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Answer :
To determine which pair of ratios is not equivalent, let's analyze each option:
A. [tex]\(\frac{7}{21}\)[/tex] and [tex]\(\frac{6}{18}\)[/tex]
- Simplify [tex]\(\frac{7}{21}\)[/tex]: Divide the numerator and the denominator by 7, which gives [tex]\(\frac{1}{3}\)[/tex].
- Simplify [tex]\(\frac{6}{18}\)[/tex]: Divide the numerator and the denominator by 6, which also gives [tex]\(\frac{1}{3}\)[/tex].
- Since both simplify to [tex]\(\frac{1}{3}\)[/tex], these ratios are equivalent.
B. [tex]\(\frac{90}{27}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]
- Simplify [tex]\(\frac{90}{27}\)[/tex]: Divide the numerator and the denominator by their greatest common divisor, which is 9. This gives [tex]\(\frac{10}{3}\)[/tex].
- [tex]\(\frac{3}{10}\)[/tex] is already in its simplest form.
- As [tex]\(\frac{10}{3}\)[/tex] is not equal to [tex]\(\frac{3}{10}\)[/tex], these ratios are not equivalent.
C. [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{15}{24}\)[/tex]
- Simplify [tex]\(\frac{15}{24}\)[/tex]: Divide the numerator and the denominator by 3, which gives [tex]\(\frac{5}{8}\)[/tex].
- Since both fractions reduce to [tex]\(\frac{5}{8}\)[/tex], these ratios are equivalent.
D. [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{10}{35}\)[/tex]
- Simplify [tex]\(\frac{20}{50}\)[/tex]: Divide the numerator and the denominator by 10, which gives [tex]\(\frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{10}{35}\)[/tex]: Divide the numerator and the denominator by 5, which gives [tex]\(\frac{2}{7}\)[/tex].
- Since [tex]\(\frac{2}{5}\)[/tex] is not equal to [tex]\(\frac{2}{7}\)[/tex], these ratios are not equivalent.
Based on our analysis, the ratios in option B, [tex]\(\frac{90}{27}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex], are not equivalent. Therefore, option B is the answer.
A. [tex]\(\frac{7}{21}\)[/tex] and [tex]\(\frac{6}{18}\)[/tex]
- Simplify [tex]\(\frac{7}{21}\)[/tex]: Divide the numerator and the denominator by 7, which gives [tex]\(\frac{1}{3}\)[/tex].
- Simplify [tex]\(\frac{6}{18}\)[/tex]: Divide the numerator and the denominator by 6, which also gives [tex]\(\frac{1}{3}\)[/tex].
- Since both simplify to [tex]\(\frac{1}{3}\)[/tex], these ratios are equivalent.
B. [tex]\(\frac{90}{27}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]
- Simplify [tex]\(\frac{90}{27}\)[/tex]: Divide the numerator and the denominator by their greatest common divisor, which is 9. This gives [tex]\(\frac{10}{3}\)[/tex].
- [tex]\(\frac{3}{10}\)[/tex] is already in its simplest form.
- As [tex]\(\frac{10}{3}\)[/tex] is not equal to [tex]\(\frac{3}{10}\)[/tex], these ratios are not equivalent.
C. [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{15}{24}\)[/tex]
- Simplify [tex]\(\frac{15}{24}\)[/tex]: Divide the numerator and the denominator by 3, which gives [tex]\(\frac{5}{8}\)[/tex].
- Since both fractions reduce to [tex]\(\frac{5}{8}\)[/tex], these ratios are equivalent.
D. [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{10}{35}\)[/tex]
- Simplify [tex]\(\frac{20}{50}\)[/tex]: Divide the numerator and the denominator by 10, which gives [tex]\(\frac{2}{5}\)[/tex].
- Simplify [tex]\(\frac{10}{35}\)[/tex]: Divide the numerator and the denominator by 5, which gives [tex]\(\frac{2}{7}\)[/tex].
- Since [tex]\(\frac{2}{5}\)[/tex] is not equal to [tex]\(\frac{2}{7}\)[/tex], these ratios are not equivalent.
Based on our analysis, the ratios in option B, [tex]\(\frac{90}{27}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex], are not equivalent. Therefore, option B is the answer.
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