Division with Parentheses Practice Problems - Free Math Worksheets

Master division of whole numbers within parentheses with step-by-step practice problems. Learn order of operations and solve complex division expressions confidently.

📚What You'll Master in This Division Practice Session
  • Apply the formula a:(b:c) = a:b×c to solve division problems
  • Use order of operations to evaluate expressions with nested parentheses
  • Convert division expressions to fractions for easier calculation
  • Solve multi-step problems like 24:(6:2) using two different methods
  • Work with algebraic expressions containing variables and division
  • Simplify complex fractions and mixed numbers in final answers

Understanding Division of Whole Numbers Within Parentheses Involving Division

Complete explanation with examples

The division of whole numbers within parentheses where there is a division refers to the situation in which we must carry out the mathematical operation of dividing a whole number by the result of dividing two elements, that is, by their quotient.

For example:

24:(6:2)24 : (6 : 2)

There are two ways to solve this type of exercises.

The first one will be to open the parentheses and extract the numbers that were inside them.

That is, in our example:

24:(6:2)=24 : (6 : 2) =

24:6×2= 24:6\times2=

4×2=8 4\times2=8

B1 - Division of Whole Numbers Within Parentheses Involving Division

Detailed explanation

Practice Division of Whole Numbers Within Parentheses Involving Division

Test your knowledge with 40 quizzes

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

Examples with solutions for Division of Whole Numbers Within Parentheses Involving Division

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

How do you solve division problems with parentheses?

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There are two main methods: 1) Use the formula a:(b:c) = a:b×c to remove parentheses, or 2) Follow order of operations by solving the expression inside parentheses first. Both methods will give you the same correct answer.

What is the rule for a:(b:c) in division?

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The rule is a:(b:c) = a:b×c. This means you can rewrite the division by a quotient as multiplication. For example, 24:(6:2) becomes 24:6×2 = 4×2 = 8.

Why do we get the same answer using different methods for division with parentheses?

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Both methods follow mathematical principles correctly. The order of operations method solves step-by-step, while the formula method uses algebraic properties to transform the expression. They're mathematically equivalent approaches.

How do you handle nested parentheses in division problems?

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Start from the innermost parentheses and work outward. Convert divisions to fractions when helpful, then multiply step by step. For example, in 10:(2:(15:7)), first solve 15:7, then 2:(15:7), finally 10 divided by that result.

What are common mistakes when dividing with parentheses?

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Common errors include: • Ignoring order of operations • Forgetting to convert division to multiplication correctly • Making arithmetic errors in fraction simplification • Not starting with innermost parentheses in nested expressions

How do you convert division expressions to fractions?

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Replace the division symbol with a fraction bar. For example, (6:2) becomes 6/2, and 24:(6:2) becomes 24÷(6/2) = 24×(2/6). This often makes calculations clearer and easier to follow.

When should I use the formula method vs order of operations?

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Use order of operations for simple expressions with whole numbers. Use the formula method (a:(b:c) = a:b×c) when working with variables, fractions, or when you want to see the algebraic structure more clearly.

How do you simplify final answers in division with parentheses problems?

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Always reduce fractions to lowest terms, convert improper fractions to mixed numbers when appropriate, and factor out common terms in algebraic expressions. For example, 75/7 becomes 10 5/7 as a mixed number.

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