Solve 25:(3:(10:35)): Evaluating Nested Division Expressions

First, we rewrite down the multiplication exercise within the inner parentheses as a fraction:$25:(3:\frac{10}{35})=$

Now we invert the fraction to create a multiplication exercise:

$25:(3\times\frac{35}{10})=$

We add the 3 to the numerator of the fraction in the multiplication exercise:

$25:\frac{3\times35}{10}=$

Now we invert the fraction to create a multiplication exercise:

$25\times\frac{10}{3\times35}=$

We add the 25 to the numerator of the fraction in the multiplication exercise:

$\frac{25\times10}{3\times35}=$

We separate the 10 and 35 into smaller multiplication exercises:

$\frac{25\times5\times2}{3\times7\times5}=$

We simplify the 5 in the numerator and denominator:

$\frac{25\times2}{3\times7}=\frac{50}{21}$

We separate the numerator of the fraction into a sum exercise:

$\frac{42+8}{21}=$

We separate into sum exercises among fractions:

$\frac{42+8}{21}=\frac{42}{21}+\frac{8}{21}=2+\frac{8}{21}=2\frac{8}{21}$