To find equivalent fractions for the given fractions [tex]\( \frac{2}{5} \)[/tex], [tex]\( \frac{3}{8} \)[/tex], and [tex]\( \frac{6}{15} \)[/tex], we can multiply both the numerator and the denominator of each fraction by the same number (k). Here, we will find three equivalent fractions for each of these fractions by multiplying the numerator and the denominator by 2, 3, and 4 respectively.
1. For the fraction [tex]\( \frac{2}{5} \)[/tex]:
- Multiplying by 2: [tex]\(\frac{2 \times 2}{5 \times 2} = \frac{4}{10}\)[/tex]
- Multiplying by 3: [tex]\(\frac{2 \times 3}{5 \times 3} = \frac{6}{15}\)[/tex]
- Multiplying by 4: [tex]\(\frac{2 \times 4}{5 \times 4} = \frac{8}{20}\)[/tex]
Thus, the equivalent fractions for [tex]\( \frac{2}{5} \)[/tex] are [tex]\( \frac{4}{10} \)[/tex], [tex]\( \frac{6}{15} \)[/tex], and [tex]\( \frac{8}{20} \)[/tex].
2. For the fraction [tex]\( \frac{3}{8} \)[/tex]:
- Multiplying by 2: [tex]\(\frac{3 \times 2}{8 \times 2} = \frac{6}{16}\)[/tex]
- Multiplying by 3: [tex]\(\frac{3 \times 3}{8 \times 3} = \frac{9}{24}\)[/tex]
- Multiplying by 4: [tex]\(\frac{3 \times 4}{8 \times 4} = \frac{12}{32}\)[/tex]
Thus, the equivalent fractions for [tex]\( \frac{3}{8} \)[/tex] are [tex]\( \frac{6}{16} \)[/tex], [tex]\( \frac{9}{24} \)[/tex], and [tex]\( \frac{12}{32} \)[/tex].
3. For the fraction [tex]\( \frac{6}{15} \)[/tex]:
- Multiplying by 2: [tex]\(\frac{6 \times 2}{15 \times 2} = \frac{12}{30}\)[/tex]
- Multiplying by 3: [tex]\(\frac{6 \times 3}{15 \times 3} = \frac{18}{45}\)[/tex]
- Multiplying by 4: [tex]\(\frac{6 \times 4}{15 \times 4} = \frac{24}{60}\)[/tex]
Thus, the equivalent fractions for [tex]\( \frac{6}{15} \)[/tex] are [tex]\( \frac{12}{30} \)[/tex], [tex]\( \frac{18}{45} \)[/tex], and [tex]\( \frac{24}{60} \)[/tex].
In summary, the equivalent fractions for each given fraction are:
- [tex]\( \frac{2}{5} \)[/tex]: [tex]\( \frac{4}{10} \)[/tex], [tex]\( \frac{6}{15} \)[/tex], [tex]\( \frac{8}{20} \)[/tex]
- [tex]\( \frac{3}{8} \)[/tex]: [tex]\( \frac{6}{16} \)[/tex], [tex]\( \frac{9}{24} \)[/tex], [tex]\( \frac{12}{32} \)[/tex]
- [tex]\( \frac{6}{15} \)[/tex]: [tex]\( \frac{12}{30} \)[/tex], [tex]\( \frac{18}{45} \)[/tex], [tex]\( \frac{24}{60} \)[/tex]
