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.

📚Practice 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:

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

Practice Subtracting Whole Numbers with Subtraction in Parentheses

Test your knowledge with 40 quizzes

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

Examples with solutions for Subtracting Whole Numbers with Subtraction in Parentheses

Step-by-step solutions included
Exercise #1

100−(5+55)= 100-(5+55)=

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+555 + 55, which gives 6060.
Step 2: Perform the subtraction 100−60100 - 60, which equals 4040.

Therefore, the solution to the problem is 40 40 .

Answer:

40

Video Solution
Exercise #2

70:(14×5)= 70:(14\times5)=

Step-by-Step Solution

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

  • Step 1: Calculate the product of 14 14 and 5 5 .
  • Step 2: Use this product to divide 70 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 14 and 5 5 . Using basic multiplication:
14×5=70 14 \times 5 = 70 Step 2: Divide 70 70 by the product, which is also 70 70 :
70÷70=1 70 \div 70 = 1

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

Answer:

1

Video Solution
Exercise #3

300:(5×6)= 300:(5\times6)=

Step-by-Step Solution

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

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

Now, let's work through each step:

Step 1: Calculate 5×6 5 \times 6 .

5×6=30 5 \times 6 = 30

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

300÷30=10 300 \div 30 = 10

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

This matches the choice: 10.

Answer:

10

Video Solution
Exercise #4

21−(6−13)= 21-(6-13)=

Step-by-Step Solution

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

  • Step 1: Evaluate the inner expression 6−136 - 13
  • Step 2: Substitute the result from Step 1 into 21−result from Step 121 - \text{result from Step 1}

Now, let's work through each step:

Step 1: Calculate 6−136 - 13. In this calculation, we subtract 13 from 6. The result is −7-7, because when subtracting a larger number from a smaller one, the result is negative.

Step 2: Substitute −7-7 into the outer expression 21−(−7)21 - (-7). Since subtracting a negative is equivalent to adding the positive opposite, this simplifies to 21+721 + 7.

Now, compute 21+721 + 7, which equals 28.

Therefore, the solution to the problem is 2828.

Answer:

28

Video Solution
Exercise #5

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

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 33:10 .
This operation is equivalent to dividing 33 by 10, which gives us:
3310=3.3\frac{33}{10} = 3.3.

Step 2: Use the result from Step 1 to perform the division 99:3.3 99:3.3 .
This operation now becomes:
993.3=30\frac{99}{3.3} = 30.

Therefore, the solution to the problem is 30 30 .

Answer:

30

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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