**Multiplying integers using a number line :**

Going through the history of ancient period and also that of medieval period, we do find the mention of statistics in many countries.

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.

After having gone through the stuff given above, we hope that the students would have understood "How to multiply integers using a number line".

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