Math worksheet for converting fractions to percentages using the denominator method.
Worksheet titled "Convert Fraction to Percent 1" with 18 fraction-to-percent conversion problems using the denominator method.
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Step-by-step solution for: Convert Fraction to Percent
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Show Answer Key & Explanations
Step-by-step solution for: Convert Fraction to Percent
To solve the problem of converting fractions to percentages using the denominator method, we need to follow these steps:
1. Understand the Denominator Method: The goal is to convert each fraction into an equivalent fraction with a denominator of 100. This is because percentages are essentially fractions with a denominator of 100.
2. Find the Equivalent Fraction: Multiply both the numerator and the denominator of the given fraction by the same number so that the denominator becomes 100.
3. Write the Percentage: Once the denominator is 100, the numerator will be the percentage value.
Let's solve each problem step by step.
---
- Step 1: Find the number to multiply the denominator (2) by to get 100.
$$
\frac{100}{2} = 50
$$
- Step 2: Multiply both the numerator and the denominator by 50.
$$
\frac{1}{2} = \frac{1 \times 50}{2 \times 50} = \frac{50}{100}
$$
- Step 3: Write the percentage.
$$
\frac{50}{100} = 50\%
$$
Answer: $\frac{1}{2} = \frac{50}{100} = 50\%$
---
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}
$$
- Step 3: Write the percentage.
$$
\frac{30}{100} = 30\%
$$
Answer: $\frac{3}{10} = \frac{30}{100} = 30\%$
---
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}
$$
- Step 3: Write the percentage.
$$
\frac{70}{100} = 70\%
$$
Answer: $\frac{7}{10} = \frac{70}{100} = 70\%$
---
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}
$$
- Step 3: Write the percentage.
$$
\frac{25}{100} = 25\%
$$
Answer: $\frac{1}{4} = \frac{25}{100} = 25\%$
---
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{1}{5} = \frac{1 \times 20}{5 \times 20} = \frac{20}{100}
$$
- Step 3: Write the percentage.
$$
\frac{20}{100} = 20\%
$$
Answer: $\frac{1}{5} = \frac{20}{100} = 20\%$
---
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}
$$
- Step 3: Write the percentage.
$$
\frac{75}{100} = 75\%
$$
Answer: $\frac{3}{4} = \frac{75}{100} = 75\%$
---
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100}
$$
- Step 3: Write the percentage.
$$
\frac{40}{100} = 40\%
$$
Answer: $\frac{2}{5} = \frac{40}{100} = 40\%$
---
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}
$$
- Step 3: Write the percentage.
$$
\frac{90}{100} = 90\%
$$
Answer: $\frac{9}{10} = \frac{90}{100} = 90\%$
---
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{1}{20} = \frac{1 \times 5}{20 \times 5} = \frac{5}{100}
$$
- Step 3: Write the percentage.
$$
\frac{5}{100} = 5\%
$$
Answer: $\frac{1}{20} = \frac{5}{100} = 5\%$
---
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{4}{5} = \frac{4 \times 20}{5 \times 20} = \frac{80}{100}
$$
- Step 3: Write the percentage.
$$
\frac{80}{100} = 80\%
$$
Answer: $\frac{4}{5} = \frac{80}{100} = 80\%$
---
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}
$$
- Step 3: Write the percentage.
$$
\frac{35}{100} = 35\%
$$
Answer: $\frac{7}{20} = \frac{35}{100} = 35\%$
---
- Step 1: Find the number to multiply the denominator (50) by to get 100.
$$
\frac{100}{50} = 2
$$
- Step 2: Multiply both the numerator and the denominator by 2.
$$
\frac{7}{50} = \frac{7 \times 2}{50 \times 2} = \frac{14}{100}
$$
- Step 3: Write the percentage.
$$
\frac{14}{100} = 14\%
$$
Answer: $\frac{7}{50} = \frac{14}{100} = 14\%$
---
- Step 1: Find the number to multiply the denominator (25) by to get 100.
$$
\frac{100}{25} = 4
$$
- Step 2: Multiply both the numerator and the denominator by 4.
