Negative Numbers

We have been working on positive and negative numbers in terms of fractions on a number.  This video may help you and your student to understand this standard a little better.

Go to www.learnzillion.com

enter quick code  LZ1137

If you can't get to the video, here is a review.  

Positive numbers always fall to the right of 0 in ascending order, 1, 2, 3, 4, etc.

Negative numbers always fall to the left of 0, falling from -1, -2, -3, -4.

Positive numbers we are more familiar with.  The larger number is FARTHER from 0.  For example, 4 is farther from 0 and 1 is, so 4 is greater.  We do this by subtracting.  1-0=1  which is the distance from 0.  4-0= 4, which is it's distance from 0.  4 has a greater magnitude therefore 4 is greater.

Negative numbers have a different set of rules.  The number CLOSER to 0 is the great number.  -1 is greater than -4.  0- (-4) = 4, which is farther from 0. 0 - (-1) = 1, which is closer to 0 meaning it that is greater than -1.  

When adding and subtracting negative numbers, if we have a subtraction sign and a negative sign next to each other, we have to use parentheses to separate.  In math, we cannot have two signs touching, they must always be separated by a number.  One way to do this is to change the sign accordingly.  Here is the rule:

+ + = +
+ - = -
- + = -
- - = +

"Like, add, write the common sign
Unlike, subtract, keep the sign of the largerrrrr"

For example, we never write 4 + (+5), because we know it is understand that is is 4 + 5.

We do write this 4 + (- 5 ) really means 4 - 5.

The opposite holds true.  4 - (+ 5) really means 4 - 5.

This is true also.  4 - (-5) really means 4 + 5.

To get even more technical, the - in front of the () is actually a -1, so this means

4 -1(-5).  Order of Operations says to multiply the -1 by the -5, and a negative times a negative is always positive.