We know how to multiply and divide whole numbers when they are all positive. Now let's look at what happens when negative integers are included in questions. The product is the answer when two numbers are multiplied together.
Your knowledge of times tables will really help you through this chapter, we just need to know what to do when one or more of the numbers we are multiplying or dividing are negative.
We just need to learn a couple of extra rules to our existing knowledge, to account for negatives.
In both of the above cases, we can take out a factor of -1, giving us -1\times4\times5=-20, and \\-1\times16\times10 respectively.
We can see that it does not matter which term is negative when we are finding the product; the product of a negative number and a positive number will always be negative. But what if both numbers are negative?
In these cases, we can think of it as taking out two factors of -1.
So (-4)\times(-5)=(-1\times-1)\times(4\times5)=1\times20= 20.
Use the following applet to explore multiplication of integers.
Select two integers to multiply by using the sliders to change the value and the check boxes to change the sign.
Blue tiles represent positive integers
Red tiles represent negative integers
The product is shown as an array
The product of two positive integers or two negative integers will result in a positive integer. The product of one positive and one negative integer will result in a negative integer.
Evaluate 5 \times (-9).
Evaluate (-6)^{3}.
As division is just the opposite of multiplication, the rules for dividing by integers are the same as the rules for multiplying integers.
To account for negatives, we can follow the same rules as we did when multiplying with integers.
Again, in both of the above cases, we can take out a negative factor of -1, giving us \dfrac{1}{-1}\times \dfrac{20}{5}=-4, and \dfrac{-1}{1}\times \dfrac{160}{10}=-16 respectively.
As before, we can see that it does not matter which term is negative when we are finding the quotient; the quotient of two numbers, when one is negative, will always be negative. But what if both numbers are negative?
Like with multiplying two negatives, we can think of it as taking out two factors of -1.
So (-20)\div(-5) = \dfrac{-1}{-1}\times\dfrac{20}{5}=1\times4=4.
Evaluate -20 \div 4.