Warm Up Solve. 1. x – 16 = a = y + 21 = 31 x 12 = 11 Course Solving Equations Containing Fractions

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

Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure 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. Course Solving Equations Containing Fractions

Course 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.

Solve. Write the answer in simplest form. Additional Example 1A: Solving Equations by Adding or Subtracting A. x – 3737 = 5757 x – 3737 = = Add to isolate x. x= 8787 = Simplify. Course Solving Equations Containing Fractions

Solve. Write the answer in simplest form. Additional Example 1B: Solving Equations by Adding or Subtracting B y = y = y – 3434 = 1818 – 3434 Subtract to isolate y. y = 1818 – 6868 y =– 5858 Find a common denominator. Subtract. You can also isolate the variable y by adding the opposite of Helpful Hint 3434, – 3434, to both sides. Course Solving Equations Containing Fractions

Solve. Write the answer in simplest form. Additional Example 1C: Solving Equations by Adding or Subtracting C t = – t =– 3838 = t– 9 24 – t= – Subtract to isolate t. Find a common denominator. Subtract. Course Solving Equations Containing Fractions t –= – 3838 –

Solve. Write the answer in simplest form. Try This: Example 1A A. x – 3838 = 7878 x – 3838 = = Add to isolate x. x = 10 8 = Simplify. Course Solving Equations Containing Fractions

Solve. Write the answer in simplest form. Try This: Example 1B B y = y = y – = – 3838 Subtract to isolate y y = – 3838 y =– 1818 Find a common denominator. Subtract. Course Solving Equations Containing Fractions

Solve. Write the answer in simplest form. Try This: Example 1C C t = – t =– 2727 Subtract to isolate t. Find a common denominator. Subtract. Course Solving Equations Containing Fractions t –= – 2727 – t = – – t= – 7 14 Simplify. t= – 1 2

Solve. Write the answer in simplest terms. Additional Example 2A: Solving Equations by Multiplying A x = x= =x 2323 Multiply by the reciprocal of Then simplify = 1414 x = To undo multiplying by Remember! 3838, you can divide by 3838 or multiply by its reciprocal, Course Solving Equations Containing Fractions

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

Solve. Write the answer in simplest terms. Try This: Example 2A A x = x= =x 2323 Multiply by the reciprocal of Then simplify = 1212 x = Course Solving Equations Containing Fractions

Try This: Example 2B B. 3x = x= x = x = 3 Multiply by the reciprocal of 3. Then simplify. Solve. Write the answer in simplest terms. Course Solving Equations Containing Fractions

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? Additional Example 3: Physical Science Application Let w represent the total weight of the sample w = w · 4343 = · 4343 w = 21 5 · w = 28 5 or Write an equation. Multiply by the reciprocal of 3434 · Write as an improper fraction. Then simplify. The sample weighs ounces. Course Solving Equations Containing Fractions

The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of zinc, what is the total weight of the sample? Try This: Example Let w represent the total weight of the sample w = w · 4141 = · 4141 w = 16 3 · 4141 w = 64 3 or Write an equation. Multiply by the reciprocal of 1414 · Write as an improper fraction. Then simplify. The sample weighs ounces. Course Solving Equations Containing Fractions

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