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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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