MULTIPLYING INTEGERS



MULTIPLYING INTEGERS

2 Possible Situations

The Signs are the Same

|Same |

|(() x (() = + |

|(+) x (+) = + |

| |

|Different |

|(() x (+) = ( |

|(+) x (() = ( |

When the factors (2 numbers that you multiply) have the same sign, the product (consider of multiplication) is positive.

Example #1:

(+5) x (+6) = +30

or

(5) (6) = 30

Example #2:

((12) x ((4) = +48

or

(12 x (4 = +48

(Figure out that it is positive, then multiply 12 x 4)

The Signs are Different

*When the factors (2 numbers that you multiply) have different signs, the product (consider of multiplication) is negative.

Example #1: Example #2:

((6) x (+8) = (48 (+9) x ((11) = (99

or or

(6 + 8= (48 +9 x (11= (99

(Figure out that it is negative, then multiply 6 x 8)

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Let’s look at how this works, but first remember:

Positive Negative

= 0

Also, Multiplication is just a shortcut for repeated addition.

+3 x +4 means ‘add’ 3 groups of 4

We use the first sign, for +3 as addition… it tells you what to do with the groups.

One group of 4

Added to another group of 4

Added to a third group of 4 = 12

Remember the language. Example: +6 x +5 means ‘add’ 6 groups of +5

What happens when the signs are different?

+3 x –4 = “add” 3 groups of –4

+ + = -12

Now let’s look at the first number being negative.

Since +3 x –4 = “add” 3 groups of –4

Then -3 x +4 = “take away” 3 groups of +4

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Remember that any equal number of - and + integers equals 0 (zero)

= 0

________________________________________________

Start at zero… then

-3 x +4 = “take away” 3 groups of +4

When we ‘take away’ 3 groups of positive 4 we are left with -12

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And now… Why is a negative times a negative = a positive?

Start at zero…

=0

–3 x –4 = “take away” 3 groups of -4

When we ‘take away’ 3 groups of negative 4 we are left with +12

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