Division of Whole Numbers Within Parentheses Involving Division

$a:(b:c)=a:b\times c$

Another way to solve this exercise is to apply the order of operations:

$24 : (6 : 2) =$

We will start by solving the expression within the parentheses according to the order of operations and we will obtain:

$24 : 3 = 8$

Assignment

$56a:(7b:3a)=\text{?}$

Solution

We will write the exercise in another way, that is, we will write the fraction in another way:

$56a:\frac{7b}{3a}$

Now we multiply

$56a\times\frac{3a}{7b}=\frac{56a\times3a}{7b}$

We reduce by: $7$

$\frac{8a\times3a}{b}$

$24\frac{a^2}{b}$

Answer

$24\frac{a^2}{b}$

Assignment

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

Solution

We start from the innermost parenthesis and write it in the form of a fraction

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

We multiply the expression inside the parenthesis

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

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

We multiply the expression

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

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

We simplify by: $2$

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

$\frac{75}{7}$

We break down the numerator

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

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

Answer

$10\frac{5}{7}$

Assignment

$30:(3:(13:2))=\text{?}$

Solution

We start from the innermost parenthesis and write it as a fraction

$30:(3:\frac{13}{2})=\text{?}$

We multiply the expression inside the parenthesis

$30:(3\times\frac{2}{13})$

$30:\frac{3\times2}{13}$

We multiply the expression

$\frac{30\times13}{3\times2}$

$\frac{5\times3\times2\times13}{3\times2}$

We simplify and solve

$5\times13=5\times10+5\times3=50+15=65$

Answer

$65$

Assignment

$10:(7:(\frac{9}{2}))=\text{?}$

Solution

We start from the innermost parenthesis and write it as a fraction

$10:(7:\frac{9}{2})$

We multiply the expression inside the parenthesis

$10:(7\times\frac{2}{9})$

$10:\frac{7\times2}{9}$

We multiply the expression

$10\times\frac{9}{7\times2}$

$\frac{10\times9}{7\times2}$

$\frac{5\times2\times9}{7\times2}$

It simplifies by: $2$

$\frac{45}{7}=\frac{42+3}{7}$

$\frac{42}{7}+\frac{3}{7}=6+\frac{3}{7}=6\frac{3}{7}$

Answer

$6\frac{3}{7}$

Assignment

$(a+b):(3\frac{4}{4})=\text{?}$

Solution

We multiply the exercise

$(a+b)\times\frac{4}{3}=\frac{4}{3}\left(a+b\right)$

Answer

$\frac{4}{3}\left(a+b\right)$