1.4 Multiplication of Integers
Interactive Rule Simulator (Tap to test multiplication sign rule):
(+) × (+) = Positive (+)
Rule 1:
When multiplying two integers that have the SAME sign, the answer is POSITIVE.
Positive × Positive = Positive → (+7) × (+10) = (+70)
Negative × Negative = Positive → (-5) × (-5) = (+25)
Rule 2:
When multiplying two integers that have DIFFERENT signs, the answer is NEGATIVE.
Positive × Negative = Negative → (+8) × (-6) = (-48)
Negative × Positive = Negative → (-5) × (+7) = (-35)
Exercise
Find the product of each of the following:
a
-12 × 2 =
b
11 × -11 × -1 =
c
-20 × -10 =
d
7 × 8 × -10 =
e
8 × -10 × 2 =
f
-3 × 2 × -1 × 10 =
1.5 Division of Integers
If both the dividend and divisor are positive or both are negative, the quotient will be positive.
Rule 1:
If both dividend and divisor have the same sign, positive or negative, the quotient will be positive.
(16) ÷ (4) = 4 (positive quotient)
(-16) ÷ (-4) = 4 (positive quotient)
Rule 2:
If either of the dividend or divisor is negative the quotient will be negative.
(16) ÷ (-4) = -4 (negative quotient)
(-16) ÷ (4) = -4 (negative quotient)
In other words (if the signs are the same, the quotient will be positive, if they are different, the quotient will be negative). This rule is for multiplication and division.
Look at this example carefully:
-1568 ÷ 13 = ............
120 Quotient
13 | 1568 Remainder
- 13↓↓
-----
026
- 26↓
-----
008 Remainder
So the answer is 120 and rem = 8, but the dividend is negative, so the answer is -120 with rem = 8.
Exercises
1 Find the following:
a15 + (-11) =
b(-20) + (-32) =
c64 - 99 =
d-340 - (-20) =
e10 + (-4) =
f(-3) + (-9) =
g-6 - (7) =
h34 - (-4) =
i324 - (-12) =
2 Find the product:
a73 × 21 =
b40 × (-37) =
c3461 × (-10) =
d(-297) × (-6) =
e(-418) × (-86) =
f(-290) × 20 =
3 Find the quotient:
a5432 ÷ 8 =
b728 ÷ 56 =
c135 ÷ 45 =
d(-216) ÷ (29) =
e(-896) ÷ (-54) =
f659 ÷ (-73) =