$$
\frac{4}{25} = \frac{4 \times 4}{25 \times 4} = \frac{16}{100}
$$
- Step 3: Write the percentage.
$$
\frac{16}{100} = 16\%
$$
Answer: $\frac{4}{25} = \frac{16}{100} = 16\%$
---
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100}
$$
- Step 3: Write the percentage.
$$
\frac{45}{100} = 45\%
$$
Answer: $\frac{9}{20} = \frac{45}{100} = 45\%$
---
- Step 1: Find the number to multiply the denominator (50) by to get 100.
$$
\frac{100}{50} = 2
$$
- Step 2: Multiply both the numerator and the denominator by 2.
$$
\frac{11}{50} = \frac{11 \times 2}{50 \times 2} = \frac{22}{100}
$$
- Step 3: Write the percentage.
$$
\frac{22}{100} = 22\%
$$
Answer: $\frac{11}{50} = \frac{22}{100} = 22\%$
---
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{6}{5} = \frac{6 \times 20}{5 \times 20} = \frac{120}{100}
$$
- Step 3: Write the percentage.
$$
\frac{120}{100} = 120\%
$$
Answer: $\frac{6}{5} = \frac{120}{100} = 120\%$
---
- Step 1: Find the number to multiply the denominator (2) by to get 100.
$$
\frac{100}{2} = 50
$$
- Step 2: Multiply both the numerator and the denominator by 50.
$$
\frac{5}{2} = \frac{5 \times 50}{2 \times 50} = \frac{250}{100}
$$
- Step 3: Write the percentage.
$$
\frac{250}{100} = 250\%
$$
Answer: $\frac{5}{2} = \frac{250}{100} = 250\%$
---
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{7}{4} = \frac{7 \times 25}{4 \times 25} = \frac{175}{100}
$$
- Step 3: Write the percentage.
$$
\frac{175}{100} = 175\%
$$
Answer: $\frac{7}{4} = \frac{175}{100} = 175\%$
---
$$
\boxed{
\begin{array}{ll}
1) & \frac{1}{2} = \frac{50}{100} = 50\% \\
2) & \frac{3}{10} = \frac{30}{100} = 30\% \\
3) & \frac{7}{10} = \frac{70}{100} = 70\% \\
4) & \frac{1}{4} = \frac{25}{100} = 25\% \\
5) & \frac{1}{5} = \frac{20}{100} = 20\% \\
6) & \frac{3}{4} = \frac{75}{100} = 75\% \\
7) & \frac{2}{5} = \frac{40}{100} = 40\% \\
8) & \frac{9}{10} = \frac{90}{100} = 90\% \\
9) & \frac{1}{20} = \frac{5}{100} = 5\% \\
10) & \frac{4}{5} = \frac{80}{100} = 80\% \\
11) & \frac{7}{20} = \frac{35}{100} = 35\% \\
12) & \frac{7}{50} = \frac{14}{100} = 14\% \\
13) & \frac{4}{25} = \frac{16}{100} = 16\% \\
14) & \frac{9}{20} = \frac{45}{100} = 45\% \\
15) & \frac{11}{50} = \frac{22}{100} = 22\% \\
16) & \frac{6}{5} = \frac{120}{100} = 120\% \\
17) & \frac{5}{2} = \frac{250}{100} = 250\% \\
18) & \frac{7}{4} = \frac{175}{100} = 175\% \\
\end{array}
}
$$
Steps:
1. Understand the Denominator Method: The goal is to convert each fraction into an equivalent fraction with a denominator of 100. This is because percentages are essentially fractions with a denominator of 100.
2. Find the Equivalent Fraction: Multiply both the numerator and the denominator of the given fraction by the same number so that the denominator becomes 100.
3. Write the Percentage: Once the denominator is 100, the numerator will be the percentage value.
Let's solve each problem step by step.
