Solve 10:(2:(15:7)) - Sequential Division with Nested Operations

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

$10:(2:\frac{15}{7})=$

Now we invert the fraction to create a multiplication exercise:

$10:(2\times\frac{7}{15})=$

We add the 2 to the numerator of the fraction in the multiplication exercise:

$10:\frac{2\times7}{15}=$

Now we invert the fraction to create a multiplication exercise:

$10\times\frac{15}{2\times7}=$

We add the 10 to the numerator of the fraction in the multiplication exercise:

$\frac{10\times15}{2\times7}=$

We break down the 10 into a smaller multiplication exercise.

$\frac{5\times2\times15}{2\times7}=$

We simplify the 2 in the numerator and denominator:

$\frac{5\times15}{7}=\frac{75}{7}$

We separate the fraction into a sum exercise between fractions:

$\frac{70+5}{7}=\frac{70}{7}+\frac{5}{7}=10+\frac{5}{7}=10\frac{5}{7}$