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Solving One-Step Equations with Fractions

Learn how to solve one-step equations that contain fractions. Practice solving equations with fractions using addition, subtraction, and multiplication. Includes quizzes and real-world applications.

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Solving One-Step Equations with Fractions

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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

  3. 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

  4. Learn to solve one-step equations that contain fractions.

  5. 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 ismade 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.

  6. 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.

  7. 3 7 5 7 x – = 3 7 5 7 3 7 3 7 + x – = + 1 7 8 7 = x = 1 Additional Example 1A: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 3 7 5 7 x – = Use the Addition Property of Equality. Add.

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

  9. 3 8 7 8 x – = 3 8 7 8 3 8 3 8 + x – = + 1 4 10 8 = 1 x = Check It Out: Example 1A Solve. Write the answer in simplest form. 3 8 7 8 = x – Use the Addition Property of Equality. Simplify.

  10. 2 7 3 14 + = – t 3 14 3 14 3 14 2 7 + – = – – t 3 14 4 14 – t = – 7 14 1 2 – – t t = = Check It Out: Example 1B Solve. Write the answer in simplest form. 3 14 2 7 – + t = Use the Subtraction Property of Equality. Find a common denominator. Subtract. Simplify.

  11. 3 8 1 4 = = x Additional Example 2A: Solving Equations by Multiplying Solve. Write the answer in simplest terms. 3 8 1 4 x = 3 8 Multiply by the reciprocal of . 2 . 3 8 1 4 8 3 . 8 3 x = Then simplify. 1 2 3 x = Caution! 3 8 To undo multiplying by 3 8 , you can divide by 8 3 or multiply by its reciprocal, .

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

  13. 3 4 1 2 = = x Check It Out: Example 2A Solve. Write the answer in simplest terms. 3 4 1 2 x = 3 4 Multiply by the reciprocal of . 2 . 3 4 1 2 4 3 . 4 3 x = Then simplify. 1 2 3 x =

  14. Check It Out: Example 2B Solve. Write the answer in simplest terms. 6 7 3x = 6 7 Multiply by the reciprocal of 3. 3x = 2 1 3 . 6 7 1 3 . x = 3 Then simplify. 1 2 7 x =

  15. 1 5 3 4 w = 4 Additional Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4ounces of copper, what is the total weight of the sample? 3 4 1 5 Let w represent the total weight of the sample. Write an equation. 3 4 4 3 4 3 1 5 w · · = 4 3 4 Multiply by the reciprocal of · 1 5 7 Write 4 as an improper 21 5 4 3 w = · fraction. 1 28 5 3 5 w = or 5 Then simplify. 3 5 The sample weighs 5 ounces.

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

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. 12 7 5 7 or 1 16 9 7 9 or 1 Lesson Quiz Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8 1 x – = 5 32 7 16 19 32 y + = x 4 3 7 = 1 3 3 4 x = 1 5. During the week, Marissa ate some apples from a basket. She left 20 apples. This was five-eights the number of apples she had bought earlier in the week. How many apples did she buy? 32

  19. Lesson Quiz for Student Response Systems 1. Solve. Write your answer in simplest form. x– = A. x =C.x = or 1 B.x = D.x = 5 7 3 7 8 7 1 7 5 8 2 7 7 8

  20. Lesson Quiz for Student Response Systems 2. Solve. Write your answer in simplest form. a+ = A. a =C.a = or B.a = D.a = 5 14 13 28 9 14 18 28 23 28 1 14 3 28

  21. Lesson Quiz for Student Response Systems 3. Solve. Write your answer in simplest form. 3m = A. m =C.m = or 1 B.m = D.m = 2 5 6 5 1 5 3 5 5 6 2 15

  22. Lesson Quiz for Student Response Systems 4. Solve. Write your answer in simplest form. e = 1 A. e =C.e = 4 B.e = or 3 D.e = or 4 1 4 1 5 1 5 3 10 24 5 4 5 1 3 10 3

  23. Lesson Quiz for Student Response Systems 5. Harry made 18 bookmarks last week. This was nine-sixths the number of bookmarks that Ruth made. How many bookmarks did Ruth make? A. 12 bookmarks B. 11 bookmarks C. 10 bookmarks D. 9 bookmarks

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