How to Use Number Lines for Multiplication by a Negative Integer?

A step-by-step guide to using number lines for multiplication by a negative integer

Use the Even-Odd rule whenever you multiply over two negative integers.
To follow the Even-Odd rule:

• Count the number of negative signs.
• If the number of negative signs is even, then the result is positive.
• If the number of negative signs is odd, then the result is negative.

Here is a step-by-step guide on how to use number lines for multiplication by a negative integer:

Step 1: Draw a Number Line: Draw a horizontal number line with zero in the center and positive numbers to the right and negative numbers to the left.

Step 2: Identify the Integer to be Multiplied: Identify the integer that needs to be multiplied by the negative integer.

Step 3: Determine the Absolute Value: Determine the absolute value of the integer that needs to be multiplied. This is the positive value of the integer without the sign.

Step 4: Start at Zero: Start at zero on the number line.

Step 5: Move to the Left: Move to the left on the number line by the absolute value of the integer that needs to be multiplied. For example, if the integer is \(3\), move three units to the left.

Step 6: Use the Direction of the Integer: Use the direction of the negative integer to determine the final direction. If the negative integer is negative, the final direction will be to the right. If the negative integer is positive, the final direction will be to the left.

Step 7: Count the Units: Count the number of units from the starting point to the ending point. This is the product of the integer and the negative integer. If the negative integer is positive, the product will be negative. If the negative integer is negative, the product will be positive.

Step 8: Practice, Practice, Practice! The more you practice using number lines for multiplication by a negative integer, the easier it will become. Try creating your number lines with different integers and negative integers to challenge yourself.

Here’s an example to help illustrate these steps:

Example: Multiply \(-2\) by \(4\).

Step 1: Draw a Number Line: Draw a number line with a zero in the center and negative numbers to the left.

Step 2: Identify the Integer to be Multiplied The integer to be multiplied is \(-2\).

Step 3: Determine the absolute value. The absolute value of \(-2\) is \(2\).

Step 4: Start at Zero: Start at zero on the number line.

Step 5: Move to the Left: Move to the left on the number line by \(2\) units.

Step 6: Use the Direction of the Integer. The negative integer is positive, so the final direction will be to the left.

Step 7: Count the Units: Count the number of units from the starting point to the ending point. There are 8 units from the starting point to the ending point, so the product of \(-2\) and \(4\) is \(-8\).

Step 8: Practice, Practice, Practice! Try creating your number lines with different integers and negative integers to further practice your skills.

Using Number Lines for Multiplication by a Negative Integer – Examples 1

Solve \(-3×-2=\)? And graph on the number line.

Solution:

Use this formula to find the sign of the product:
(negative)\(×\)(negative)\(=\)positive
To graph \(-3×-2\):
Step 1: Start from\(0\).
Step 2: Jump \(2\) units to the right side \(3\) times.
Step 3: The last jump ends at \(6\).

Using Number Lines for Multiplication by a Negative Integer – Examples 2

Solve \(4×-3=\)? And graph on the number line.
Solution:

Use this formula to find the sign of the product:
(negative)\(×\)(positive)\(=\)negative
To graph \(4×-3\):
Step 1: Start from \(0\).
Step 2: Jump \(3\) units to the left side \(4\) times.
Step 3: The last jump ends at \(-12\).