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:

$12 - (3-2) =$

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:

$12 - (3-2) =$

$12 - 3 + 2 =$

$9 + 2 = 11$

When distributing the parentheses, we will place a $-$ in front of the number $3$ and a $+$ before the $2$ .
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:

$12 - (3-2) =$

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

$12 - 1 = 11$

Detailed explanation

Practice Subtracting Whole Numbers with Subtraction in Parentheses

Test your knowledge with 40 quizzes

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

Examples with solutions for Subtracting Whole Numbers with Subtraction in Parentheses

Step-by-step solutions included

Exercise #1

$13-(7+4)=$

Step-by-Step Solution

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

$7+4=11$

Now we subtract:

$13-11=2$

Answer:

$2$

Video Solution

Exercise #2

$2-(1+1)=$

Step-by-Step Solution

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

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

Therefore, the solution to the expression is $0$ .

Answer:

Video Solution

Exercise #3

$100-(30-21)=$

Step-by-Step Solution

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

$30-21=9$

Now we obtain:

$100-9=91$

Answer:

$91$

Video Solution

Exercise #4

$100-(5+55)=$

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 $5 + 55$ , which gives $60$ .
Step 2: Perform the subtraction $100 - 60$ , which equals $40$ .

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

Answer:

Video Solution

Exercise #5

$12:(2\times2)=$

Step-by-Step Solution

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

$2\times2=4$

Now we divide:

$12:4=3$

Answer:

$3$

Video Solution

Frequently Asked Questions

Everything you need to know about Subtracting Whole Numbers with Subtraction in Parentheses

How do you subtract numbers with parentheses?

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?

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?

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?

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?

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?

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?

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?

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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Subtraction with Parentheses Practice Problems & Solutions

Understanding Subtracting Whole Numbers with Subtraction in Parentheses

Practice Subtracting Whole Numbers with Subtraction in Parentheses

Examples with solutions for Subtracting Whole Numbers with Subtraction in Parentheses

Frequently Asked Questions

How do you subtract numbers with parentheses?

What happens to signs when removing parentheses in subtraction?

What is the order of operations with parentheses?

How do you solve nested parentheses in subtraction?

Why do signs change when distributing through parentheses?

What are common mistakes when subtracting with parentheses?

How do you check your answer in parentheses subtraction problems?

When do you use parentheses in subtraction problems?

More Subtracting Whole Numbers with Subtraction in Parentheses Questions

Additional Arithmetic Rules

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Suggested Topics to Practice in Advance

Topics Learned in Later Sections

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