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Scuba Diver. A scuba diver studying marine life is 4 feet below sea level. From that depth, the diver descends 72 feet to the ocean floor and then rises 61 feet. The diver rests there to avoid decompression illness. Where is the diver relative to sea level?

EXAMPLE 1

Find the sum –5 + (–3) using a number line.

Start at 0. Move 5 units to the left.

Then move 3 more units to the left.

ANSWER The final position is –8, so –5 + (–3) = –8.

SOLUTION

Adding Integers - Rules

1. Same sign: Add the absolute values and use the common sign.

2. Different Signs: Subtract the lesser absolute value from the greater absolute value and use the sign of the number with greater absolute value.

3. Opposites: The sum of a number and its opposite is 0.

8 + 12 = 20-6 + (-4) = -10

5 + (-8) = -3-11 + 13 = 2

7 + (-7) = 0

GUIDED PRACTICE for Examples 1 and 2

Use a number line (if needed) to find the sum.

1. –9 + (–5)

ANSWER –14

2. –7 + 4

ANSWER –3

3. 6 + (–13)

ANSWER –7

4. 12 + (–9)

ANSWER 3

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A scuba diver studying marine life is 4 feet below sea level. From that depth, the diver descends 72 feet to the ocean floor and then rises 61 feet. The diver rests there to avoid decompression illness. Where is the diver relative to sea level?

Solution?

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To answer the question about the position of the scuba diver, you can find the sum -4 + (-72) + 61.

Solution: -4 + (-72) + 61 = -76 + 61 (add -4 and -72.)

= -15 (add -76 and 61)

ANSWER: The diver is -15, so the diver is 15 feet below sea level.

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Eruptions have caused the volcano to grow. In 1962, the summit elevation of Kick-’em-Jenny was –235 meters. In 2002, the summit elevation was –182 meters. By how many meters did the elevation of the volcano change? You will use integer subtraction to answer this question.

Earth Science Kick-’em-Jenny is an underwater volcano in the Caribbean Sea.

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As you can see from the number lines below, the expression 5 – 4 and 5 + (–4) have the same value, 1.

These equivalent expressions suggest the following rule for subtracting integers.

5 – 4 5 + (–4)

40 1 2 3 65–1 40 1 2 3 65–1

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Subtracting Integers

Words To subtract an integer, add its opposite.

Numbers 3 – 7 = 3 + (–7) = –4

Algebra a – b = a + (–b)

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Subtracting IntegersEXAMPLE 1

4 – 10 = To subtract 10, add its opposite, –10.

= –6

4 + (–10)

Add 4 and –10.

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Subtracting IntegersEXAMPLE 1

7 – (–5) = To subtract –5, add its opposite, 5.

= 12

7 + 5

Add 7 and 5.

4 – 10 = To subtract 10, add its opposite, –10.

= –6

4 + (–10)

Add 4 and –10.

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Subtracting IntegersEXAMPLE 1

7 – (–5) = To subtract –5, add its opposite, 5.

= 12

7 + 5

Add 7 and 5.

4 – 10 = To subtract 10, add its opposite, –10.

= –6

4 + (–10)

Add 4 and –10.

–2 – (–9) = To subtract –9, add its opposite, 9.

= 7

–2 + 9

Add –2 and 9.

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Evaluating Variable ExpressionsEXAMPLE 2

x – (–40)

To subtract –40, add 40.

= 31

= –9 + 40

Add –9 and 40.

Evaluate the expression when x = –9.

x – (–40) = Substitute –9 for x.–9 – (–40)

SOLUTION

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Evaluating Variable ExpressionsEXAMPLE 2

7 – x

To subtract –9, add 9.

= 16

= 7 + 9

Add 7 and 9.

Evaluate the expression when x = –9.

7 – x = Substitute –9 for x.7 – (–9)

SOLUTION

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Evaluating Change You can use subtraction to find the change in a variable quantity such as elevation or temperature. Subtract the original value of the quantity from the value after the change.

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Evaluating ChangeEXAMPLE 3

By how many meters did the elevation of the volcano Kick-’em-Jenny change if the elevation in 1962 was –235 meters and –182 meters in 2002? To answer this question, you can subtract the elevation in 1962 from the elevation in 2002. Write a verbal model.

ANSWER

Change inelevation =

Elevation in2002

– Elevation in1962

The difference is 53, so the summit elevation of Kick-’em-Jenny increased by 53 meters from 1962 to 2002.

To subtract –235, add 235.

= 53

= –182 + 235

Add –182 and 235.

Substitute values.= –182 – (–235)

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