Algebra Demystified 2nd Ed

78 algebra De mystif ieD

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 4

To understand why some of the rules for negative number arithmetic are true,

we will consider the readings on a thermometer. A reading of −10° means the

temperature is 10° below 0 °, and that the temperature would need to increase

10 ° to reach 0°. A reading of 10° means the temperature would need to decrease

10 ° to reach 0°, so the sign in front of the number tells us on which side of 0

the number lies.

Suppose the temperature is −15°. If the temperature rises by 10°, the tem-

perature, –5°, is still 5 ° below 0°.

Increase 10° This shows that –15 + 10 = –5.

–25° –20° –15° –10° –5° 0 ° 5 ° 10 ° 15 ° 20 ° 25 °

FIGURE 4-1

FIGURE 4-2

–25° –20°

Increase 20°

–15° –10° –5° 0 ° 5 ° 10 ° 15 ° 20 ° 25 °

This shows that –15 + 20 = 5.

The Sum of a Positive Number and a Negative Number

From these examples, we see that the sum of a negative number and a positive

number might be positive or might be negative, depending on whether the

positive number is large enough. When adding a positive number to a negative

number (or a negative number to a positive number), we take the difference of

the numbers. The sum is positive if the “larger” number is positive. The sum is

negative if the sign of the “larger” number is negative.

EXAMPLES

Find the sum.

−+= 82 30 ____.

The difference of 82 and 30 is 52. Because 82 is larger than 30, we use the

sign on –82 for the sum: −+=− 82 30 52.

−+ 125 75 = ____.

If the temperature increases by 20°, then the temperature is 5° above 0°.

EXAMPLES

Find the sum.