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

Question

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

00:10 Let's solve the problem together.

00:13 Remember, always tackle the parentheses first. Even if they're within other sets of parentheses.

00:20 Begin with the innermost set of parentheses.

00:24 Convert division into a fraction.

00:28 Think of division as multiplying by the reciprocal. This will help us simplify.

00:33 Multiply the numerators together and the denominators together.

00:41 Remember, division becomes multiplication by the reciprocal.

00:49 Again, multiply numerators by numerators and denominators by denominators.

00:55 Now, let's reduce, or simplify, what we can.

01:02 Break down the number eight into factors of two and four.

01:07 And simplify any further if possible.

01:11 And that's how we find the solution to our question! Great job!

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:

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

$\frac{5}{12}$