3-12 Solving Equations Containing Fractions Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Warm Up Multiply or divide 7 9 3 6 7 18 1. · 9 8 5 6 27 20 7 or 1 2. ÷ 2 77 5 or 15 1 5 3. 2 · 7 1 2 1 4 4. 2 ÷ 1 2

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Warm Up – one step equations Solve. 1. x – 16 = 8 2. 7a = 35 3. 4. y + 21 = 31 x = 24 a = 5 x 12 x = 132 = 11 y = 10

Dividing Fractions and Mixed Numbers Course 2 3-11 Dividing Fractions and Mixed Numbers Find the reciprocal 7 9 5 6 3 6 9 8 1 4 7 1 2 1 5 2 3

Course 2 3-12 Solving Equations Containing Fractions Learning Objective: to solve one-step equations that contain fractions.

Additional Example 2A: Solving Equations by Multiplying Course 2 3-12 Solving Equations Containing Fractions Additional Example 2A: Solving Equations by Multiplying Solve. Write the answer in simplest terms. 3 8 1 4 x = 3 8 = 1 4 x 3 8 Multiply by the reciprocal of . 2 3 8 . 8 3 1 4 . 8 3 x = Then simplify. 1 2 3 x = Caution! To undo multiplying by 3 8 3 8 , you can divide by 8 3 or multiply by its reciprocal, .

Additional Example 2B: Solving Equations by Multiplying Course 2 3-12 Solving Equations Containing Fractions Additional Example 2B: Solving Equations by Multiplying Solve. Write the answer in simplest terms. 8 9 4x = 8 9 4x = Multiply by the reciprocal of 4. 2 . 1 4 8 9 . 1 4 4 x = Then simplify. 1 2 9 x =

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 2A Solve. Write the answer in simplest terms. 3 4 1 2 x = 3 4 = 1 2 x 3 4 Multiply by the reciprocal of . 2 3 4 . 4 3 1 2 . 4 3 x = Then simplify. 1 2 3 x =

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 2B Solve. Write the answer in simplest terms. 6 7 3x = 6 7 3x = Multiply by the reciprocal of 3. 2 . 1 3 6 7 . 1 3 3 x = Then simplify. 1 2 7 x =

Additional Example 3: Physical Science Application Course 2 3-12 Solving Equations Containing Fractions Additional Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4 ounces of copper, what is the total weight of the sample? 3 4 1 5 Let w represent the total weight of the sample. 3 4 w = 4 1 5 Write an equation. 3 4 w · 4 3 1 5 4 3 = 4 · Multiply by the reciprocal of 3 4 · 7 1 5 Write 4 as an improper w = 21 5 4 3 · fraction. 1 28 5 w = or 5 3 5 Then simplify. 3 5 The sample weighs 5 ounces.

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 3 The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of copper, what is the total weight of the sample? 1 4 1 3 Let w represent the total weight of the sample. 1 4 w = 5 3 Write an equation. 1 4 w · 4 1 1 3 4 1 = 5 · Multiply by the reciprocal of 1 4 · 1 3 Write 5 as an improper w = 16 3 4 1 · fraction. 64 3 w = or 21 1 3 Then simplify. 1 3 The sample weighs 21 ounces.

Insert Lesson Title Here Course 2 3-12 Solving Equations Containing Fractions Insert Lesson Title Here Lesson Quiz Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8 x – = 1 7 16 19 32 5 32 y + = x 4 3 7 12 7 5 or 1 = 3 4 1 3 16 9 7 or 1 x = 1 5. Over the course of a week, Marissa ate some apples from a basket on the table. She left 20 apples in the basket. This was five-eights the number of apples her mother had picked earlier in the week. How many apples did her mother pick? 32