Chapter 3: Order of Operations and Integers 41But what if things were reversed and you gained 3 yards and then lost 14 yards? That’s 3 + -14.
Start from 0 again. A gain of 3 moves you 3 to the right, but then the loss moves you back to the
left. You give up the 3 you had gained and keep moving left another 11 spaces. 3 + -14 = -11.A big gain overpowered a small loss, resulting in a gain, but a big loss overpowered a small
gain, leaving you with a loss. In mathematical terms, the number with the larger absolute value
dominates the addition and gives its sign to the result. The absolute value of the answer is the
difference between the absolute values of those two competing forces.
To add numbers with different signs:- Subtract the absolute values.
- Take the sign from the number with the larger absolute value.
-11-10-9-8-7 -6-5 -4 -3 1234567891011+3-2 -1 0-14CHECK POINT
Complete each addition problem. Use a number line to help.- -15 + 25
- 19+ -12
- -23 + 14
19. -58 + -22
20. 147 + -200
Subtracting Signed Numbers
There’s a simple rule for subtracting signed numbers: don’t. This doesn’t mean you can just
ignore those problems. Subtraction, as you saw in the last chapter, is the opposite, or undoing, of
addition, and learning a lot of new and separate rules for subtraction is effort you don’t need to
expend.
When you’re asked to subtract, add the opposite. Instead of 12 – 8, which you know equals 4,
think of 12 + -8, which also equals 4. Then when you’re asked to do -14 – 7, you can just think
of -14 + -7 and quickly arrive at -21. 6 – (-3) will become 6 + 3, which is clearly 9. This rule
is sometimes referred to as “keep, change, change” because you keep the first number as it is,
change to addition, and change the second number to its opposite.