U2.L4

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1 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. Subtracting Integers 1.6 LESSON

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2 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) 4 0 1 2 3 6 5 –1 4 0 1 2 3 6 5 –1 Subtracting Integers 1.6 LESSON

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3 Subtracting Integers Words To subtract an integer, add its opposite. Numbers 3 – 7 = 3 + (–7) = –4 Algebra a – b = a + (– b ) Subtracting Integers 1.6 LESSON

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4 Subtracting Integers EXAMPLE 1 4 – 10 = To subtract 10 , add its opposite, –10 . = –6 4 + ( – 10 ) Add 4 and –10 . Subtracting Integers 1.6 LESSON

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5 Subtracting Integers EXAMPLE 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 . Subtracting Integers 1.6 LESSON

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6 Subtracting Integers EXAMPLE 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 . Subtracting Integers 1.6 LESSON

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7 Evaluating Variable Expressions EXAMPLE 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 Subtracting Integers 1.6 LESSON

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8 Evaluating Variable Expressions EXAMPLE 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 Subtracting Integers 1.6 LESSON

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9 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. Subtracting Integers 1.6 LESSON

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10 Evaluating Change EXAMPLE 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 in elevation = Elevation in 2002 – Elevation in 1962 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 ) Subtracting Integers 1.6 LESSON