Percentage Worksheet-1 - skoolon.com - Free Printable

Problem Explanation and Solution

The worksheet involves three main tasks:
1. Converting fractions to percentages.
2. Converting percentages to fractions.
3. Finding what percent one number is of another.

Let's solve each part step by step.

---

Q1. Change the fraction to a percentage.

#### a) \( \frac{4}{6} \)
- Simplify the fraction: \( \frac{4}{6} = \frac{2}{3} \).
- Convert to a decimal: \( \frac{2}{3} \approx 0.6667 \).
- Convert to a percentage: \( 0.6667 \times 100 = 66.67\% \).

Answer: \( 66.67\% \)

#### b) \( \frac{5}{8} \)
- Convert to a decimal: \( \frac{5}{8} = 0.625 \).
- Convert to a percentage: \( 0.625 \times 100 = 62.5\% \).

Answer: \( 62.5\% \)

#### c) \( \frac{8}{16} \)
- Simplify the fraction: \( \frac{8}{16} = \frac{1}{2} \).
- Convert to a decimal: \( \frac{1}{2} = 0.5 \).
- Convert to a percentage: \( 0.5 \times 100 = 50\% \).

Answer: \( 50\% \)

#### d) \( \frac{3}{15} \)
- Simplify the fraction: \( \frac{3}{15} = \frac{1}{5} \).
- Convert to a decimal: \( \frac{1}{5} = 0.2 \).
- Convert to a percentage: \( 0.2 \times 100 = 20\% \).

Answer: \( 20\% \)

#### e) \( \frac{4}{25} \)
- Convert to a decimal: \( \frac{4}{25} = 0.16 \).
- Convert to a percentage: \( 0.16 \times 100 = 16\% \).

Answer: \( 16\% \)

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Q2. Change the percentage to a fraction.

#### a) \( 35\% \)
- Write as a fraction over 100: \( 35\% = \frac{35}{100} \).
- Simplify the fraction: \( \frac{35}{100} = \frac{7}{20} \).

Answer: \( \frac{7}{20} \)

#### b) \( 75\% \)
- Write as a fraction over 100: \( 75\% = \frac{75}{100} \).
- Simplify the fraction: \( \frac{75}{100} = \frac{3}{4} \).

Answer: \( \frac{3}{4} \)

#### c) \( 24\% \)
- Write as a fraction over 100: \( 24\% = \frac{24}{100} \).
- Simplify the fraction: \( \frac{24}{100} = \frac{6}{25} \).

Answer: \( \frac{6}{25} \)

#### d) \( 32\% \)
- Write as a fraction over 100: \( 32\% = \frac{32}{100} \).
- Simplify the fraction: \( \frac{32}{100} = \frac{8}{25} \).

Answer: \( \frac{8}{25} \)

#### e) \( 105\% \)
- Write as a fraction over 100: \( 105\% = \frac{105}{100} \).
- Simplify the fraction: \( \frac{105}{100} = \frac{21}{20} \).

Answer: \( \frac{21}{20} \)

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Q3. What percent is 24 of 80?

To find what percent 24 is of 80, use the formula:
\[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
\]
- Part = 24
- Whole = 80

\[
\text{Percentage} = \left( \frac{24}{80} \right) \times 100
\]

Simplify the fraction:
\[
\frac{24}{80} = \frac{3}{10}
\]

Convert to a decimal:
\[
\frac{3}{10} = 0.3
\]

Convert to a percentage:
\[
0.3 \times 100 = 30\%
\]

Answer: \( 30\% \)

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Final Answers:

1. Fractions to Percentages:
- a) \( 66.67\% \)
- b) \( 62.5\% \)
- c) \( 50\% \)
- d) \( 20\% \)
- e) \( 16\% \)

2. Percentages to Fractions:
- a) \( \frac{7}{20} \)
- b) \( \frac{3}{4} \)
- c) \( \frac{6}{25} \)
- d) \( \frac{8}{25} \)
- e) \( \frac{21}{20} \)

3. What percent is 24 of 80?
- \( 30\% \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Q1: } \text{a) } 66.67\%, \text{ b) } 62.5\%, \text{ c) } 50\%, \text{ d) } 20\%, \text{ e) } 16\% \\
\text{Q2: } \text{a) } \frac{7}{20}, \text{ b) } \frac{3}{4}, \text{ c) } \frac{6}{25}, \text{ d) } \frac{8}{25}, \text{ e) } \frac{21}{20} \\
\text{Q3: } 30\%
\end{array}
}
\]