Subtraction with Parentheses Practice Problems & Solutions

Master subtracting whole numbers with subtraction in parentheses through step-by-step practice problems. Learn order of operations and sign rules with examples.

πŸ“šPractice Subtraction with Parentheses - Build Your Skills
  • Solve subtraction problems with multiple nested parentheses step-by-step
  • Apply the order of operations (PEMDAS) to expressions with parentheses
  • Master sign rules when removing parentheses in subtraction expressions
  • Practice distributing negative signs through parentheses correctly
  • Work with positive and negative integers in parenthetical expressions
  • Build confidence solving complex subtraction problems with grouping symbols

Understanding Subtracting Whole Numbers with Subtraction in Parentheses

Complete explanation with examples

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:

12βˆ’(3βˆ’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:

12βˆ’(3βˆ’2)=12 - (3-2) =

12βˆ’3+2=12 - 3 + 2 =

9+2=119 + 2 = 11

When distributing the parentheses, we will place a βˆ’ - 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:

12βˆ’(3βˆ’2)=12 - (3-2) =

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

12βˆ’1=1112 - 1 = 11


Detailed explanation

Practice Subtracting Whole Numbers with Subtraction in Parentheses

Test your knowledge with 40 quizzes

\( 99:(33:10)= \)

Examples with solutions for Subtracting Whole Numbers with Subtraction in Parentheses

Step-by-step solutions included
Exercise #1

15:(2Γ—5)= 15:(2\times5)= ?

Step-by-Step Solution

First we need to apply the following formula:

a:(bΓ—c)=a:b:c a:(b\times c)=a:b:c

Therefore, we get:

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

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

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

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

152Γ—15= \frac{15}{2}\times\frac{1}{5}=

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

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

Answer:

112 1\frac{1}{2}

Video Solution
Exercise #2

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

Step-by-Step Solution

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

Step 1: Evaluate the inner division 10:5 10 : 5 .
When we compute 10:5 10 : 5 , we are finding how many times 5 fits into 10. This calculation can be expressed as:
105=2 \frac{10}{5} = 2 .

Step 2: Substitute the result from step 1 into the outer division.
Now, we substitute 10:(10:5) 10 : (10 : 5) with 10:2 10 : 2 . Once again, we apply division:
102=5 \frac{10}{2} = 5 .

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

Answer:

5 5

Video Solution
Exercise #3

18:(6Γ—3)= 18:(6\times3)=

Step-by-Step Solution

To solve the expression 18Γ·(6Γ—3) 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: (6Γ—3)(6 \times 3).
    We multiply 66 by 33 to get 1818.
  • Step 2: Replace the multiplication expression in the original division: 18Γ·1818 \div 18.
  • Step 3: Perform the division: 18Γ·18=118 \div 18 = 1.

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

Answer:

1

Video Solution
Exercise #4

2βˆ’(1+1)= 2-(1+1)=

Step-by-Step Solution

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

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

Therefore, the solution to the expression is 0 0 .

Answer:

0

Video Solution
Exercise #5

19βˆ’(5+11)= 19-(5+11)=

Step-by-Step Solution

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

  • Step 1: Evaluate the expression inside the parentheses. This means we need to calculate 5+115 + 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+115 + 11 which equals 16.

Step 2: Substitute 16 in place of 5+115 + 11 in the original expression. You have 19βˆ’1619 - 16.

Now, solve 19βˆ’1619 - 16, which equals 3.

Therefore, the solution to the problem is 33.

Answer:

3

Video Solution

Frequently Asked Questions

How do you subtract numbers with parentheses?

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When subtracting numbers with parentheses, first solve the expression inside the parentheses using the order of operations. Then perform the subtraction with the result. For example, in 12 - (3-2), first solve (3-2) = 1, then calculate 12 - 1 = 11.

What happens to signs when removing parentheses in subtraction?

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When removing parentheses preceded by a minus sign, all signs inside the parentheses change to their opposite. A positive becomes negative, and a negative becomes positive. For example, 15 - (3-2) becomes 15 - 3 + 2.

What is the order of operations with parentheses?

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Follow PEMDAS: Parentheses first, then Exponents, Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). Always solve expressions inside parentheses before performing operations outside them.

How do you solve nested parentheses in subtraction?

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Work from the innermost parentheses outward. Solve the deepest nested expression first, then move to the next level of parentheses. For example, in -30-[(-41)-[(-4)-(-8)]], start with (-4)-(-8) = 4, then work outward step by step.

Why do signs change when distributing through parentheses?

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Signs change because of the distributive property and multiplication rules. When you have a minus sign before parentheses, you're multiplying each term inside by -1, which changes positive terms to negative and negative terms to positive.

What are common mistakes when subtracting with parentheses?

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Common mistakes include: 1) Forgetting to change signs when removing parentheses, 2) Not following order of operations, 3) Making arithmetic errors with negative numbers, and 4) Not working from innermost to outermost parentheses in nested expressions.

How do you check your answer in parentheses subtraction problems?

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Check by substituting your answer back into the original expression or by solving the problem using a different method. You can also use the distributive method versus the order of operations method to verify your result matches.

When do you use parentheses in subtraction problems?

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Parentheses are used to group operations that should be performed first, to clarify the order of operations, or when subtracting an entire expression. They're essential when you need to subtract the result of multiple operations from another number.

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