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5-5 6th grade math Solving Addition and Subtraction Equations Objectives • To solve equations involving fractions and mixed numbers. Why? To be able to solve more complicated equations. .. The stepping stones to solving Algebra problems. California State Standards • AF 1.1 : Write and solve one-step linear equations in one variable. • NS 2.0 : Calculate and solve problems involving addition, subtraction, … • NS 2.1: Solve problems involving addition, subtraction, … of positive fractions and explain why a particular operation was used for a given situation. Vocabulary • Equations – A number sentence stating that two expressions are equal. • X – 26 = 85 • W + 41.8 = 55.9 * 4x = 16 * v/6 = 3.6 • Variables – A letter used to stand for a number in an expression or equation. • 45 + x = 67 • Inverse Operations – Two operations with an opposite effect. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. • 256x = 1024 256 ÷ 256 x = 1024 ÷ 256 x=4 How to Solve Addition Equations ½+x=¾ 1. Undo the addition by subtracting (½) from both sides 2. Write the fractions with their LCD 3. Solve 4. Simplify, if possible ½+x=¾ 1. ½ - ½ + x = ¾ - ½ 2. X = ¾ - 2/4 3. X = 1/4 How to Solve Subtraction Equations m – 3 = 18 3/5 1. Undo the subtraction by addition (3 2/3) from both sides 2. Write the fractions with their LCD 3. Solve 4. Simplify, if possible m – 3 = 18 3/5 1. m – 3 + 3 = 18 3/5 + 3 2. M = 18 9 15 3 10 + 15 21 19/15 = 22 4/15 Try It! 1. n + 3/5 = 1 1. n = 2/5 2. 2 = x + 2 1/18 2. x = 5/18 3. a – 5/6 = 1/16 3. a = 43/48 4. y + 2 1/18 = 3 ¼ 4. y = 1 7/36 Here’s How It Works… 1. n + 3/5 = 1 1) n + 3/5 – 3/5 = 1 – 3/5 5/5 – 3/5 = 2/5 2. 2 = x + 2 1/18 2) x + 2 1/18 – 2 1/18= 2 - 2 1/18 x = 2 6/18 - 2 1/18 x = 5/18 3) a – 5/6 = 1/16 3) a – 5/6 + 5/6 = 1/16 + 5/6 a = 3/48 + 40/48 a = 43/48 4) y + 2 1/18 = 3 ¼ 4) y + 2 1/18 – 2 1/18 = 3 ¼ - 1/18 y = 3 9/36 – 2 2/36 y = 1 7/36 Objectives Review • To solve equations involving fractions and mixed numbers. • Why? You can solve more complicated equations. .. These are the stepping stones to solving Algebra problems (your future career in education). Independent Practice • Complete problems 6-11 • Copy original problem first. • Show ALL work! • If time, complete Mixed Review: 12-18. • If still more time, work on Accelerated Math