Two Simple Rules for Multiplying & Dividing Integers  

When you see the words algebra, integers, or signed numbers, don’t panic. Mathematics is a wonderful subject that rewards you every time you use the rules. When you follow the steps accurately, you always arrive at the correct answer.

So, don’t be afraid of algebra.

Here are two rules to make multiplying and dividing integers (signed numbers) a breeze.

An integer = a whole number (not a fractional number) that can be positive (+), negative (-) or zero.

Multiplying or dividing two integers

Rule #1     

If the signs are the same, the answer will be a positive number. In other words, if you have two positive numbers, the answer is positive; and, if you have two negative numbers, the answer is positive.

          -6 x -8 = +48                           -63 ÷ -7 = +9

          -127 x -82 = +10 414               -180 ÷ -12 = +15

          +15 x + 3 = +45                       -12 ÷ -4 = +3

 

Rule #2

If the signs are different, the answer will be a negative number. In other words, if you have one negative number and one positive number (in either order), the answer is negative.

          -7 x 4 =-28                               -56 ÷ +8 = -7

          9 x -3 =-27                               +90 ÷ -10 = -9

          436 x -5 =-2180                       -1302 ÷ +42 = -31

 

Multiplying more than two integers

What if you are trying to do more than two integers at once?

You can simply multiply two at a time until you are done. For many students, that is the easiest and safest way. However, you can also look at the following.

If all the signs are positive the answer will be positive.

                   +6 x +3 x +4 = +72

If all the signs are negative, the answer’s sign depends on the number of integers.

A.      If you have an odd number of integers, the answer will be negative.

                   -3 x - 7 x -5 = -105

                   -20 x -3 x -6 x -2 x -4 = -2880

B.      If you have an even number of integers, the answer will be positive.

                   -3 x -7 x -5 x -9 = +945

                   -8 x -2 x -1 x -5 x -6 x -4 = +1920

When you have mixed signs, simply work from left to right or combine the signs. In other words, collect the negatives and positives together and follow the rules above.

-8 x +3 x -6 x + 2 x -5 = ?

You have three negative numbers, -8 x -6 x -5 = -240

You have two positive numbers, +3 x +2 = +6

-240 x +6 = -1440

 

What should you do to improve?

Play!

Set yourself some challenges with lists of questions and play with them. The more you access mathematics, the easier the concepts, rules, and procedures become. With just a little effort, you can make a game of it, and we all learn better when we are having fun.

 

 

This week’s video – Multiplying & Dividing Integers