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Answer :
To solve this problem, we need to identify a pair of fractions from the given options that are not equivalent to [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex].
Let's analyze each option and check for equivalence with the given fractions:
1. Option A: [tex]\(\frac{12}{30}\)[/tex] and [tex]\(\frac{3}{30}\)[/tex]
- Check [tex]\(\frac{12}{30}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{12}{30}\)[/tex]: [tex]\(\frac{12 \div 6}{30 \div 6} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{3}{30}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{3}{30}\)[/tex]: [tex]\(\frac{3 \div 3}{30 \div 3} = \frac{1}{10}\)[/tex]. They are equivalent.
2. Option B: [tex]\(\frac{6}{15}\)[/tex] and [tex]\(\frac{5}{15}\)[/tex]
- Check [tex]\(\frac{6}{15}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{6}{15}\)[/tex]: [tex]\(\frac{6 \div 3}{15 \div 3} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{5}{15}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{5}{15}\)[/tex]: [tex]\(\frac{5 \div 5}{15 \div 5} = \frac{1}{3}\)[/tex]. This is not equivalent to [tex]\(\frac{1}{10}\)[/tex].
3. Option C: [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{10}{100}\)[/tex]
- Check [tex]\(\frac{20}{50}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{20}{50}\)[/tex]: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{10}{100}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{10}{100}\)[/tex]: [tex]\(\frac{10 \div 10}{100 \div 10} = \frac{1}{10}\)[/tex]. They are equivalent.
4. Option D: [tex]\(\frac{8}{20}\)[/tex] and [tex]\(\frac{2}{20}\)[/tex]
- Check [tex]\(\frac{8}{20}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{8}{20}\)[/tex]: [tex]\(\frac{8 \div 4}{20 \div 4} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{2}{20}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{2}{20}\)[/tex]: [tex]\(\frac{2 \div 2}{20 \div 2} = \frac{1}{10}\)[/tex]. They are equivalent.
After comparing each set of fractions with the given fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], we find that Option B ([tex]\(\frac{6}{15}\)[/tex] and [tex]\(\frac{5}{15}\)[/tex]) has fractions that are not equivalent to both given fractions. Therefore, the pair that is not equivalent to [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is Option B.
Let's analyze each option and check for equivalence with the given fractions:
1. Option A: [tex]\(\frac{12}{30}\)[/tex] and [tex]\(\frac{3}{30}\)[/tex]
- Check [tex]\(\frac{12}{30}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{12}{30}\)[/tex]: [tex]\(\frac{12 \div 6}{30 \div 6} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{3}{30}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{3}{30}\)[/tex]: [tex]\(\frac{3 \div 3}{30 \div 3} = \frac{1}{10}\)[/tex]. They are equivalent.
2. Option B: [tex]\(\frac{6}{15}\)[/tex] and [tex]\(\frac{5}{15}\)[/tex]
- Check [tex]\(\frac{6}{15}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{6}{15}\)[/tex]: [tex]\(\frac{6 \div 3}{15 \div 3} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{5}{15}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{5}{15}\)[/tex]: [tex]\(\frac{5 \div 5}{15 \div 5} = \frac{1}{3}\)[/tex]. This is not equivalent to [tex]\(\frac{1}{10}\)[/tex].
3. Option C: [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{10}{100}\)[/tex]
- Check [tex]\(\frac{20}{50}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{20}{50}\)[/tex]: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{10}{100}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{10}{100}\)[/tex]: [tex]\(\frac{10 \div 10}{100 \div 10} = \frac{1}{10}\)[/tex]. They are equivalent.
4. Option D: [tex]\(\frac{8}{20}\)[/tex] and [tex]\(\frac{2}{20}\)[/tex]
- Check [tex]\(\frac{8}{20}\)[/tex] with [tex]\(\frac{2}{5}\)[/tex]:
- Simplify [tex]\(\frac{8}{20}\)[/tex]: [tex]\(\frac{8 \div 4}{20 \div 4} = \frac{2}{5}\)[/tex]. They are equivalent.
- Check [tex]\(\frac{2}{20}\)[/tex] with [tex]\(\frac{1}{10}\)[/tex]:
- Simplify [tex]\(\frac{2}{20}\)[/tex]: [tex]\(\frac{2 \div 2}{20 \div 2} = \frac{1}{10}\)[/tex]. They are equivalent.
After comparing each set of fractions with the given fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], we find that Option B ([tex]\(\frac{6}{15}\)[/tex] and [tex]\(\frac{5}{15}\)[/tex]) has fractions that are not equivalent to both given fractions. Therefore, the pair that is not equivalent to [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is Option B.
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