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Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

Division Strategies

Division is a fundamental mathematical operation that helps distribute quantities into equal parts. It is closely related to multiplication, as division is essentially the process of finding out how many times one number is contained within another. This lesson explores different strategies for division and demonstrates its connection to multiplication.

Division as the Inverse of Multiplication

Division and multiplcation are inverse operations. If you know that: \(a\times b=c\) then the related division facts are: \(c\div a=b\) and \(c\div b = a\).

Example:

If \(6 \times 4 = 24\), then:

\(24 \div 6 = 4\) and \(24 \div 4 = 6\)

This relationship helps verify division results by checking with multiplication.

Long Division Method

Recognize how many multiples of the divisor go into parts of the dividend

Steps:

  1. Divide the dividend by the divisor
  2. Multiply the quotient by the divisor
  3. Subtract the product from the dividend
  4. Bring down the next digit (if any) and repeat

Example:

Solve \(125 \div 5\):

  1. 5 goes 2 times into 12 (remainder 2)
  2. Bring down 5, making it 25
  3. 5 goes 5 times into 25
  4. The quotient is 25

When multiples are recognized quickly, then this method can be reduced to short division by using mental math.

Partial Quotients Method

You can break the dividend into smaller, more manageable parts.

Example:

Solve \(196 \div 7\):

  1. Recognize that 7 goes into 196 multiple times.
  2. We can subtract large known multiples such as \(7 \times 20 = 140\) from the dividend, \(196-140=56\)
  3. Subtract \(7 \times 8=56\), leaving 0.
  4. Add up the partial quotients, \(20+8=28\)

Estimation and Rounding in Division

For quick approximations, round numbers before dividing.

Example:

Solve \(198 \div 4\) by estimation:

  • Round 198 to 200
  • \(200 \div 4 =50\) (approximate answer)
  • Exact answer is 49.5

Repeated Subtraction Method

Division can be understood as repeated subtraction of the divisor from the dividend.

Example:

Solve \(20 \div 5\) using repeated subtraction:

  • 20 - 5 =15
  • 15 - 5 =10
  • 10 - 5 = 5
  • 5 - 5 =0
  • Since we subtracted 5 four times, the quotient is 4.

Understanding multiple division strategies enhances problem-solving skills and reinforces the connection between division and multiplication. Mastering these approaches allows for flexibility in tackling division problems efficiently.


Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

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