Division with Multiplication in Parentheses Practice Problems

Master dividing whole numbers with multiplication in parentheses using PEMDAS and the special formula a:(b×c)=a:b:c through step-by-step practice exercises

📚Practice Division Problems with Multiplication in Parentheses
  • Apply the formula a:(b×c)=a:b:c to eliminate parentheses efficiently
  • Use PEMDAS order of operations to solve complex division expressions
  • Work with nested parentheses in multi-step division problems
  • Convert mixed numbers and fractions in division calculations
  • Master both parentheses elimination and order of operations methods
  • Solve real-world problems involving division with grouped multiplication

Understanding Division of Whole Numbers with Multiplication in Parentheses

Complete explanation with examples

Division of whole numbers with multiplication in parentheses

For example:

24:(6×2)=24 : (6\times2) =

One way to solve this exercise will be to remove the parentheses. To do this, we must remember the rule that states that, in order to remove the parentheses, we must divide the whole number by each of the terms of the multiplication operation in parenthese.

That is, in our example:

24:(6×2)= 24:(6\times2)=

24:6:2=24 : 6 : 2 =

4:2=24 : 2 = 2

Detailed explanation

Practice Division of Whole Numbers with Multiplication in Parentheses

Test your knowledge with 40 quizzes

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

Examples with solutions for Division of Whole Numbers with Multiplication 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 10060100 - 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(613)= 21-(6-13)=

Step-by-Step Solution

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

  • Step 1: Evaluate the inner expression 6136 - 13
  • Step 2: Substitute the result from Step 1 into 21result from Step 121 - \text{result from Step 1}

Now, let's work through each step:

Step 1: Calculate 6136 - 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

What is the rule for dividing by multiplication in parentheses?

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The rule states that a:(b×c) = a:b:c. This means you can divide the whole number by each term in the multiplication separately, or use order of operations to solve the parentheses first then divide.

How do you solve 24:(6×2) step by step?

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Method 1: Use the formula 24:(6×2) = 24:6:2 = 4:2 = 2. Method 2: Use order of operations 24:(6×2) = 24:12 = 2. Both methods give the same answer.

What is PEMDAS and how does it apply to division with parentheses?

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PEMDAS stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. For division with parentheses, you solve the multiplication inside parentheses first, then perform the division operation.

Can you use the a:(b×c)=a:b:c formula with nested parentheses?

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Yes, but work from the innermost parentheses outward. For example, in 87:(12×(35:(2×12))), first solve (2×12), then (35:24), then apply the formula to the outer expression.

What's the difference between 60:(10×2) and 60:10×2?

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With parentheses 60:(10×2) = 60:20 = 3. Without parentheses 60:10×2 = 6×2 = 12. Parentheses change the order of operations completely, making them crucial for correct answers.

How do you handle fractions when dividing with multiplication in parentheses?

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Convert the division to fraction form: a:(b×c) = a/(b×c). Then simplify by canceling common factors. For example, 35:(2×7) = 35/(2×7) = 35/14 = 5/2 = 2½.

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

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Use the formula a:(b×c)=a:b:c when you can easily divide by each factor separately. Use order of operations when the multiplication in parentheses creates a simpler number to work with.

What are common mistakes students make with division and parentheses?

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Common mistakes include: ignoring parentheses completely, applying operations in wrong order, forgetting to solve innermost parentheses first in nested expressions, and not recognizing when to apply the special division formula.

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