# Division of Whole Numbers Within Parentheses Involving Division

The division of whole numbers within parentheses where there is a division refers to the situation in which we must carry out the mathematical operation of dividing a whole number by the result of dividing two elements, that is, by their quotient.

For example:

$24 : (6 : 2)$

There are two ways to solve this type of exercises.

The first one will be to open the parentheses and extract the numbers that were inside them.

That is, in our example:

$24 : (6 : 2) =$

$24:6\times2=$

$4\times2=8$

## Test yourself on additional arithmetic rules!

$$100-(5+55)=$$

## In general, this operation can be expressed using the following formula:

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

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:

$24 : 3 = 8$

## Exercises on dividing integers within parentheses where there is a division

### Exercise 1

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: $7$

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

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

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

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### Exercise 2

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

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

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

$10\frac{5}{7}$

### Exercise 3

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

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

$65$

Do you know what the answer is?

### Exercise 4

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: $2$

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

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

$6\frac{3}{7}$

### Exercise 5

Assignment

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

Solution

We multiply the exercise

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

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

## examples with solutions for division of whole numbers within parentheses involving division

### Exercise #1

$38-(18+20)=$

### Step-by-Step Solution

According to the order of operations, first we solve the exercise within parentheses:

$18+20=38$

Now, the exercise obtained is:

$38-38=0$

$0$

### Exercise #2

$8-(2+1)=$

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2+1=3$

Now we solve the rest of the exercise:

$8-3=5$

$5$

### Exercise #3

$22-(28-3)=$

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$28-3=25$

Now we obtain the exercise:

$22-25=-3$

$-3$

### Exercise #4

$12:(2\times2)=$

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$2\times2=4$

Now we divide:

$12:4=3$

$3$

### Exercise #5

$100-(30-21)=$

### Step-by-Step Solution

According to the order of operations, we first solve the exercise within parentheses:

$30-21=9$

Now we obtain:

$100-9=91$

$91$