---
Problem 1: $\frac{1}{2}$
- Step 1: Find the number to multiply the denominator (2) by to get 100.
$$
\frac{100}{2} = 50
$$
- Step 2: Multiply both the numerator and the denominator by 50.
$$
\frac{1}{2} = \frac{1 \times 50}{2 \times 50} = \frac{50}{100}
$$
- Step 3: Write the percentage.
$$
\frac{50}{100} = 50\%
$$
Answer: $\frac{1}{2} = \frac{50}{100} = 50\%$
---
Problem 2: $\frac{3}{10}$
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}
$$
- Step 3: Write the percentage.
$$
\frac{30}{100} = 30\%
$$
Answer: $\frac{3}{10} = \frac{30}{100} = 30\%$
---
Problem 3: $\frac{7}{10}$
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}
$$
- Step 3: Write the percentage.
$$
\frac{70}{100} = 70\%
$$
Answer: $\frac{7}{10} = \frac{70}{100} = 70\%$
---
Problem 4: $\frac{1}{4}$
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}
$$
- Step 3: Write the percentage.
$$
\frac{25}{100} = 25\%
$$
Answer: $\frac{1}{4} = \frac{25}{100} = 25\%$
---
Problem 5: $\frac{1}{5}$
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{1}{5} = \frac{1 \times 20}{5 \times 20} = \frac{20}{100}
$$
- Step 3: Write the percentage.
$$
\frac{20}{100} = 20\%
$$
Answer: $\frac{1}{5} = \frac{20}{100} = 20\%$
---
Problem 6: $\frac{3}{4}$
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}
$$
- Step 3: Write the percentage.
$$
\frac{75}{100} = 75\%
$$
Answer: $\frac{3}{4} = \frac{75}{100} = 75\%$
---
Problem 7: $\frac{2}{5}$
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100}
$$
- Step 3: Write the percentage.
$$
\frac{40}{100} = 40\%
$$
Answer: $\frac{2}{5} = \frac{40}{100} = 40\%$
---
Problem 8: $\frac{9}{10}$
- Step 1: Find the number to multiply the denominator (10) by to get 100.
$$
\frac{100}{10} = 10
$$
- Step 2: Multiply both the numerator and the denominator by 10.
$$
\frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}
$$
- Step 3: Write the percentage.
$$
\frac{90}{100} = 90\%
$$
Answer: $\frac{9}{10} = \frac{90}{100} = 90\%$
---
Problem 9: $\frac{1}{20}$
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{1}{20} = \frac{1 \times 5}{20 \times 5} = \frac{5}{100}
$$
- Step 3: Write the percentage.
$$
\frac{5}{100} = 5\%
$$
Answer: $\frac{1}{20} = \frac{5}{100} = 5\%$
---
Problem 10: $\frac{4}{5}$
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{4}{5} = \frac{4 \times 20}{5 \times 20} = \frac{80}{100}
$$
- Step 3: Write the percentage.
$$
\frac{80}{100} = 80\%
$$
Answer: $\frac{4}{5} = \frac{80}{100} = 80\%$
---
Problem 11: $\frac{7}{20}$
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}
$$
- Step 3: Write the percentage.
$$
\frac{35}{100} = 35\%
$$
Answer: $\frac{7}{20} = \frac{35}{100} = 35\%$
---
Problem 12: $\frac{7}{50}$
- Step 1: Find the number to multiply the denominator (50) by to get 100.
$$
\frac{100}{50} = 2
$$
- Step 2: Multiply both the numerator and the denominator by 2.
$$
\frac{7}{50} = \frac{7 \times 2}{50 \times 2} = \frac{14}{100}
$$
- Step 3: Write the percentage.
$$
\frac{14}{100} = 14\%
$$
Answer: $\frac{7}{50} = \frac{14}{100} = 14\%$
---
Problem 13: $\frac{4}{25}$
- Step 1: Find the number to multiply the denominator (25) by to get 100.
$$
\frac{100}{25} = 4
$$
- Step 2: Multiply both the numerator and the denominator by 4.
$$
\frac{4}{25} = \frac{4 \times 4}{25 \times 4} = \frac{16}{100}
$$
- Step 3: Write the percentage.
