ADDING AND SUBTRACTING INTEGERS



ADDING AND SUBTRACTING INTEGERS

|Rules for Addition |

|Positive + Positive |Positive |

|Positive + Negative |Depends |

|Negative + Positive |Depends |

|Negative + Negative |Negative |

Numbers Can be Positive or Negative:

|[pic] |

|Negative Numbers (-) |Positive Numbers (+) |

|(This is the Number Line, read about Using The Number Line) |

|[pic] |[pic] |

|"-" is the negative sign. |"+" is the positive |

 

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

Adding Positive Numbers

Adding positive numbers is just simple addtion.

Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

You could write it as (+2) + (+3) = (+5)

Subtracting Positive Numbers

Subtracting positive numbers is just simple subtraction.

Example: 6 - 3 = 3

is really saying

"Positive 6 minus Positive 3 equals Positive 3"

You could write it as (+6) - (+3) = (+3)

But what happens if we have negative numbers ... ?

For example, what is 6 - (-3) ?

 

|[pic] |Subtracting a Negative is the same as Adding |

|[pic] |Ally can be naughty or nice. So Ally's parents have said |

| |"If you are nice we will add 3 points (+3). If you are naughty, we take away 3 points (-3). When you |

| |reach 30 Points you get a toy." |

| |Ally starts the day with 9 Points: |

|[pic] |Ally's Mum discovers spilt milk: | |

| |9-3 = 6 | |

| | | |

| |  | |

| | | |

| | | |

| |Then Dad confesses he spilt the milk and writes "undo". Mum calculates: | |

| |6-(-3) = 6+3 = 9 | |

| | | |

So if you subtract a negative, you gain points

(ie the same as adding points).

What About Positive and Negative Together ... ?

You can also have questions like:

What is 6 + (-3) ?

or what is 6 - (+3) ?

They are really the same! Both are subtraction:

|[pic] |Subtracting a Positive |

| |or |

| |Adding a Negative |

| |is |

| |Subtraction |

|[pic] |A few days later. Ally has 12 points. | |

| |  | |

| | | |

| | | |

| | | |

| | | |

| |Mum adds 3 points because Ally's room is clean. | |

| |12+3 = 15 | |

| | | |

| | | |

| | | |

| | | |

| |Dad says "I cleaned that room" and writes "undo" on the chart. Mum calculates: | |

| |15 - (+3) = 12 | |

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| | | |

| | | |

| | | |

| |Dad sees Ally brushing the dog. Writes "+3" on the chart. Mum calculates: | |

| |12 + (+3) = 15 | |

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| | | |

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| | | |

| |Ally throws a stone against the window. Dad writes "-3" on the chart. Mum calculates: | |

| |15 + (-3) = 12 | |

| | | |

See: both "15 - (+3)" and "15 + (-3)" result in 12.

So:

It doesn't matter if you subtract positive points

or add negative points,

you still end up losing points.

Now, Here Are The Rules

|  |Rule |  |Example |

|[pic] |Two like signs become a positive sign |+(+) |3+(+2) = 3 + 2 = 5 |

| | |-(-) |6-(-3) = 6 + 3 = 9 |

|  |  |  |  |

|[pic] |Two unlike signs become a negative sign |+(-) |7+(-2) = 7 - 2 = 5 |

| | |-(+) |8-(+2) = 8 - 2 = 6 |

|  |  |  |  |

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

Example: What is 5+(-2) ?

+(-) are unlike signs, so they become a negative sign.

5+(-2) = 5 - 2 = 3

Answer: 5+(-2) = 3

Example: What is -6+(+3) ?

+(+) are like signs, so they become a positive sign.

-6+(+3) = -6 + 3

Start at -6 on the number line, move forward 3, and you end up at -3

Answer: -6+(+3) = -3

Example: What is 25-(-4) ?

-(-) are like signs, so they become a positive sign.

25-(-4) = 25+4

Start at 25 on the number line, move forward 4, and you end up at 29

Answer: 25-(-4) = 29

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