To determine which pair of fractions are equivalent, we need to compare the given fractions by cross-multiplying. Two fractions [tex]\(\frac{a}{b}\)[/tex] and [tex]\(\frac{c}{d}\)[/tex] are equivalent if [tex]\(a \times d = b \times c\)[/tex].
Here are the pairs of fractions given:
A) [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]
B) [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{12}{20}\)[/tex]
C) [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex]
D) [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{15}{32}\)[/tex]
Let's analyze each pair:
A) [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex]:
Cross-multiplying gives:
[tex]\[ 1 \times 5 = 5 \][/tex]
[tex]\[ 3 \times 2 = 6 \][/tex]
Since [tex]\(5 \neq 6\)[/tex], this pair is not equivalent.
B) [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{12}{20}\)[/tex]:
Cross-multiplying gives:
[tex]\[ 3 \times 20 = 60 \][/tex]
[tex]\[ 8 \times 12 = 96 \][/tex]
Since [tex]\(60 \neq 96\)[/tex], this pair is not equivalent.
C) [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex]:
Cross-multiplying gives:
[tex]\[ 4 \times 25 = 100 \][/tex]
[tex]\[ 5 \times 20 = 100 \][/tex]
Since [tex]\(100 = 100\)[/tex], this pair is equivalent.
D) [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{15}{32}\)[/tex]:
Cross-multiplying gives:
[tex]\[ 5 \times 32 = 160 \][/tex]
[tex]\[ 6 \times 15 = 90 \][/tex]
Since [tex]\(160 \neq 90\)[/tex], this pair is not equivalent.
Thus, the pair of fractions that are equivalent is:
C) [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{20}{25}\)[/tex].