$$
\frac{16}{100} = 16\%
$$
Answer: $\frac{4}{25} = \frac{16}{100} = 16\%$
---
Problem 14: $\frac{9}{20}$
- Step 1: Find the number to multiply the denominator (20) by to get 100.
$$
\frac{100}{20} = 5
$$
- Step 2: Multiply both the numerator and the denominator by 5.
$$
\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100}
$$
- Step 3: Write the percentage.
$$
\frac{45}{100} = 45\%
$$
Answer: $\frac{9}{20} = \frac{45}{100} = 45\%$
---
Problem 15: $\frac{11}{50}$
- Step 1: Find the number to multiply the denominator (50) by to get 100.
$$
\frac{100}{50} = 2
$$
- Step 2: Multiply both the numerator and the denominator by 2.
$$
\frac{11}{50} = \frac{11 \times 2}{50 \times 2} = \frac{22}{100}
$$
- Step 3: Write the percentage.
$$
\frac{22}{100} = 22\%
$$
Answer: $\frac{11}{50} = \frac{22}{100} = 22\%$
---
Problem 16: $\frac{6}{5}$
- Step 1: Find the number to multiply the denominator (5) by to get 100.
$$
\frac{100}{5} = 20
$$
- Step 2: Multiply both the numerator and the denominator by 20.
$$
\frac{6}{5} = \frac{6 \times 20}{5 \times 20} = \frac{120}{100}
$$
- Step 3: Write the percentage.
$$
\frac{120}{100} = 120\%
$$
Answer: $\frac{6}{5} = \frac{120}{100} = 120\%$
---
Problem 17: $\frac{5}{2}$
- Step 1: Find the number to multiply the denominator (2) by to get 100.
$$
\frac{100}{2} = 50
$$
- Step 2: Multiply both the numerator and the denominator by 50.
$$
\frac{5}{2} = \frac{5 \times 50}{2 \times 50} = \frac{250}{100}
$$
- Step 3: Write the percentage.
$$
\frac{250}{100} = 250\%
$$
Answer: $\frac{5}{2} = \frac{250}{100} = 250\%$
---
Problem 18: $\frac{7}{4}$
- Step 1: Find the number to multiply the denominator (4) by to get 100.
$$
\frac{100}{4} = 25
$$
- Step 2: Multiply both the numerator and the denominator by 25.
$$
\frac{7}{4} = \frac{7 \times 25}{4 \times 25} = \frac{175}{100}
$$
- Step 3: Write the percentage.
$$
\frac{175}{100} = 175\%
$$
Answer: $\frac{7}{4} = \frac{175}{100} = 175\%$
---
Final Answer:
$$
\boxed{
\begin{array}{ll}
1) & \frac{1}{2} = \frac{50}{100} = 50\% \\
2) & \frac{3}{10} = \frac{30}{100} = 30\% \\
3) & \frac{7}{10} = \frac{70}{100} = 70\% \\
4) & \frac{1}{4} = \frac{25}{100} = 25\% \\
5) & \frac{1}{5} = \frac{20}{100} = 20\% \\
6) & \frac{3}{4} = \frac{75}{100} = 75\% \\
7) & \frac{2}{5} = \frac{40}{100} = 40\% \\
8) & \frac{9}{10} = \frac{90}{100} = 90\% \\
9) & \frac{1}{20} = \frac{5}{100} = 5\% \\
10) & \frac{4}{5} = \frac{80}{100} = 80\% \\
11) & \frac{7}{20} = \frac{35}{100} = 35\% \\
12) & \frac{7}{50} = \frac{14}{100} = 14\% \\
13) & \frac{4}{25} = \frac{16}{100} = 16\% \\
14) & \frac{9}{20} = \frac{45}{100} = 45\% \\
15) & \frac{11}{50} = \frac{22}{100} = 22\% \\
16) & \frac{6}{5} = \frac{120}{100} = 120\% \\
17) & \frac{5}{2} = \frac{250}{100} = 250\% \\
18) & \frac{7}{4} = \frac{175}{100} = 175\% \\
\end{array}
}
$$
Parent Tip: Review the logic above to help your child master the concept of changing fractions to percentages worksheet.
