Subtraction with Addition in Parentheses Practice Problems

Master subtraction of whole numbers with addition in parentheses through step-by-step practice problems. Learn the distributive rule a-(b+c)=a-b-c with examples.

📚Practice Subtraction with Addition in Parentheses
  • Apply the rule a-(b+c)=a-b-c to solve subtraction problems with parentheses
  • Subtract each term in parentheses separately from the first number
  • Solve expressions like 25-(10+5) using order of operations
  • Work with negative numbers in subtraction with addition in parentheses
  • Master two different methods: distribute subtraction or solve parentheses first
  • Build confidence with step-by-step guided practice problems

Understanding Subtracting Whole Numbers with Addition in Parentheses

Complete explanation with examples

Subtraction of whole numbers with addition in parentheses refers to a situation where we must perform the mathematical operation of subtraction on the sum of some terms that are in parentheses.
In this case, we must remember that the subtraction will be performed on each and every term separately.

The rule is as follows:

a−(b+c)=a−b−ca - (b +c) = a - b - c

a - (b +c) = a - b - c

Each of the terms has its own numerical value.

Detailed explanation

Practice Subtracting Whole Numbers with Addition in Parentheses

Test your knowledge with 40 quizzes

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

Examples with solutions for Subtracting Whole Numbers with Addition in Parentheses

Step-by-step solutions included
Exercise #1

60:(10×2)= 60:(10\times2)=

Step-by-Step Solution

We write the exercise in fraction form:

6010×2= \frac{60}{10\times2}=

Let's separate the numerator into a multiplication exercise:

10×610×2= \frac{10\times6}{10\times2}=

We simplify the 10 in the numerator and denominator, obtaining:

62=3 \frac{6}{2}=3

Answer:

3 3

Video Solution
Exercise #2

12:(2×2)= 12:(2\times2)=

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

Video Solution
Exercise #3

7−(4+2)= 7-(4+2)=

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

Video Solution
Exercise #4

8−(2+1)= 8-(2+1)=

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

Video Solution
Exercise #5

13−(7+4)= 13-(7+4)=

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

Video Solution

Frequently Asked Questions

What is the rule for subtraction with addition in parentheses?

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The rule is a-(b+c)=a-b-c. When subtracting a sum in parentheses, you subtract each term separately from the first number. For example, 12-(3+2) becomes 12-3-2=7.

How do you solve 25-(10+5) step by step?

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Method 1: Apply the rule 25-(10+5)=25-10-5=15-5=10. Method 2: Solve parentheses first 25-(15)=25-15=10. Both methods give the same answer.

What are common mistakes when subtracting addition in parentheses?

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Common mistakes include: 1) Only subtracting the first term in parentheses, 2) Adding instead of subtracting when distributing the negative sign, 3) Forgetting to change signs when removing parentheses, 4) Not following order of operations correctly.

How do negative numbers work in subtraction with parentheses?

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When you have expressions like -4-(-14+(-23)), first solve inside parentheses: -4-(-37). Then apply sign rules: subtracting a negative becomes addition, so -4-(-37)=-4+37=33.

Why does a-(b+c) equal a-b-c?

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This follows the distributive property of subtraction over addition. The negative sign in front of parentheses distributes to each term inside, changing their signs. So -(b+c) becomes -b-c, making a-(b+c)=a-b-c.

What grade level learns subtraction with addition in parentheses?

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This concept is typically introduced in middle school (grades 6-8) as part of order of operations and pre-algebra. Students learn it after mastering basic arithmetic and before moving to more complex algebraic expressions.

How is this different from regular subtraction?

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Regular subtraction involves two numbers: a-b. Subtraction with addition in parentheses involves multiple terms: a-(b+c+d). You must either solve the parentheses first or distribute the subtraction to each term inside the parentheses.

What real-world problems use subtraction with parentheses?

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Examples include calculating change when buying multiple items, finding temperature differences, budget calculations where you subtract total expenses, and measuring distances when accounting for multiple segments or detours.

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