Subtracting Whole Numbers with Subtraction in Parentheses - Examples, Exercises and Solutions

Question Types:
Additional Arithmetic Rules: Applying the formulaAdditional Arithmetic Rules: Number of termsAdditional Arithmetic Rules: Exercises with 2 termsAdditional Arithmetic Rules: Using multiple rulesAdditional Arithmetic Rules: Using variables

Subtraction of whole numbers with subtractions in parentheses refers to a situation where we perform the mathematical operation of subtraction on the difference of some terms that are in parentheses.

For example:

12−(3−2)=12 - (3-2) =

One way to solve this exercise will be to distribute the parentheses. To do this, we must remember that according to the law of signs of addition/ subtraction, after removing parentheses, the expressions that were inside them change their sign.

C - Subtracting Whole Numbers with Subtraction in Parentheses

That is, in our example:

12−(3−2)=12 - (3-2) =

12−3+2=12 - 3 + 2 =

9+2=119 + 2 = 11

When distributing the parentheses, we will place a − - in front of the number 3 3 and a + + before the 2 2 .
As you can see, in both cases the sign that was inside the parentheses has switched to the opposite sign.

Another way to solve this exercise is to use the order of operations, that is to say:

12−(3−2)=12 - (3-2) =

We will start by solving the expression in parentheses by using the order of operations and we will get:

12−1=1112 - 1 = 11

Detailed explanation

Suggested Topics to Practice in Advance

  1. The commutative property
  2. The Commutative Property of Addition
  3. The Commutative Property of Multiplication
  4. The Distributive Property
  5. The Distributive Property for Seventh Graders
  6. The Distributive Property of Division
  7. The Distributive Property in the Case of Multiplication
  8. The commutative properties of addition and multiplication, and the distributive property
  9. The Associative Property
  10. The Associative Property of Addition
  11. The Associative Property of Multiplication

Practice Subtracting Whole Numbers with Subtraction in Parentheses

Question 1

\( 21:(30:10)= \)

Question 2

\( 15:(2\times5)= \)

Question 3

\( 12:(2\times2)= \)

Question 4

\( 7-(4+2)= \)

Question 5

\( 8-(2+1)= \)

Examples with solutions for Subtracting Whole Numbers with Subtraction in Parentheses

Exercise #1

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

Video Solution

Step-by-Step Solution

We will use the formula:

a:(b:c)=a:b×c a:(b:c)=a:b\times c

Therefore, we will get:

21:30×10= 21:30\times10=

Let's write the division exercise as a fraction:

2130=710 \frac{21}{30}=\frac{7}{10}

Now let's multiply by 10:

710×101= \frac{7}{10}\times\frac{10}{1}=

We'll reduce the 10 and get:

71=7 \frac{7}{1}=7

Answer

7 7

Exercise #2

15:(2×5)= 15:(2\times5)=

Video Solution

Step-by-Step Solution

We will use the formula:

a:(b×c)=a:b:c a:(b\times c)=a:b:c

Therefore, we get:

15:2:5= 15:2:5=

Let's write the exercise as a fraction:

1525= \frac{\frac{15}{2}}{5}=

We'll convert it to a multiplication of two fractions:

152×15= \frac{15}{2}\times\frac{1}{5}=

We multiply numerator by numerator and denominator by denominator, and we get:

1510=1510=112 \frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}

Answer

112 1\frac{1}{2}

Exercise #3

12:(2×2)= 12:(2\times2)=

Video Solution

Step-by-Step Solution

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

2×2=4 2\times2=4

Now we divide:

12:4=3 12:4=3

Answer

3 3

Exercise #4

7−(4+2)= 7-(4+2)=

Video Solution

Step-by-Step Solution

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

4+2=6 4+2=6

Now we solve the rest of the exercise:

7−6=1 7-6=1

Answer

1 1

Exercise #5

8−(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:

8−3=5 8-3=5

Answer

5 5

Question 1

\( 13-(7+4)= \)

Question 2

\( 38-(18+20)= \)

Question 3

\( 28-(4+9)= \)

Question 4

\( 55-(8+21)= \)

Question 5

\( 37-(4-7)= \)

Exercise #6

13−(7+4)= 13-(7+4)=

Video Solution

Step-by-Step Solution

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

7+4=11 7+4=11

Now we subtract:

13−11=2 13-11=2

Answer

2 2

Exercise #7

38−(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:

38−38=0 38-38=0

Answer

0 0

Exercise #8

28−(4+9)= 28-(4+9)=

Video Solution

Step-by-Step Solution

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

4+9=13 4+9=13

Now we obtain the exercise:

28−13=15 28-13=15

Answer

15 15

Exercise #9

55−(8+21)= 55-(8+21)=

Video Solution

Step-by-Step Solution

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

8+21=29 8+21=29

Now we obtain the exercise:

55−29=26 55-29=26

Answer

26 26

Exercise #10

37−(4−7)= 37-(4-7)=

Video Solution

Step-by-Step Solution

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

4−7=−3 4-7=-3

Now we obtain:

37−(−3)= 37-(-3)=

Remember that the product of a negative and a negative results in a positive, therefore:

−(−3)=+3 -(-3)=+3

Now we obtain:

37+3=40 37+3=40

Answer

40 40

Question 1

\( 80-(4-12)= \)

Question 2

\( 100-(30-21)= \)

Question 3

\( 66-(15-10)= \)

Question 4

\( 22-(28-3)= \)

Question 5

\( 60:(5\times3)= \)

Exercise #11

80−(4−12)= 80-(4-12)=

Video Solution

Step-by-Step Solution

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

4−12=−8 4-12=-8

Now we obtain the exercise:

80−(−8)= 80-(-8)=

Remember that the product of plus and plus gives us a positive:

−(−8)=+8 -(-8)=+8

Now we obtain:

80+8=88 80+8=88

Answer

88 88

Exercise #12

100−(30−21)= 100-(30-21)=

Video Solution

Step-by-Step Solution

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

30−21=9 30-21=9

Now we obtain:

100−9=91 100-9=91

Answer

91 91

Exercise #13

66−(15−10)= 66-(15-10)=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first solve the expression inside of the parentheses:

15−10=5 15-10=5

We obtain the following expression:

66−5=61 66-5=61

Answer

61 61

Exercise #14

22−(28−3)= 22-(28-3)=

Video Solution

Step-by-Step Solution

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

28−3=25 28-3=25

Now we obtain the exercise:

22−25=−3 22-25=-3

Answer

−3 -3

Exercise #15

60:(5×3)= 60:(5\times3)=

Video Solution

Step-by-Step Solution

We write the exercise in fraction form:

605×3 \frac{60}{5\times3}

We break down 60 into a multiplication exercise:

20×35×3= \frac{20\times3}{5\times3}=

We simplify the 3s and obtain:

205 \frac{20}{5}

We break down the 5 into a multiplication exercise:

5×45= \frac{5\times4}{5}=

We simplify the 5 and obtain:

41=4 \frac{4}{1}=4

Answer

4 4

Topics learned in later sections

  1. Advanced Arithmetic Operations
  2. Subtracting Whole Numbers with Addition in Parentheses
  3. Division of Whole Numbers Within Parentheses Involving Division
  4. Division of Whole Numbers with Multiplication in Parentheses