Nimme: \( \qquad \) DECMMALS AND PEREENTAGES N-GEN MIATH 7 HIOMEVVORK FIUENEY 1. For each of the following percent values, give the fraction of the whole it represent the decimal version of the fraction. The first is done as an example. (a) \( 22 \% \) fraction: \( \frac{22}{100} \) decimal: 0.22

Sure, I’d be happy to help you with converting percentages to fractions and decimals. Let's walk through the process using your example and provide some additional examples for practice. ### **Understanding the Conversion** 1. **Percentage to Fraction:** - A percentage represents a part out of 100. To convert a percentage to a fraction, you place the percentage number over 100 and simplify if possible. - **Formula:** \[ \text{Fraction} = \frac{\text{Percentage Value}}{100} \] 2. **Percentage to Decimal:** - To convert a percentage to a decimal, divide the percentage number by 100. - **Formula:** \[ \text{Decimal} = \frac{\text{Percentage Value}}{100} \] ### **Example Provided** **(a) \( 22\% \)** - **Fraction:** \[ \frac{22}{100} \] - This can be simplified by dividing both numerator and denominator by 2: \[ \frac{22 \div 2}{100 \div 2} = \frac{11}{50} \] - **Decimal:** \[ 0.22 \] ### **Additional Examples** Let's go through a few more examples to solidify your understanding. --- **(b) \( 45\% \)** - **Fraction:** \[ \frac{45}{100} \] - Simplify by dividing numerator and denominator by 5: \[ \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \] - **Decimal:** \[ 0.45 \] --- **(c) \( 12.5\% \)** - **Fraction:** \[ \frac{12.5}{100} \] - Since the numerator is a decimal, you can multiply both numerator and denominator by 10 to eliminate the decimal: \[ \frac{12.5 \times 10}{100 \times 10} = \frac{125}{1000} \] - Simplify by dividing numerator and denominator by 125: \[ \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \] - **Decimal:** \[ 0.125 \] --- **(d) \( 60\% \)** - **Fraction:** \[ \frac{60}{100} \] - Simplify by dividing numerator and denominator by 20: \[ \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \] - **Decimal:** \[ 0.60 \text{ or simply } 0.6 \] --- **(e) \( 7.5\% \)** - **Fraction:** \[ \frac{7.5}{100} \] - Eliminate the decimal by multiplying numerator and denominator by 10: \[ \frac{7.5 \times 10}{100 \times 10} = \frac{75}{1000} \] - Simplify by dividing numerator and denominator by 25: \[ \frac{75 \div 25}{1000 \div 25} = \frac{3}{40} \] - **Decimal:** \[ 0.075 \] --- ### **Summary** - **To convert a percentage to a fraction:** 1. Write the percentage as a fraction with denominator 100. 2. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). - **To convert a percentage to a decimal:** 1. Divide the percentage by 100. 2. Move the decimal point two places to the left. ### **Practice Problems** Try converting the following percentages to fractions and decimals: 1. \( 50\% \) 2. \( 18\% \) 3. \( 33.3\% \) 4. \( 80\% \) 5. \( 2.5\% \) **Solutions:** 1. **\( 50\% \)** - **Fraction:** \( \frac{50}{100} = \frac{1}{2} \) - **Decimal:** \( 0.50 \) or \( 0.5 \) 2. **\( 18\% \)** - **Fraction:** \( \frac{18}{100} = \frac{9}{50} \) - **Decimal:** \( 0.18 \) 3. **\( 33.3\% \)** - **Fraction:** \( \frac{33.3}{100} = \frac{333}{1000} \) (simplified as needed) - **Decimal:** \( 0.333 \) 4. **\( 80\% \)** - **Fraction:** \( \frac{80}{100} = \frac{4}{5} \) - **Decimal:** \( 0.80 \) or \( 0.8 \) 5. **\( 2.5\% \)** - **Fraction:** \( \frac{2.5}{100} = \frac{25}{1000} = \frac{1}{40} \) - **Decimal:** \( 0.025 \) --- Feel free to ask if you have any more questions or need further clarification!