Chapter 3: Fractions, decimals and percentages Worksheet B 1 Convert the following percentages to fractions or mixed numbers in their simplest form. a \( 62.5 \% \) b \( \frac{6.5}{100}-\frac{62.5}{100 \times 10} \) b \( 375 \% \)

**Problem 1(a): Convert \( 62.5\% \) to a fraction in simplest form.** 1. Write the percentage as a fraction over 100: \[ 62.5\% = \frac{62.5}{100} \] 2. To eliminate the decimal in the numerator, multiply both numerator and denominator by 10: \[ \frac{62.5 \times 10}{100 \times 10} = \frac{625}{1000} \] 3. Simplify the fraction by dividing numerator and denominator by their greatest common divisor. Notice that \[ 625 \div 125 = 5 \quad \text{and} \quad 1000 \div 125 = 8. \] Thus, \[ \frac{625}{1000} = \frac{5}{8}. \] The simplest form is \[ \boxed{\frac{5}{8}}. \] --- **Problem 1(b): Convert \( 375\% \) to a fraction or mixed number in simplest form.** 1. Write the percentage as a fraction over 100: \[ 375\% = \frac{375}{100} \] 2. Simplify the fraction by dividing numerator and denominator by their common factor. Both 375 and 100 are divisible by 25: \[ 375 \div 25 = 15 \quad \text{and} \quad 100 \div 25 = 4. \] So, \[ \frac{375}{100} = \frac{15}{4}. \] 3. Express the improper fraction as a mixed number. Divide 15 by 4: \[ 15 \div 4 = 3 \text{ remainder } 3. \] Hence, \[ \frac{15}{4} = 3\frac{3}{4}. \] The simplest form is either \[ \boxed{\frac{15}{4}} \quad \text{or} \quad \boxed{3\frac{3}{4}}. \]