MULTIPLYING INTEGERS USING A NUMBER LINE

We can use a number line to see what happens when you multiply a positive number by a negative number.

Example 1 :

Henry made three withdrawals of $2 each from his savings account. What was the change in his balance ?

Solution : 

To know the change in balance, we have to find 3(-2).

Making withdrawal from account will reduce the balance. To indicate the reduce in balance, we use negative sign. 

Since the withdrawal is made of $2, we can use -2.  

To graph -2, we have to start at 0 and move 2 units to the left.

3(-2) means (-2) + (-2) + (-2)

To graph 3(-2), start at 0 and move 2 units to the left 3 times. 

(Here, we move to the left, because of the negative sign we have with 2)

From 0, when we move 2 units to the left 3 times, we get a total move of 6 units. 

The result is -6. 

Hence, the change in Henry’s balance was -$6. 

(The negative sign indicates the reduce in balance)

Example 2 :

Lisa plays a video game in which she loses points. She loses 3 points 2 times. What is the change in her score ?

Solution : 

To know the change in balance, we have to find 2(-3).

Loosing points will reduce the existing score. To indicate the reduce in score, we use negative sign. 

Since she is loosing 3 points, we can use -3.  

To graph -3, we have to start at 0 and move 3 units to the left.

2(-3) means (-3) + (-3)

To graph 2(-3), start at 0 and move 3 units to the left 2 times. 

(Here, we move to the left, because of the negative sign we have with 3)

From 0, when we move 3 units to the left 2 times, we get a total move of 6 units. 

The result is -6. 

Hence, the change in Lisa's score is -6. 

(The negative sign indicates the reduce in score)

Example 3 : 

What do you notice about the product of two integers with different signs ?

Solution : 

When we find the product of two integers with different signs, always the result is negative. 

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