Section 1.5 Subtracting Integers.

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Presentation transcript:

Section 1.5 Subtracting Integers

Objectives Subtract integers. (NS 1.2) Simplify expressions and use properties of rational numbers to justify the process used. (AF 1.3)

Subtracting Integers ADD the OPPOSITE To subtract an integer b from an integer a, add the opposite of b to a. a – b = a + (-b) 3 – 4 = 3 + (-4) = -1 In Words In Algebra In Arithmetic

Symbols and Directions + Addition Subtraction - Walk Forward Turn Around Always Start At 0 -4 -3 -2 -1 1 2 3 4

Symbols and Directions + Positive Negative - Walk Forward Walk Backwards Always Start At 0 -4 -3 -2 -1 1 2 3 4

Subtracting Integers On a Number Line ( ) + + 1 4 - 3 = 1 4 - 3 + = Add the opposite Walk Forward 4 Spaces Walk Backwards 3 Spaces -4 -3 -2 -1 1 2 3 4

Subtracting Integers ( ) 1 - 3 - 4 -1 - 3 = -4 - + = Add the opposite Walk Backwards 1 Space Walk Backwards 3 Spaces -4 -3 -2 -1 1 2 3 4

Subtracting Integers Add the opposite + + ( ) 1 3 4 1- (-3) = 4 + = Walk Forwards 3 Spaces Walk Forward 1 Space -4 -3 -2 -1 1 2 3 4

Two negatives make a happy face ( ) 2 4 - - - - Smile + 6 =

Making Zero Pairs Positives + Negatives - Zero Pair

Finding the Difference Using Markers + ( ) 5 - 7 5 - 7 + Add the opposite 2 Negatives Zero Pairs - 2 =

Finding the Difference Using Markers ( ) - -5 - 7 5 - 7 + Add the opposite 12 Negatives 1 2 = -

Finding the Difference Using Markers + ( ) 5 - (-7) 5 7 + + Happy Face 12 Positives + 1 2 =

Application The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool? 10 – (–12) Subtract the depth of the pool from the height of the high dive. 10 + 12 Add the opposite of –12. 22 It is 22 feet from the diving board to the bottom of the pool.

Now You Try Number Line or Markers -17 4 -4 10 31 6 -13 -10 – 7 Hint: rewrite as adding the opposite  -17 -10 – 7 -5 – (-5) 7 – 9 – (-12) -5 – 10 – (-2) 19 – 15 5 – 9 23 – (-8) 2 – (-4) 4 -4 10 31 6 -13

Lesson Quiz Subtract. 1. –6 – (–4) 3. 4 – (–5) 2. –3 – 3 –2 3. 4 – (–5) 9 2. –3 – 3 –6 Evaluate each expression for the given value of the variable. 4. 9 – s for s = –5 14 5. –4 – w + 5 for w = 21 –20 6. Loretta is flying in an airplane and rises an additional 20 feet. Then she descends 190 feet toward the ground. How far below her original height did Loretta go? 170 feet