96.GARDENING The illustration shows the depths at which the bottoms of various types of flower bulbs should be planted. (The symbol represents inches.)

a.At what depth should a tulip bulb be planted?

b.How much deeper are hyacinth bulbs planted than gladiolus bulbs?

c.Which bulb must be planted the deepest? How deep?

Ground level

Anemone

–1"

Sparaxis

–2"

Ranunculus

–3"

Narcissus

–4"

Freesia

–5"

Gladiolus

–6"

Hyacinth

–7" Tulip

–8"

Daffodil

–9"

–10"

Planting –11" Chart

WRITING

97.Explain the concept of the opposite of a number.

98.What real-life situation do you think gave rise to the concept of a negative number?

99.Explain why the absolute value of a number is never negative.

100.Give an example of the use of the number line that you have seen in another course.

101.DIVING Divers use the terms positive buoyancy, neutral buoyancy, and negative buoyancy as shown. What do you think each of these terms means?

Positive buoyancy

Neutral buoyancy

Negative buoyancy

102.GEOGRAPHY Much of the Netherlands is lowlying, with half of the country below sea level. Explain why it is not under water.

103.Suppose integer A is greater than integer B. Is the opposite of integer A greater than integer B? Explain why or why not. Use an example.

104.Explain why 11 is less than 10.

REVIEW

105.Round 23,456 to the nearest hundred.

106.Evaluate: 19 2 3

107.Subtract 2,081 from 2,842.

108.Divide 346 by 15.

109.Give the name of the property shown below: (13 2) 5 13 (2 5)

110.Write four times five using three different symbols.

SOUTH DAKOTA

? 7:32 A.M.

Spearfish

49° increase

7:30 A.M.

Self Check 1

Add:

a.7 ( 2)

b.25 ( 48)

c.325 ( 169)

Now Try Problems 19, 23, and 27

The Language of Mathematics When writing additions that involve integers, write negative integers within parentheses to separate the negative sign from the plus symbol .

Strategy We will use the rule for adding two integers that have the same sign.

WHY In each case, we are asked to add two negative integers.

Solution

a.To add two negative integers, we add the absolute values of the integers and make the final answer negative. Since 0 3 0 3 and 0 5 0 5, we have

Success Tip Calculations that you cannot perform in your head should be shown outside the steps of your solution.

The Language of Mathematics Two negative integers, as well as two positive integers, are said to have like signs.

2 Add two integers that have different signs.

To find 4 ( 3) on a number line, we begin at 0 and draw an arrow 4 units long that points to the right. This represents positive 4. From the tip of that arrow, we draw a second arrow, 3 units long, that points to the left. It represents 3. Since we end up at 1, it follows that 4 ( 3) 1.

Begin

−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8

In terms of money, if you won $4 and then lost $3 ( 3), overall, you would have $1 left.

To find 4 3 on a number line, we begin at 0 and draw an arrow 4 units long that points to the left. It represents 4. From the tip of that arrow, we draw a second

Adding Two Integers That Have Different (Unlike) Signs

To add a positive integer and a negative integer, subtract the smaller absolute value from the larger.

1.If the positive integer has the larger absolute value, the final answer is positive.

2.If the negative integer has the larger absolute value, make the final answer negative.

EXAMPLE 2 Add: 5 ( 7)

Strategy We will use the rule for adding two integers that have different signs.

WHY The addend 5 is positive and the addend 7 is negative.

Solution

The Language of Mathematics A positive integer and a negative integer are said to have unlike signs.

Self Check 2

Add: 6 ( 9)

Now Try Problem 31