To make the fractions equivalent, it's essential to find a common denominator or multiply the numerator and denominator by the same factor for each fraction in a group. Here is a detailed, step-by-step solution for each given set of fractions:
a. [tex]\(\frac{3}{5} = \frac{6}{10} = \frac{9}{15}\)[/tex]
- Fraction [tex]\(\frac{3}{5}\)[/tex]
- Multiply the numerator and denominator by 2: [tex]\(\frac{3 \times 2}{5 \times 2} = \frac{6}{10}\)[/tex]
- Multiply the numerator and denominator by 3: [tex]\(\frac{3 \times 3}{5 \times 3} = \frac{9}{15}\)[/tex]
b. [tex]\(\frac{2}{5} = \frac{8}{20} = \frac{10}{25}\)[/tex]
- Fraction [tex]\(\frac{2}{5}\)[/tex]
- Multiply the numerator and denominator by 4: [tex]\(\frac{2 \times 4}{5 \times 4} = \frac{8}{20}\)[/tex]
- Multiply the numerator and denominator by 5: [tex]\(\frac{2 \times 5}{5 \times 5} = \frac{10}{25}\)[/tex]
c. [tex]\(\frac{4}{7} = \frac{8}{14} = \frac{12}{21}\)[/tex]
- Fraction [tex]\(\frac{4}{7}\)[/tex]
- Multiply the numerator and denominator by 2: [tex]\(\frac{4 \times 2}{7 \times 2} = \frac{8}{14}\)[/tex]
- Multiply the numerator and denominator by 3: [tex]\(\frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)[/tex]
d. [tex]\(\frac{3}{4} = \frac{6}{8} = \frac{9}{12}\)[/tex]
- Fraction [tex]\(\frac{3}{4}\)[/tex]
- Multiply the numerator and denominator by 2: [tex]\(\frac{3 \times 2}{4 \times 2} = \frac{6}{8}\)[/tex]
- Multiply the numerator and denominator by 3: [tex]\(\frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)[/tex]
e. [tex]\(\frac{3}{7} = \frac{6}{14} = \frac{9}{21}\)[/tex]
- Fraction [tex]\(\frac{3}{7}\)[/tex]
- Multiply the numerator and denominator by 2: [tex]\(\frac{3 \times 2}{7 \times 2} = \frac{6}{14}\)[/tex]
- Multiply the numerator and denominator by 3: [tex]\(\frac{3 \times 3}{7 \times 3} = \frac{9}{21}\)[/tex]
f. [tex]\(\frac{1}{4} = \frac{2}{8} = \frac{3}{12}\)[/tex]
- Fraction [tex]\(\frac{1}{4}\)[/tex]
- Multiply the numerator and denominator by 2: [tex]\(\frac{1 \times 2}{4 \times 2} = \frac{2}{8}\)[/tex]
- Multiply the numerator and denominator by 3: [tex]\(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\)[/tex]
