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✔ Final Answers Summary:

1. a. $ \frac{27}{50} $ b. $ \frac{2}{1} $ c. $ \frac{9}{200} $
2. a. $ 0.04 $ b. $ 0.72 $ c. $ 3.5 $
3. a. $ 28\% $ b. $ 2.4\% $
4. $ 83.33\% $
5. $ 3:2 $
6. $ 1.15 $ is larger
7. $ 1000 $
8. $ 133.33\% $
9. $ 50,000 $
10. ₹36,000

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