42 Part 1: The World of Numbers
To subtract signed numbers:- Leave the first number as is.
- Change to addition.
- Change the second number to its opposite.
- Add, following the rules for addition.
CHECK POINT
Complete each subtraction by adding the opposite.- -17 – 4
- 39 – 24
- 26 – -12
24. -83 – 37
25. -48 – -32
Multiplying and Dividing Signed Numbers
Because multiplication is a shortcut for repeated addition, it’s fair to ask if you can use some of
the addition rules to help with multiplication of signed numbers, and because division is the
opposite or undoing of multiplication, you’d certainly expect to be able to apply some of the
same rules about signs. Let’s look at multiplication first, and then you’ll see that there’s very
little more to say about division.
Multiplication is really repeated addition. 5 v 12 means “add 5 twelves together” (or 12 fives, if
you prefer). 5 v 12 = 12 + 12 + 12 + 12 + 12, and adding positive numbers gives you a positive
number. 5 v 12 = 60. Nothing new there.
What if you multiply a positive number by a negative number? What is 3 v -4? It means “add 3
copies of the number -4” or “take 3 losses of 4 each.” That’s -4 + -4 + -4, and adding negative
numbers gives you a negative. 3 v -4 = -12. If you’re wondering what to do with a negative times
a positive, like -5 v 7, remember that multiplication is commutative. -5 v 7 = 7 v -5 = -35, and
no new rules are necessary.
When you multiply a negative number by a negative number, remember that the negative sign
means “the opposite of.” This means -5 v 7 is the opposite of 5 v 7, or the opposite of 35, or -35.
If both numbers are negative, as in -2 v -4, you’re asking for the opposite of 2 v -4. You know
that 2 v -4 is -8, and the opposite of that is 8. -2 v -4 = 8. A negative multiplied by a negative is
a positive.