Solve the Nested Division: 2/7 ÷ (3/5 ÷ (7÷8))

Question

$\frac{2}{7}:(\frac{3}{5}:(7:8))=\text{?}$

00:00 Solve

00:03 Always solve parentheses first, the rule applies even within parentheses

00:06 Start with the innermost parentheses

00:09 Write division as a fraction

00:14 Division is also multiplication by the reciprocal

00:23 Be sure to multiply numerator by numerator and denominator by denominator

00:31 Division is also multiplication by the reciprocal

00:39 Be sure to multiply numerator by numerator and denominator by denominator

00:45 Reduce what we can

00:52 Break down 8 into factors 2 and 4

00:56 Reduce what we can

01:01 And this is the solution to the question

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$\frac{2}{7}:(\frac{3}{5}:\frac{7}{8})=$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}:(\frac{3}{5}\times\frac{8}{7})=\frac{2}{7}:(\frac{3\times8}{5\times7})$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}\times\frac{5\times7}{3\times8}=\frac{2\times5\times7}{7\times3\times8}$

We simplify the 7 in the numerator and denominator:

$\frac{2\times5}{3\times8}=$

We break down the 8 into a shorter multiplication exercise:

$\frac{2\times5}{3\times2\times4}=$

We simplify the 2 in the numerator and denominator:

$\frac{5}{3\times4}=\frac{5}{12}$

$\frac{5}{12}$