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

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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

$70:(14\times5)=$

Question 2

$300:(5\times6)=$

Question 3

$$ 21-(6-13)= $$

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

$$ 99:(33:10)= $$

Question 2

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

Question 3

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

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

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

Question 2

$$ 66:(360:60)= $$

Question 3

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

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

Exercise #1

$100-(5+55)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the sum inside the parentheses.
Step 2: Subtract the result of the sum from 100.

Now, let's work through each step:
Step 1: Calculate $5 + 55$ , which gives $60$ .
Step 2: Perform the subtraction $100 - 60$ , which equals $40$ .

Therefore, the solution to the problem is $40$ .

Answer

Exercise #2

$70:(14\times5)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the product of $14$ and $5$ .
Step 2: Use this product to divide $70$ .
Step 3: Compare the calculated result with the given choices.

Now, let's work through each step:
Step 1: First, calculate the product of $14$ and $5$ . Using basic multiplication:
$14 \times 5 = 70$ Step 2: Divide $70$ by the product, which is also $70$ :
$70 \div 70 = 1$

Therefore, the solution to the problem is $1$ . This matches choice 1 from the provided options.

Answer

Exercise #3

$300:(5\times6)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Compute the product $5 \times 6$ .
Step 2: Perform the division operation $300 \div 30$ .

Now, let's work through each step:

Step 1: Calculate $5 \times 6$ .

$5 \times 6 = 30$

Step 2: Divide 300 by the result from Step 1.

$300 \div 30 = 10$

Therefore, the solution to the problem is $\boxed{10}$ .

This matches the choice: 10.

Answer

Exercise #4

$21-(6-13)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the inner expression $6 - 13$
Step 2: Substitute the result from Step 1 into $21 - \text{result from Step 1}$

Now, let's work through each step:

Step 1: Calculate $6 - 13$ . In this calculation, we subtract 13 from 6. The result is $-7$ , because when subtracting a larger number from a smaller one, the result is negative.

Step 2: Substitute $-7$ into the outer expression $21 - (-7)$ . Since subtracting a negative is equivalent to adding the positive opposite, this simplifies to $21 + 7$ .

Now, compute $21 + 7$ , which equals 28.

Therefore, the solution to the problem is $28$ .

Answer

Exercise #5

$99:(33:10)=$

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Perform the inner division operation.
Step 2: Use the result of Step 1 in the outer division operation.

Now, let's work through each step:

Step 1: Calculate $33:10$ .
This operation is equivalent to dividing 33 by 10, which gives us:
$\frac{33}{10} = 3.3$ .

Step 2: Use the result from Step 1 to perform the division $99:3.3$ .
This operation now becomes:
$\frac{99}{3.3} = 30$ .

Therefore, the solution to the problem is $30$ .

Answer

Start practice

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