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Answer :
To determine which pair of fractions is equivalent, we can compare each pair by simplifying them to see if they have the same value.
Let's examine each pair:
1. Pair: [tex]\(\frac{15}{25}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]
To simplify [tex]\(\frac{15}{25}\)[/tex], divide both the numerator and the denominator by 5:
[tex]\[
\frac{15}{25} = \frac{15 \div 5}{25 \div 5} = \frac{3}{5}
\][/tex]
To simplify [tex]\(\frac{24}{30}\)[/tex], divide both the numerator and the denominator by 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
Since [tex]\(\frac{3}{5} \neq \frac{4}{5}\)[/tex], these fractions are not equivalent.
2. Pair: [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
Both fractions have the same denominator, but different numerators. Hence, they are not equivalent.
[tex]\[
\frac{12}{35} \neq \frac{14}{35}
\][/tex]
3. Pair: [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
To simplify [tex]\(\frac{18}{45}\)[/tex], divide both the numerator and the denominator by 9:
[tex]\[
\frac{18}{45} = \frac{18 \div 9}{45 \div 9} = \frac{2}{5}
\][/tex]
To simplify [tex]\(\frac{14}{35}\)[/tex], divide both the numerator and the denominator by 7:
[tex]\[
\frac{14}{35} = \frac{14 \div 7}{35 \div 7} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{5} = \frac{2}{5}\)[/tex], these fractions are equivalent.
4. Pair: [tex]\(\frac{14}{21}\)[/tex] and [tex]\(\frac{8}{20}\)[/tex]
To simplify [tex]\(\frac{14}{21}\)[/tex], divide both the numerator and the denominator by 7:
[tex]\[
\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}
\][/tex]
To simplify [tex]\(\frac{8}{20}\)[/tex], divide both the numerator and the denominator by 4:
[tex]\[
\frac{8}{20} = \frac{8 \div 4}{20 \div 4} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{3} \neq \frac{2}{5}\)[/tex], these fractions are not equivalent.
Based on the comparisons above, the pair of fractions [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex] are equivalent.
Let's examine each pair:
1. Pair: [tex]\(\frac{15}{25}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]
To simplify [tex]\(\frac{15}{25}\)[/tex], divide both the numerator and the denominator by 5:
[tex]\[
\frac{15}{25} = \frac{15 \div 5}{25 \div 5} = \frac{3}{5}
\][/tex]
To simplify [tex]\(\frac{24}{30}\)[/tex], divide both the numerator and the denominator by 6:
[tex]\[
\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
Since [tex]\(\frac{3}{5} \neq \frac{4}{5}\)[/tex], these fractions are not equivalent.
2. Pair: [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
Both fractions have the same denominator, but different numerators. Hence, they are not equivalent.
[tex]\[
\frac{12}{35} \neq \frac{14}{35}
\][/tex]
3. Pair: [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
To simplify [tex]\(\frac{18}{45}\)[/tex], divide both the numerator and the denominator by 9:
[tex]\[
\frac{18}{45} = \frac{18 \div 9}{45 \div 9} = \frac{2}{5}
\][/tex]
To simplify [tex]\(\frac{14}{35}\)[/tex], divide both the numerator and the denominator by 7:
[tex]\[
\frac{14}{35} = \frac{14 \div 7}{35 \div 7} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{5} = \frac{2}{5}\)[/tex], these fractions are equivalent.
4. Pair: [tex]\(\frac{14}{21}\)[/tex] and [tex]\(\frac{8}{20}\)[/tex]
To simplify [tex]\(\frac{14}{21}\)[/tex], divide both the numerator and the denominator by 7:
[tex]\[
\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}
\][/tex]
To simplify [tex]\(\frac{8}{20}\)[/tex], divide both the numerator and the denominator by 4:
[tex]\[
\frac{8}{20} = \frac{8 \div 4}{20 \div 4} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{3} \neq \frac{2}{5}\)[/tex], these fractions are not equivalent.
Based on the comparisons above, the pair of fractions [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex] are equivalent.
Thanks for taking the time to read Which of the following fraction pairs is equivalent A tex frac 15 25 tex and tex frac 24 30 tex B tex frac 12 35. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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