Answer :
To evaluate the expression [tex]\(\frac{7}{6}-\frac{4}{5}\)[/tex] using equivalent fractions, we need to find a common denominator for the fractions. Here’s how you can do it:
1. Find the Least Common Denominator (LCD):
- The denominators we have are 6 and 5.
- The least common multiple of 6 and 5 is 30. Therefore, 30 will be our common denominator.
2. Convert Each Fraction to an Equivalent Fraction with the Denominator 30:
- For [tex]\(\frac{7}{6}\)[/tex]:
- Multiply both the numerator and the denominator by 5 (since [tex]\(6 \times 5 = 30\)[/tex]):
[tex]\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]:
- Multiply both the numerator and the denominator by 6 (since [tex]\(5 \times 6 = 30\)[/tex]):
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
3. Subtract the Equivalent Fractions:
- Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{35}{30} - \frac{24}{30} = \frac{35 - 24}{30} = \frac{11}{30}
\][/tex]
From this analysis, the equation that shows how to use equivalent fractions to evaluate [tex]\(\frac{7}{6}-\frac{4}{5}\)[/tex] is:
[tex]\[
\frac{7}{6}-\frac{4}{5}=\frac{35}{30}-\frac{24}{30}
\][/tex]
Thus, the correct answer is (D) [tex]\(\frac{7}{6}-\frac{4}{5}=\frac{35}{30}-\frac{24}{30}\)[/tex].
1. Find the Least Common Denominator (LCD):
- The denominators we have are 6 and 5.
- The least common multiple of 6 and 5 is 30. Therefore, 30 will be our common denominator.
2. Convert Each Fraction to an Equivalent Fraction with the Denominator 30:
- For [tex]\(\frac{7}{6}\)[/tex]:
- Multiply both the numerator and the denominator by 5 (since [tex]\(6 \times 5 = 30\)[/tex]):
[tex]\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]:
- Multiply both the numerator and the denominator by 6 (since [tex]\(5 \times 6 = 30\)[/tex]):
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
3. Subtract the Equivalent Fractions:
- Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{35}{30} - \frac{24}{30} = \frac{35 - 24}{30} = \frac{11}{30}
\][/tex]
From this analysis, the equation that shows how to use equivalent fractions to evaluate [tex]\(\frac{7}{6}-\frac{4}{5}\)[/tex] is:
[tex]\[
\frac{7}{6}-\frac{4}{5}=\frac{35}{30}-\frac{24}{30}
\][/tex]
Thus, the correct answer is (D) [tex]\(\frac{7}{6}-\frac{4}{5}=\frac{35}{30}-\frac{24}{30}\)[/tex].
