Integer Multiplication

 You can only master this topic if you know multiplication.
To review the Fast Multiplication topic, see here.


FACT
    1 × -1 = -1     and     -1 × -1 = 1    


Breakdown of how integer multiplication works

-4 × 7 = (4 × -1) × 7   -3 × -5 = (3 × -1) × (-1 × 5)
= -1 × (4 × 7) = (-1 × -1) × (3 × 5)
= -1 × 28 = 1 × 15
= -28 = 15
Steps for integer multiplication:
  1. Count the number of negative integers
  2. Ignore the negative signs and multiply as usual
  3. If needed, add a negative sign to the answer in Step 2
        Odd number of negative integers = negative product
        Even number of negative integers = positive product


Example 1:   -2 × -3 × -7

Step 1: Count the negatives
There are 3 negative integers in the equation.

Step 2: Multiply
2 × 3 × 7 = 42

Step 3: Add negative sign?
Since there are 3 negative integers, the product must be negative.

-2 × -3 × -7 = -42


Example 2:   -1 × 4 × -3 × 4

Step 1: Count the negatives
There are 2 negative integers in the equation.

Step 2: Multiply
1 × 4 × 3 × 4 = 48

Step 3: Add negative sign?
Since there are 2 negative integers, the product must be positive.

-1 × 4 × -3 × 4 = 48

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