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:

$24 : (6 : 2) =$

$24:6\times2=$

$4\times2=8$

B1 - Division of Whole Numbers Within Parentheses Involving Division

Detailed explanation

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$70:(14\times5)=$

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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: $7$

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

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

Answer

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

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Question 1

$$ 21:(30:10)= $$

Question 2

$$ 10:(10:5)= $$

Question 3

$15:(2\times5)=$ ?

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

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

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

Answer

$10\frac{5}{7}$

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

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

Answer

$65$

Do you know what the answer is?

Question 1

$$ 500:(2000:25)= $$

Question 2

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

Question 3

$$ 87-(7+0)= $$

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: $2$

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

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

Answer

$6\frac{3}{7}$

Exercise 5

Assignment

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

Solution

We multiply the exercise

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

Answer

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

Check your understanding

Question 1

$$ 2-(1+1)= $$

Question 2

$$ 19-(5+11)= $$

Question 3

$$ 26-(11-2)= $$

Examples with solutions for Division of Whole Numbers Within Parentheses Involving Division

Exercise #1

$15:(2\times5)=$ ?

Video Solution

Step-by-Step Solution

First we need to apply the following formula:

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

Therefore, we get:

$15:2:5=$

Now, let's rewrite the exercise as a fraction:

$\frac{\frac{15}{2}}{5}=$

Then we'll convert it to a multiplication of two fractions:

$\frac{15}{2}\times\frac{1}{5}=$

Finally, we multiply numerator by numerator and denominator by denominator, leaving us with:

$\frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}$

Answer

$1\frac{1}{2}$

Exercise #2

$10:(10:5)=$

Video Solution

Step-by-Step Solution

To solve the expression $10 : (10 : 5)$ , we will apply the order of operations systematically.

Step 1: Evaluate the inner division $10 : 5$ .
When we compute $10 : 5$ , we are finding how many times 5 fits into 10. This calculation can be expressed as:
$\frac{10}{5} = 2$ .

Step 2: Substitute the result from step 1 into the outer division.
Now, we substitute $10 : (10 : 5)$ with $10 : 2$ . Once again, we apply division:
$\frac{10}{2} = 5$ .

Therefore, the solution to the expression $10 : (10 : 5)$ is $5$ .

Answer

$5$

Exercise #3

$18:(6\times3)=$

Video Solution

Step-by-Step Solution

To solve the expression $18 \div (6 \times 3)$ , we need to follow the order of operations, which specifies that multiplication should be performed before division. Therefore, we proceed as follows:

Step 1: Calculate the operation inside the parentheses: $(6 \times 3)$ .
We multiply $6$ by $3$ to get $18$ .
Step 2: Replace the multiplication expression in the original division: $18 \div 18$ .
Step 3: Perform the division: $18 \div 18 = 1$ .

Thus, the result of the expression $18 \div (6 \times 3)$ is $\mathbf{1}$ .

Answer

Exercise #4

$2-(1+1)=$

Video Solution

Step-by-Step Solution

To solve the expression $2 - (1 + 1)$ , follow these steps:

First, evaluate the expression inside the parentheses: $1 + 1$ .
This gives $2$ .
Now replace the parentheses with this result, transforming the expression to $2 - 2$ .
The result of $2 - 2$ is $0$ .

Therefore, the solution to the expression is $0$ .

Answer

Exercise #5

$19-(5+11)=$

Video Solution

Step-by-Step Solution

To solve the problem $19 - (5 + 11)$ , we will follow these steps:

Step 1: Evaluate the expression inside the parentheses. This means we need to calculate $5 + 11$ .
Step 2: Once the sum inside the parentheses is found, subtract this sum from 19.

Let's work through each step:

Step 1: Calculate $5 + 11$ which equals 16.

Step 2: Substitute 16 in place of $5 + 11$ in the original expression. You have $19 - 16$ .

Now, solve $19 - 16$ , which equals 3.

Therefore, the solution to the problem is $3$ .

Answer

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Division of Whole Numbers Within Parentheses Involving Division

Test yourself on additional arithmetic rules!

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

Exercises on dividing integers within parentheses where there is a division

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Examples with solutions for Division of Whole Numbers Within Parentheses Involving Division

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Additional Arithmetic Rules