Basic Mathematics for College Students

196 Chapter 2 The Integers

SECTION 2.3 Subtracting Integers

The rule for subtraction is helpful when

subtracting signed numbers.

To subtract two integers, add the first integer

to the opposite of the integer to be subtracted.

Subtracting is the same as adding the opposite.

After rewriting a subtraction as addition of the

opposite, use one of the rules for the addition

of signed numbers discussed in Section 2.2 to

find the result.

Subtract:

Add the opposite of 5, which is 5.

 4 ( 7 ) 4  7  3 Add the opposite of 7, which is 7.

 3  5  3 ( 5 ) 8

DEFINITIONS AND CONCEPTS EXAMPLES

Subtract:

Use the rule for adding two integers

with the same sign.

3 ( 5 ) 3  5  8

3 (5)

Expressions can involve repeated subtraction

or combinations of subtraction and addition.To

evaluate them, we use the order of operations

rulediscussed in Section 1.9.

Evaluate:

Within the parentheses,

add the opposite of 15,

which is 15.

Within the brackets, add 6 and

15.

Add the opposite of 21, which is 21.

Use the rule for adding integers that

have different signs.

 22

 43  21

 43 [21]

 43 ( 6  15 ) 43 [ 6 (15)]

43 ( 6 15)

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.

GEOGRAPHY The highest point in the United States is Mt. McKinley

at 20,230 feet. The lowest point is feet at Death Valley, California.

Find the range between the highest and lowest points.

Add the opposite of 282, which is 282.

Do the addition.

The range between the highest point and lowest point in the United

States is 20,602 feet.

20,602

20,320 282

Range20,320(282)

 282

To find the change in a quantity, we subtract

the earlier valuefrom the later value.

Change later value earlier value

SUBMARINES A submarine was traveling at a depth of 165 feet below

sea level. The captain ordered it to a new position of only 8 feet below

the surface. Find the change in the depth of the submarine.

We can represent 165 feet below sea level as feet and 8 feet below

the surface as feet.

Subtract the earlier depth from

the later depth.

Add the opposite of 165, which is 165.

Use the rule for adding integers that

have different signs.

The change in the depth of the submarine was 157 feet.

 157

 8  165

Change of depth 8 (165)

 8

 165

Be careful when translating the instruction to

subtract one number fromanother number.

Subtract from.

 9 (6) The number to be subtracted is 6.

 6  9

... the opposite

Add...





Check using addition: 8(5) 3