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The first column remains (-3)
(-3) × 3 = - 9
(-3) × 2 = - 6
(-3) × 1 = - 3
(-3) × 0 = 0
(-3) × (-1) = 3
(-3) × (-2) = 6
(-3) × (-1) = 3
The sign on the second number determine the number of chips
4 × (-3) Since the first number in this combination (4) is positive we combine 4 groups of (-3) red chips
- 4 × 3, in this case
The first number is (-4) is negative, which indicates that we should "take away 4 groups of black chips).
How to do it
Add an equal number of red and black chips to the set.
After taking away 4 groups of 3 black chips, the resulting set has 12 red chips or a value of -12.
12 blacks + 12 reds inserted.
Take away 4 groups of 3 blacks
-12 remain ( 12 red chips remain)
Multiplying a positive and a negative (+) × (-)
If a is positive and b is positive (thus (-b) is negative) , then
a (a-b) = - (ab),
where ab is the whole-number product of a and b. That is, the product of a positive and a negative is NEGATIVE.
Multiplying two negatives
If a and b are positive, then
(-a) (-b) = ab,
where ab is the whole-number product of a and b. That is, the product of two negatives is POSITIVE.
Identity Property for Integer Multiplication
1 is the unique integer such that a × 1 = a = 1 × a for all a
Distributivity of Multiplication over Addition of Integers
Let a, b and c, be any integers then:
a (b + c) = ab + ac
Let a and b be any integers. Then
(-a)(-b) = ab for all integers a, b
is read: "the opposite of a times the opposite of b is ab"
Multiplication Cancellation Property
Let a, b and c, be any integers with c ≠ 0.
If ac = bc, then a = b
c ≠ 0 because:
3 × 0 = 2 × 0, but 3 ≠ 2!
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