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

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

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Problem of the Day Write 15 positive integers less than 1,000 with digits that, when added together, total 4. 4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 310, 400

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

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure. 3 4 1 4 The remaining of 18-karat gold is made up of one or more different metals, such as silver, copper, or zinc. The color of gold varies, depending on the type and amount of each metal added to the pure gold.

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Equations can help you determine the amounts of metals in different kinds of gold. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to isolate the variable on one side of the equation.

Additional Example 1A: Solving Equations by Adding or Subtracting Course 2 3-12 Solving Equations Containing Fractions Additional Example 1A: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 3 7 5 7 x – = x – 3 7 = 5 x – 3 7 + = 5 Add to isolate x. x = 8 7 1 Simplify.

Additional Example 1B: Solving Equations by Adding or Subtracting Course 2 3-12 Solving Equations Containing Fractions Additional Example 1B: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 5 12 3 8 + t = 5 12 + t = 3 8 5 12 + t – = 3 8 Subtract to isolate t. = t 9 24 – 10 Find a common denominator. t = 1 24 – Subtract.

Additional Example 1C: Solving Equations by Adding or Subtracting Course 2 3-12 Solving Equations Containing Fractions Additional Example 1C: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 4 9 -1 2 + r = 4 9 r -1 2 + = 4 9 r 4 9 -1 2 4 9 + – = – Subtract to isolate r. r -9 18 8 18 = Find a common denominator. – 17 18 r = – Subtract. You can also isolate the variable r by adding the opposite of Helpful Hint 4 9 , – 4 9 , to both sides.

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 1A Solve. Write the answer in simplest form. 3 8 7 8 x – = x – 3 8 = 7 x – 3 8 + = 7 Add to isolate x. x = 10 8 = 1 1 4 Simplify.

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 1B Solve. Write the answer in simplest form. 3 8 1 4 + y = 3 8 + y = 1 4 3 8 1 4 + y – = Subtract to isolate y. 2 8 y = – 3 Find a common denominator. y = – 1 8 Subtract.

Solving Equations Containing Fractions Course 2 3-12 Solving Equations Containing Fractions Check It Out: Example 1C Solve. Write the answer in simplest form. 3 14 2 7 + t = – 3 14 + t = – 2 7 3 14 + t – = 2 7 Subtract to isolate t. t = – – 3 14 4 Find a common denominator. t = – 7 14 Subtract. t = – 1 2 Simplify.

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