Multiplication As Repeated Addition

Hi there. This is a quick overview of multiplication through the persepective of repeated addition. Instead of memorizing time tables right off the start, consider multiplication through repeated addition for more understanding.

 

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Topics

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• Using Repeated Addition For Multiplication
• Count By Method As Another Strategy
• Multiplication With Variables (Grade Nine And Above Level)
• Cases With Zero

 
 

Using Repeated Addition For Multiplication

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Multiplication can be viewed as repeated addition where we have the size of one group and the number of equal groups in a collection. Here are some motivating examples.

 

• Two groups of ten students is 20 as 10 + 10 = 20.

• One dozen (12) of eggs is 12 eggs from one 12.

• Seven bags with 7 cats in each bag is 49 cats in total. This is from 7 + 7 + 7 + 7 + 7 + 7 + 7.

 

The multiplication operator/sign between two numbers indicates the number of groups with the size of each group. Each group has the same number of items in the group.

• The number 5 two times is represented by 2 x 5. As repeated addition, this is 5 + 5 = 10.

• Five mistakes 3 times a week is 15 mistakes a week. This is from 5 + 5 + 5 = 3 x 5 = 15.

• Seven bags with 7 cats in each bag is 49 cats in total. This is 7 x 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49.

 
 

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Count By Method As Another Strategy

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Another way to look at multiplication is to count by a number.

Example One - Counting By Two For Multiplying By Two

Counting by twos starting at two yields the two times table of up to 12.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

 

The number 2 is from 1 x 2 which is one group of two. Four is from 2 x 2 or two groups of two. It goes up to 24 which 12 groups of two or 12 x 2..

 

Example Two - Counting By Five For Multiplying By Five

To obtain the five times table, count by fives.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

 

The number 5 is from 1 x 5 which is one group of five. Ten is from 2 x 5 which is two groups of five. From the list above we go up to 60 which 12 x 5.

 

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Multiplication With Variables (Grade Nine And Above Level)

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At around the high school level math students are introduced to unknown variables in the form of x, y and z.

• Having 5x is the unknown quantity x 5 times or five groups with each group has x items. As repeated additon this is x + x + x + x + x.

• The quantity 2y is the unknown quantity y 2 times. As repeated addition this y + y = 2y.

• If we have xy this means that each group has y items and it appears x times. This is written as y + y + y + ... + y where the number of ys appear x times (assume x a positve integer).

 

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Cases With Zero

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This section looks at cases with zero groups, groups with zero in each group and zero multiplied by zero.
 

• Zero groups of anything is zero as there is nothing. An example would be 0 x 2 = 0 which is zero groups of two.

• A number of groups with zero in each group results in a total of zero. An example of this would be 3 x 0 = 0 as there are three groups of zero.

• Zero multiplied by zero is zero as there are zero groups of zero.

 

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