Division of Whole Numbers Within Parentheses Involving Division

πŸ†Practice additional arithmetic rules

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)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 : 2) =

24:6Γ—2= 24:6\times2=

4Γ—2=8 4\times2=8

B1 - Division of Whole Numbers Within Parentheses Involving Division

Start practice

Test yourself on additional arithmetic rules!

einstein

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

Practice more now

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

a:(b:c)=a:bΓ—c a:(b:c)=a:b\times c

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

24:(6:2)=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=824 : 3 = 8


Exercises on dividing integers within parentheses where there is a division

Exercise 1

Assignment

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

Solution

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

56a:7b3a 56a:\frac{7b}{3a}

Now we multiply

56aΓ—3a7b=56aΓ—3a7b 56a\times\frac{3a}{7b}=\frac{56a\times3a}{7b}

We reduce by: 7 7

8aΓ—3ab \frac{8a\times3a}{b}

24a2b 24\frac{a^2}{b}

Answer

24a2b 24\frac{a^2}{b}


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Exercise 2

Assignment

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

Solution

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

10:(2:157) 10:(2:\frac{15}{7})

We multiply the expression inside the parenthesis

10:(2Γ—157) 10:(2\times\frac{15}{7})

10:2Γ—715 10:\frac{2\times7}{15}

We multiply the expression

10Γ—152Γ—7 10\times\frac{15}{2\times7}

10Γ—152Γ—7 \frac{10\times15}{2\times7}

We simplify by: 2 2

5Γ—157 \frac{5\times15}{7}

757 \frac{75}{7}

We break down the numerator

70+57 \frac{70+5}{7}

10+57=1057 10+\frac{5}{7}=10\frac{5}{7}

Answer

1057 10\frac{5}{7}


Exercise 3

Assignment

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

Solution

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

30:(3:132)=? 30:(3:\frac{13}{2})=\text{?}

We multiply the expression inside the parenthesis

30:(3Γ—213) 30:(3\times\frac{2}{13})

30:3Γ—213 30:\frac{3\times2}{13}

We multiply the expression

30Γ—133Γ—2 \frac{30\times13}{3\times2}

5Γ—3Γ—2Γ—133Γ—2 \frac{5\times3\times2\times13}{3\times2}

We simplify and solve

5Γ—13=5Γ—10+5Γ—3=50+15=65 5\times13=5\times10+5\times3=50+15=65

Answer

65 65


Do you know what the answer is?

Exercise 4

Assignment

10:(7:(92))=? 10:(7:(\frac{9}{2}))=\text{?}

Solution

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

10:(7:92) 10:(7:\frac{9}{2})

We multiply the expression inside the parenthesis

10:(7Γ—29) 10:(7\times\frac{2}{9})

10:7Γ—29 10:\frac{7\times2}{9}

We multiply the expression

10Γ—97Γ—2 10\times\frac{9}{7\times2}

10Γ—97Γ—2 \frac{10\times9}{7\times2}

5Γ—2Γ—97Γ—2 \frac{5\times2\times9}{7\times2}

It simplifies by: 2 2

457=42+37 \frac{45}{7}=\frac{42+3}{7}

427+37=6+37=637 \frac{42}{7}+\frac{3}{7}=6+\frac{3}{7}=6\frac{3}{7}

Answer

637 6\frac{3}{7}


Exercise 5

Assignment

(a+b):(344)=? (a+b):(3\frac{4}{4})=\text{?}

Solution

We multiply the exercise

(a+b)Γ—43=43(a+b) (a+b)\times\frac{4}{3}=\frac{4}{3}\left(a+b\right)

Answer

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


Check your understanding

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

Exercise #1

38βˆ’(18+20)= 38-(18+20)=

Video Solution

Step-by-Step Solution

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

18+20=38 18+20=38

Now, the exercise obtained is:

38βˆ’38=0 38-38=0

Answer

0 0

Exercise #2

8βˆ’(2+1)= 8-(2+1)=

Video Solution

Step-by-Step Solution

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

2+1=3 2+1=3

Now we solve the rest of the exercise:

8βˆ’3=5 8-3=5

Answer

5 5

Exercise #3

22βˆ’(28βˆ’3)= 22-(28-3)=

Video Solution

Step-by-Step Solution

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

28βˆ’3=25 28-3=25

Now we obtain the exercise:

22βˆ’25=βˆ’3 22-25=-3

Answer

βˆ’3 -3

Exercise #4

12:(2Γ—2)= 12:(2\times2)=

Video Solution

Step-by-Step Solution

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

2Γ—2=4 2\times2=4

Now we divide:

12:4=3 12:4=3

Answer

3 3

Exercise #5

100βˆ’(30βˆ’21)= 100-(30-21)=

Video Solution

Step-by-Step Solution

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

30βˆ’21=9 30-21=9

Now we obtain:

100βˆ’9=91 100-9=91

Answer

91 91

Start practice