Rules for Integers
or
"
How to work problems with positive and negative numbers"
Addition
If the signs of the numbers are the same, add the numbers and keep the same sign.
Examples:
5+12=17
7+8=15
-4 + -6 = -10
-9 + -5 = -14
If the signs of the numbers are different, subtract the numbers and keep the sign of the larger number.
Examples:
8 + -5 = 3
9 + -15 = -6
-12 + 7 = -5
-5 + 10 = 5
Step by Step
Here is a problem
-5 + 4 = ?
Step one - identify the signs
Are the signs of the two numbers the same or different?
well...5 is a negative number because it has a negative sign in front of it
4 is a positive number
so the signs are different!
If the signs are different, the rules say to subtract the numbers and keep the sign of the larger number.
Step two - identify the larger number
5 is larger than 4
Step three - write the sign of the larger number for your answer (rules say to keep the sign of the larger number)
5 is larger, and its sign is negative, so my answer will be negative.
[Now my problem looks like -5 + 4 = -?]
Step four - subtract the smaller number from the larger number
Subtract 4 from 5 and get 1
[Now my problem looks like -5 + 4 = -1]
Let's try one where the signs are the same
-12 + (-3) = ?
Step one - identify the signs
Both numbers are negative
Rule says of the signs of both numbere are the same, to keep the sign and add the 2 numbers
Step two - Keep the sign of the two numbers
Both numbers are negative, so my answer will be negative
[Now my problem looks like this: -12 + (-3) = -?}
Step three - add the two numbers
12+3=15, so my problem now looks like this :: -12 + (-3) = -15
Subtraction
All subtraction problems are changed to addition problems by changing the subtraction sign to a plus sign and changing the sign of the second number. Then the rules for addition apply.
examples:
12 - 18 becomes 12 + (-18) = -6
8 - (-5) becomes 8 + 5 = 13
-14 - 6 becomes -14 + (-6) = -20
-10 - (-5) becomes -10 + 5 = -5
Step by Step
-5 - 8 = ?
Step one and two (these go together) - change the subtraction sign to a plus sign...
-5 + 8 = ?
AND THEN
change the sign of the second number (in this case, 8)
now we have
-5 + -8 = ?
Step two - look at your rules of addition - in this problem the signs are the same, so we keep the sign ( - ) and add the numbers
-5 + -8 = -13
Multiplication and Division
The rules for multiplication and division are the same. If the signs are the same, the answer is positive and if the signs are different, the answer is negative.
6 x 8 = 48
-7 x -8 = 56
-5 x 7 = -35
4 x -3 = -12
44 ÷ 11 = 4
-30 ÷ -6 = 5
-45 ÷ 5 = -9
36 ÷ -12 = -3
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