Answer :
To evaluate [tex]\(\frac{7}{6} - \frac{4}{5}\)[/tex], we need to follow these steps:
1. Find a common denominator: The denominators 6 and 5 need a common denominator. The least common multiple (LCM) of 6 and 5 is 30.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{7}{6}\)[/tex]: Multiply both the numerator and denominator by 5 (since [tex]\(30 \div 6 = 5\)[/tex]). This gives us:
[tex]\[
\frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]: Multiply both the numerator and denominator by 6 (since [tex]\(30 \div 5 = 6\)[/tex]). This gives us:
[tex]\[
\frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
3. Subtract the 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]
The correct choice for the equation that shows how to evaluate [tex]\(\frac{7}{6} - \frac{4}{5}\)[/tex] is option (C):
[tex]\[
\frac{7}{6} - \frac{4}{5} = \frac{35}{30} - \frac{24}{30} = \frac{11}{30}
\][/tex]
1. Find a common denominator: The denominators 6 and 5 need a common denominator. The least common multiple (LCM) of 6 and 5 is 30.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{7}{6}\)[/tex]: Multiply both the numerator and denominator by 5 (since [tex]\(30 \div 6 = 5\)[/tex]). This gives us:
[tex]\[
\frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\][/tex]
- For [tex]\(\frac{4}{5}\)[/tex]: Multiply both the numerator and denominator by 6 (since [tex]\(30 \div 5 = 6\)[/tex]). This gives us:
[tex]\[
\frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\][/tex]
3. Subtract the 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]
The correct choice for the equation that shows how to evaluate [tex]\(\frac{7}{6} - \frac{4}{5}\)[/tex] is option (C):
[tex]\[
\frac{7}{6} - \frac{4}{5} = \frac{35}{30} - \frac{24}{30} = \frac{11}{30}
\][/tex]
