Math worksheet for converting fractions, decimals, and percents.

Here are the solutions to the problems on the worksheet.

A) Convert the following.

1) $\frac{2}{5}$
* Decimal: To turn a fraction into a decimal, divide the top number by the bottom number ($2 \div 5$).
$2 \div 5 = 0.4$
* Percent: To turn a decimal into a percent, multiply by 100.
$0.4 \times 100 = 40\%$

2) $0.5$
* Fraction: The number 5 is in the tenths place, so write it as $\frac{5}{10}$. Then simplify by dividing both numbers by 5.
$\frac{5}{10} = \frac{1}{2}$
* Percent: Multiply the decimal by 100.
$0.5 \times 100 = 50\%$

3) $35\%$
* Decimal: Divide the percent by 100 (move the decimal point two places to the left).
$35 \div 100 = 0.35$
* Fraction: Write 35 over 100 ($\frac{35}{100}$). Simplify by dividing both numbers by 5.
$\frac{35 \div 5}{100 \div 5} = \frac{7}{20}$

4) $\frac{3}{12}$
* Percent: First, simplify the fraction. Both 3 and 12 can be divided by 3.
$\frac{3}{12} = \frac{1}{4}$
We know that $\frac{1}{4}$ is equal to $25\%$.
* Decimal: Divide 1 by 4.
$1 \div 4 = 0.25$

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B) Complete the table.

Row 1)
* Given: Decimal $0.3$
* Fractions: $0.3$ means 3 tenths, or $\frac{3}{10}$.
* Percents: $0.3 \times 100 = 30\%$

Row 2)
* Given: Fraction $\frac{7}{4}$
* Decimals: Divide 7 by 4.
$7 \div 4 = 1.75$
* Percents: $1.75 \times 100 = 175\%$

Row 3)
* Given: Percent $2\%$
* Decimals: $2 \div 100 = 0.02$
* Fractions: Write as $\frac{2}{100}$. Simplify by dividing by 2.
$\frac{2 \div 2}{100 \div 2} = \frac{1}{50}$

Row 4)
* Given: Decimal $1.8$
* Fractions: This is 1 and 8 tenths ($1 \frac{8}{10}$). Simplify the fraction part: $\frac{8}{10} = \frac{4}{5}$. So, the mixed number is $1 \frac{4}{5}$. As an improper fraction: $\frac{9}{5}$.
* Percents: $1.8 \times 100 = 180\%$

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Final Answer:

A) Convert the following.
1) Decimal: 0.4, Percent: 40%
2) Fraction: 1/2, Percent: 50%
3) Decimal: 0.35, Fraction: 7/20
4) Percent: 25%, Decimal: 0.25

B) Complete the table.
1) Fractions: 3/10, Percents: 30%
2) Decimals: 1.75, Percents: 175%
3) Fractions: 1/50, Decimals: 0.02
4) Fractions: 9/5 (or 1 4/5), Percents: 180%