Answer :
Sure! Let's work through each pair of fractions to find equivalent fractions with a common denominator by multiplying their denominators.
1. Fractions: [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{2}{6}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(3 \times 6 = 18\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{3} \times \frac{6}{6} = \frac{12}{18}\)[/tex]
- [tex]\(\frac{2}{6} \times \frac{3}{3} = \frac{6}{18}\)[/tex]
2. Fractions: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(5 \times 10 = 50\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}\)[/tex]
- [tex]\(\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}\)[/tex]
3. Fractions: [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(4 \times 8 = 32\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{4} \times \frac{8}{8} = \frac{8}{32}\)[/tex]
- [tex]\(\frac{1}{8} \times \frac{4}{4} = \frac{4}{32}\)[/tex]
4. Fractions: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(2 \times 3 = 6\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}\)[/tex]
- [tex]\(\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}\)[/tex]
5. Fractions: [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(8 \times 3 = 24\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{3}{8} \times \frac{3}{3} = \frac{9}{24}\)[/tex]
- [tex]\(\frac{1}{3} \times \frac{8}{8} = \frac{8}{24}\)[/tex]
These steps provide the equivalent fractions for each pair with a common denominator.
1. Fractions: [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{2}{6}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(3 \times 6 = 18\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{3} \times \frac{6}{6} = \frac{12}{18}\)[/tex]
- [tex]\(\frac{2}{6} \times \frac{3}{3} = \frac{6}{18}\)[/tex]
2. Fractions: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(5 \times 10 = 50\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}\)[/tex]
- [tex]\(\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}\)[/tex]
3. Fractions: [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(4 \times 8 = 32\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{4} \times \frac{8}{8} = \frac{8}{32}\)[/tex]
- [tex]\(\frac{1}{8} \times \frac{4}{4} = \frac{4}{32}\)[/tex]
4. Fractions: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(2 \times 3 = 6\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}\)[/tex]
- [tex]\(\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}\)[/tex]
5. Fractions: [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- Common Denominator: Multiply the denominators, [tex]\(8 \times 3 = 24\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{3}{8} \times \frac{3}{3} = \frac{9}{24}\)[/tex]
- [tex]\(\frac{1}{3} \times \frac{8}{8} = \frac{8}{24}\)[/tex]
These steps provide the equivalent fractions for each pair with a common denominator.