Basic Mathematics for College Students

160 Chapter 2 The Integers

3 Solve application problems by subtracting integers.

Subtraction finds the differencebetween two numbers. When we find the difference

between the maximum value and the minimum value of a collection of measurements,

we are finding the rangeof the values.

EXAMPLE (^6) The Windy City The record high
temperature for Chicago, Illinois, is 104ºF. The record low is

. Find the temperature range for these extremes. (Source:
The World Almanac and Book of Facts,2009)

StrategyWe will subtract the lowest temperature

from the highest temperature (104ºF).

WHYThe rangeof a collection of data indicates the spread of the data. It is the

difference between the largest and smallest values.

SolutionWe apply the rule for subtraction and add the opposite of.

104º is the highest temperature and 27º is the lowest.

The temperature range for these extremes is 131ºF.

 131

104 (27) 104  27

 27

(27°F)

27°F

Self Check 6

THE GATEWAY CITYThe record

high temperature for St. Louis,

Missouri, is 107ºF. The record low

temperature is. Find the

temperature range for these

extremes. (Source:The World

Almanac and Book of Facts,

2009)

Now TryProblem 101

18°F

Springfield

Chicago

ILLINOIS

Things are constantly changing in our daily lives. The amount of money we have

in the bank, the price of gasoline, and our ages are examples. In mathematics, the

operation of subtraction is used to measure change. To find the changein a quantity,

we subtract the earlier value from the later value.

Change later value earlier value

The five-step problem-solving strategy introduced in Section 1.6 can be used to

solve more complicated application problems.

WHYIt is easy to make an error when subtracting signed numbers. We will

probably be more accurate if we write each subtraction as addition of the opposite.

SolutionWe apply the rule for subtraction twice. Then we will add the positives

and the negatives separately, and add those results. (By the commutative and

associative properties of addition, we can add the integers in any order.)

Simplify: (6) 6. Add the opposite of 4,

which is 4, and add the opposite of 51,

which is 51.

Reorder the integers. Then group the positives

together and group the negatives together.

Add the positives within the parentheses.

Add the negatives within the brackets.

 35 Use the rule for adding integers that have different signs.

 57 (22)

(651)[(18)(4)]

 6 (18)(4) 51

(6)(18) 4 (51)

EXAMPLE 7

Water Management On Monday,

the water level in a city storage tank

was 16 feet above normal. By Friday,

the level had fallen to a mark 14 feet

below normal. Find the change in the

water level from Monday to Friday.

Monday: 16 ft

Normal

Friday: –14 ft