Answer:
[tex]$ \mbox{\Large $ \frac{5}{8}$ } $[/tex]
Step-by-step explanation:
1.) Rewrite the given problem in a mathematical expression or form.
⇒ [tex]$ \mbox{\Large $ \frac{2}{3} \times (\frac{6}{8} \div \frac{4}{5}) = \ ?$ } $[/tex]
2.) Flip or reverse the numerator and denominator of the second fraction or get the reciprocal of the second fraction, and change the sign used, from division to multiplication.
⇒ [tex]\textnormal{Reciprocal of} \ \frac{4}{5} \ \textnormal{is} \ \frac{5}{4}.[/tex]
⇒ [tex]$ \mbox{\Large $ \frac{2}{3} \times (\frac{6}{8} \div \frac{4}{5}) = \frac{2}{3} \times (\frac{6}{8} \times \frac{5}{4})$ } $[/tex]
3.) Multiply the numerators and denominators and cancel any common factors when necessary.
⇒ [tex]$ \mbox{\Large $ \frac{2}{3} \times (\frac{6}{8} \times \frac{5}{4}) = \frac{2 \times 6 \times 5}{3 \times 8 \times 4} = \frac{2 \times (2 \times 3) \times 5}{3 \times (2 \times 2 \times 2) \times (2 \times 2)} = \frac{5}{2 \times 2 \times 2} = \bold{\frac{5}{8}}$ } $[/tex]
4.) Therefore, the product of [tex]\frac{2}{3}[/tex] and the quotient of [tex]\frac{6}{8}[/tex] and [tex]\frac{4}{5}[/tex] is [tex]\frac{5}{8}[/tex].
I hope this helps you understand this concept in Mathematics.
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