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Answer :
To solve the problem [tex]\(\frac{7}{6} - \frac{4}{5}\)[/tex] using equivalent fractions with a common denominator, follow these steps:
1. Identify the Denominators:
The fractions we are dealing with are [tex]\(\frac{7}{6}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex], which have denominators of 6 and 5, respectively.
2. Find the Common Denominator:
The common denominator for 6 and 5 is found by multiplying them together: [tex]\(6 \times 5 = 30\)[/tex]. So, the common denominator is 30.
3. Convert Each Fraction to have the Common Denominator:
- For [tex]\(\frac{7}{6}\)[/tex]: Multiply the numerator and the denominator by 5 to get the equivalent fraction:
[tex]\[
\frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]: Multiply the numerator and the denominator by 6 to get the equivalent fraction:
[tex]\[
\frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
4. 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]
Therefore, 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]
So, the correct answer choice is (D).
1. Identify the Denominators:
The fractions we are dealing with are [tex]\(\frac{7}{6}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex], which have denominators of 6 and 5, respectively.
2. Find the Common Denominator:
The common denominator for 6 and 5 is found by multiplying them together: [tex]\(6 \times 5 = 30\)[/tex]. So, the common denominator is 30.
3. Convert Each Fraction to have the Common Denominator:
- For [tex]\(\frac{7}{6}\)[/tex]: Multiply the numerator and the denominator by 5 to get the equivalent fraction:
[tex]\[
\frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]: Multiply the numerator and the denominator by 6 to get the equivalent fraction:
[tex]\[
\frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
4. 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]
Therefore, 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]
So, the correct answer choice is (D).
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