Multiplying Integers

Multiplying integers is really easy, especially when you're multiplying 2 positive integers. What if you're multipling a negative integer with another negative integer? Or a negative and a positive? Here's a list that you should remember – a little investment in time to learn this will go a long way.




If you multiply 2 integers with the same sign, the result is always positive.

Example 1 - Same signs

2 × 2 = 4

(-2) × (-2) = 4

If you multiply 2 integers with different signs, the result is always negative.

Example 2 – Different signs

(-2) × 2 = -4

2 × (-2) = -4


Multiply Integers – 3 or more members

What about 3 or more integer multiplication? Just solve them in groups of 2.

Example 1 – When multiplying integers, order does not matter

Method 1: Group the first 2 multiplication members, then group the result with the third member.
2 × (-3) × 4
= (2 × (-3)) × 4
= (-6) × 4
= -24

Method 2: Group the last 2 multiplication members, then group the result with the first member.
2 × (-3) × 4
= 2 × ((-3) × 4)
= 2 × (-12)
= -24

This example shows that when mutiplying integers, whichever pair you solve first doesn't matter, so long as you solve it in pairs.

Tip
Pairing multiplication members to solve can be very time consuming. To solve multiple integer multiplication quickly, do the following:

1. Multiply out the numbers, ignoring the signs.
2. Count the number of negative signs in the multiplication. An odd number means that your result is negative. An even number means your result it positive.

Why does it work? Remember that same sign integer multiplication gives you a positive result. If you have an even number of negative signs, you get a positive result because they pair together to give you positive results, and positive multiplied by positive is positive. And if it's odd, well, you get the picture.

Example 2 – Odd number of negative signs

Solve 2 × (-3) × 4 × (-4) × (-2)

2 × (-3) × 4 × (-4) × (-2)
= -192 (Since we have 3 negatives)

Example 3 - Odd number of negative signs

Solve 2 × (-3) ×(-4) × (-4) × (-2)

2 × (-3) ×(-4) × (-4) × (-2)
= 192 (Since we have 4 negatives)


Multiplying Integers by 0

Multiplying any integer by 0 is very very very simple. The end result is 0, no matter how large or small, negative or positive the multiplication members are.

Example
2 × (-3) × 4 × 0 = 0

1 × 0 = 0

0 × 0 = 0

0 × 1 × 100 × 1000 = 0




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