2 Chapter Chapter 2 Integers and Introduction to Variables.

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Presentation transcript:

2 Chapter Chapter 2 Integers and Introduction to Variables

Section 2.3 Adding Integers

Objective A Add Integers.

Adding Integers Adding Integers Adding integers can be visualized by using a number line. A positive number can be represented on the number line by an arrow of appropriate length pointing to the right, and a negative number by an arrow of appropriate length pointing to the left. Objective A 4

Example Example Add using a number line. −2 + (−3) end start −2 + (−3) = −5 Objective A 5

Adding Signed Numbers Adding Integers Adding Two Numbers with the Same Sign Step 1: Add their absolute values. Step 2: Use their common sign as the sign of the sum. Objective A 6

Example Example Add: −14 + (−9) Step 1: Step 2: Therefore the common sign is negative, so the sum is negative. Objective A 7

Adding Signed Numbers Different Signs Adding Two Numbers with Different Sign Step 1: Find the larger absolute value minus the smaller absolute value. Step 2: Use the sign of the number with the larger absolute value as the sign of the sum. Objective A 8

Example Example Add: −11 + 18 Step 1: Step 2: 18 has the larger absolute value and its sign is an understood + so the sum is positive. Objective A −11 + 18 = +7 or 7 9

Example Example Add: 8 + (−13) Step 1: Step 2: −13 has the larger absolute value and its sign is − so the sum is negative. Objective A 8 + (−13) = −5 10

Opposites If a is a number, then −a is its opposite. Also, Objective A 11

Example Example Add: 5 + (−7) + 3 5 + (−7) + 3 = −2 + 3 = 1 Objective A 12

Evaluate an Algebraic Expression by Adding. Objective B Evaluate an Algebraic Expression by Adding.

Evaluating Expressions Example Evaluate 3x + y for x = 2 and y = – 6. Replace x with 2 and y with –6 in 3x + y. 3x + y = 3 · 2 + (–6) = 6 + (–6) Objective B = 0

Solve Problems by Adding Integers. Objective C Solve Problems by Adding Integers.

Example Example The temperature at 4 p.m. on February 2 was −10° Celsius. By 11 p.m. the temperature had risen 12 degrees. Find the temperature at 11 p.m. = 2 Objective A The temperature at 11 p.m. is 2°Celsius. 16