Let's solve the given division of fractions problem step by step:
We are given:
[tex]\[
\frac{8}{7} \div \frac{10}{6}
\][/tex]
Step 1: Understand that dividing by a fraction is equivalent to multiplying by its reciprocal. So, rewrite the division as multiplication:
[tex]\[
\frac{8}{7} \times \frac{6}{10}
\][/tex]
Step 2: Multiply the numerators and the denominators:
Numerator:
[tex]\[
8 \times 6 = 48
\][/tex]
Denominator:
[tex]\[
7 \times 10 = 70
\][/tex]
Thus, we get:
[tex]\[
\frac{8}{7} \times \frac{6}{10} = \frac{48}{70}
\][/tex]
Step 3: Simplify the fraction [tex]$\frac{48}{70}$[/tex] by finding the greatest common divisor (GCD) of 48 and 70. The GCD of 48 and 70 is 2. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{48 \div 2}{70 \div 2} = \frac{24}{35}
\][/tex]
So, the simplified result of the division [tex]$\frac{8}{7} \div \frac{10}{6}$[/tex] is:
[tex]\[
\frac{24}{35}
\][/tex]
Now, let's match this result with the given options:
a. [tex]\(\frac{5}{6}\)[/tex]
b. [tex]\(\frac{15}{24}\)[/tex]
Neither of the provided options ([tex]\(\frac{5}{6}\)[/tex] nor [tex]\(\frac{15}{24}\)[/tex]) matches our simplified result [tex]\(\frac{24}{35}\)[/tex]. Therefore, there is no correct option provided in the set of given choices.
To summarize:
- The result of dividing [tex]\(\frac{8}{7}\)[/tex] by [tex]\(\frac{10}{6}\)[/tex] is [tex]\(\frac{24}{35}\)[/tex].
- None of the provided answers ([tex]\(\frac{5}{6}\)[/tex] or [tex]\(\frac{15}{24}\)[/tex]) is correct for this problem.
