Multiply and divide integers
Key Notes:
Integer multiplication and division rules
When 2 integers have the same sign, the product is positive:
positive × positive = positive
negative × negative = positive
When 2 integers have different signs, the product is negative:
positive × negative = negative
negative × positive = negative
| positive ÷ positive = positive | 2 ÷ 2 = 1 |
| negative ÷ negative = positive | -6 ÷ -2 = 3 |
| positive ÷ negative = negative | 15 ÷ -3 = -5 |
| negative ÷ positive = negative | -24 ÷ 4 = -6 |
| positive × positive = positive | 2 x 2 = 4 |
| negative × negative = positive | -3 x -2 = 6 |
| positive × negative = negative | 5 x -3 = -15 |
| negative × positive = negative | -2 x 4 = -8 |
When 2 integers have the same sign, the quotient is positive:
positive ÷ positive = positive
negative ÷ negative = positive
When 2 integers have different signs, the quotient is negative:
positive ÷ negative = negative
negative ÷ positive = negative
When 2 integers have the same sign, the product is positive:
- positive × positive = positive
- negative × negative = positive
When 2 integers have different signs, the product is negative:
- positive × negative = negative
- negative × positive = negative
Ex:
875 is positive. -95 is negative. Use the rule:
positive × negative = negative
So, 875 × -95 is negative.
Now check your answer by doing the maths.
875 × -95 = -83,125
Yes, the answer is negative.
When 2 integers have the same sign, the quotient is positive:
- positive ÷ positive = positive
- negative ÷ negative = positive
When 2 integers have different signs, the quotient is negative:
- positive ÷ negative = negative
- negative ÷ positive = negative
EX:
3,264 is positive. -48 is negative. Use the rule:
positive ÷ negative = negative
So, 3,264 ÷ -48 is negative.
Now check your answer by doing the maths.
3,264 ÷ -48 = -68
Yes, the answer is negative.
Learn with an example
➡️ Divide:
-21 ÷ 3 =
First, ignore any negatives and divide:
21 ÷ 3 = 7
Now find the sign of the result. Since you divided a negative number, -21, by a positive number, 3, the result should be negative: -7.
So, -21 ÷ 3 = -7.
➡️ Divide:
-9 / 9 =
First, ignore any negatives and divide:
9/9 = 1
Now find the sign of the result. Since you divided a negative number, -9, by a positive number, 9, the result should be negative: -1.
So:
-9/9 = -1
➡️ Multiply:
-8 × -5 =
First, ignore any negatives and multiply:
8 × 5 = 40
Now find the sign of the result. Since you multiplied a negative number, –8, by a negative number, –5, the result should be positive: 40.
So, –8 × –5 = 40.
Try some practice problems!
