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

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

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

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 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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