This worksheet challenges 8th-grade students with percentage conversions and practical application problems.

Let’s solve each problem one by one, step by step.

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1. Express each of the following as a fraction.

a. 54%
→ Percent means “per hundred”, so 54% = 54/100
Simplify: divide numerator and denominator by 2 → 27/50

b. 200%
→ 200/100 = 2/1 or just 2

c. 4.5%
→ 4.5/100 = 45/1000 (multiply top and bottom by 10 to remove decimal)
Simplify: divide by 5 → 9/200 → 9/200

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2. Express each of the following as a decimal.

a. 4%
→ Divide by 100 → 4 ÷ 100 = 0.04

b. 72%
→ 72 ÷ 100 = 0.72

c. 350%
→ 350 ÷ 100 = 3.5

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3. Convert each of the following as a percentage.

a. 7/25
→ Multiply by 100 → (7/25) × 100 = 7 × 4 = 28%

b. 3/125
→ (3/125) × 100 = 300 ÷ 125 = 2.4 → 2.4%

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4. Convert 5 : 6 to percentage.

Ratio 5:6 means 5 out of 6 parts → 5/6
Convert to percent: (5/6) × 100 = 500 ÷ 6 ≈ 83.333... → 83⅓% or 83.33% (rounded)

But since it's exact, better to write as 83⅓%

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5. Express 150% as a ratio.

150% = 150/100 = 3/2 → So ratio is 3 : 2

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6. Which is largest in 2⅓%, 1.15?

First, convert both to same form — let’s use decimals.

2⅓% = (7/3)% = 7/3 ÷ 100 = 7/(3×100) = 7/300 ≈ 0.0233

1.15 is already a decimal → 1.15

Clearly, 1.15 > 0.0233 → So 1.15 is larger

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7. 40% of ? = 400

Let the number be x.

40% of x = 400 → (40/100) × x = 400 → 0.4x = 400

x = 400 ÷ 0.4 = 1000

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8. What per cent of 90 is 120?

We want: ?% of 90 = 120

So, (?/100) × 90 = 120

? × 90 = 120 × 100 = 12000

? = 12000 ÷ 90 = 133.333... → 133⅓%

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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?

This is reverse percentage.

If 2018 population is after 6% increase from 2017, then:

Let 2017 population = P

Then, P + 6% of P = 53,000 → P(1 + 0.06) = 53,000 → 1.06P = 53,000

P = 53,000 ÷ 1.06

Calculate: 53000 ÷ 1.06

Multiply numerator and denominator by 100: 5,300,000 ÷ 106

Divide: 5,300,000 ÷ 106 = 50,000

Check: 50,000 × 1.06 = 53,000 ✔️

So, 50,000

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

Let salary = S

8% of S = 2880 → (8/100) × S = 2880

S = 2880 × (100/8) = 2880 × 12.5

Or: 2880 ÷ 8 = 360, then × 100 = 36,000

So, monthly salary = ₹36,000

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Final Answer:

1. a. 27/50, b. 2, c. 9/200
2. a. 0.04, b. 0.72, c. 3.5
3. a. 28%, b. 2.4%
4. 83⅓%
5. 3 : 2
6. 1.15
7. 1000
8. 133⅓%
9. 50,000
10. ₹36,000