Solving algebraic eqn

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Solving algebraic eqn

  1. 1. Course 1 5-10 Solving Fraction Equations: Multiplication and Division5-10 Solving Fraction Equations: Multiplication and Division Course 1 Lesson PresentationLesson Presentation Problem of the DayProblem of the Day Warm UpWarm Up
  2. 2. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Warm Up Solve. 1. x – 5 = 17 2. 5x = 125 3. x + 12 = 86 4. 9x = 108 x = 22 x = 25 x = 74 x = 12
  3. 3. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Problem of the Day Stephen forgot his locker number, but he remembered that the sum of the digits is 11 and that the digits are all odd numbers. The locker numbers are from 1 to 120. What is Stephen’s locker number? 119
  4. 4. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions.
  5. 5. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Dividing by a number is the same as multiplying by its reciprocal. Remember!
  6. 6. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1A: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. j = 25 3 5 __ j ÷ = 25 ÷ 3 5 __ 3 5 __ 3 5 __ j • = 25 • 3 5 __ 5 3 __ 5 3 __ j = 25 • 5 1 • 3 _____ j = 25 • 5 3 __ j = , or 41 125 3 ___ 2 3 __ Divide both sides of the equation by . 3 5 __ Multiply by , the reciprocal of . 3 5 __5 3 __
  7. 7. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1B: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 7x = 2 5 __ 7x 1 __ 2 5 __ 1 7 __1 7 __ • = • x = 2 • 1 5 • 7 ____ x = 2 35 __ Multiply both sides by the reciprocal of 7. The answer is in simplest form.
  8. 8. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1C: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. = 6 5y 8 __ 5y 8 __ 6 1 __ 5 8 __5 8 __ ÷ = ÷ y = , or 9 48 5 __ Divide both sides by . 5 8 __ 5y 8 __ 6 1 __ 8 5 __8 5 __ • = • 3 5 __ 5 8 Multiply by the reciprocal of . __
  9. 9. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. j = 19 3 4 __ j ÷ = 19 ÷ 3 4 __ 3 4 __ 3 4 __ j • = 19 • __3 4 __ 4 3 4 3 __ j = 19 • 4 1 • 3 _____ 4 j = 19 • 3 __ 76___ 1 3 j = , or 25 3 __ Divide both sides of the equation by . 3 4 __ Multiply by , the reciprocal of . 3 4 __4 3 __
  10. 10. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1B Solve each equation. Write the answer in simplest form. 3x = 1 7 __ 3x 1 __ 1 7 __ 1 3 __1 3 __ • = • x = 1 • 1 7 • 3 ____ x = 1 21 __ Multiply both sides by the reciprocal of 3. The answer is in simplest form.
  11. 11. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1C Solve each equation. Write the answer in simplest form. = 4 6y 7 __ 6y 7 __ 4 1 __ 6 7 __6 7 __ ÷ = ÷ y = , or 4 28 6 __ Divide both sides by . Multiply by the reciprocal of . 6 7 __ 6y 7 __ 4 1 __ 7 6 __7 6 __ • = • 2 3 __ 6 7 __
  12. 12. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 2: Problem Solving Application 2 3 __ Dexter makes of a recipe, and he uses 12 cups of powdered milk. How many cups of powdered milk are in the recipe?
  13. 13. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 2 Continued 11 Understand the Problem The answer will be the number of cups of powdered milk in the recipe. List the important information: 2 3 __ • He makes of the recipe. • He uses 12 cups of powdered milk.
  14. 14. Course 1 5-10 Solving Fraction Equations: Multiplication and Division 22 Make a Plan You can write and solve an equation. Let x represent the number of cups in the recipe. He uses 12 cups, which is two-thirds of the amount of the recipe. 2 3 __12 = x Additional Example 2 Continued
  15. 15. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Solve33 2 3 __12 = x 12 • = x • 3 2 __ 2 3 __ 3 2 __ 12 1 __ 3 2 __• = x 6 1 18 = x There are 18 cups of powdered milk in the recipe. Multiply both sides by , the reciprocal of . 3 2 __ 2 3 __ Simplify. Then multiply. Additional Example 2 Continued
  16. 16. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Look Back44 Check 12 = x 2 3 __ 2 3 __12 = ? (18) 36 3 __12 = ? 12 = 12 ? Substitute 18 for x. Multiply and simplify. 18 is the solution. Additional Example 2 Continued 12 1
  17. 17. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 2 2 5 __ Nick makes of a recipe, and he uses 8 cups of wheat flour. How many cups of wheat flour are in the recipe?
  18. 18. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 2 Continued 11 Understand the Problem The answer will be the number of cups of wheat flour in the recipe. 2 5 __ List the important information: • He makes of the recipe. • He uses 8 cups of wheat flour.
  19. 19. Course 1 5-10 Solving Fraction Equations: Multiplication and Division 22 Make a Plan You can write and solve an equation. Let y represent the number of cups in the recipe. He uses 8 cups, which is two-fifths of the amount of the recipe. 2 5 __8 = y Check It Out: Example 2 Continued
  20. 20. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Solve33 2 5 __8 = y 8 • = y • 5 2 __ 2 5 __ 5 2 __ 8 1 __ 5 2 __• = y 4 1 20 = y There are 20 cups of wheat flour in the recipe. Multiply both sides by , the reciprocal of . 5 2 __ 2 5 __ Simplify. Then multiply. Check It Out: Example 2 Continued
  21. 21. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Look Back44 Check 8 = y 2 5 __ 2 5 __8 = ? (20) 40 5 __8 = ? 8 = 8 ? Substitute 20 for y. Multiply and simplify. 20 is the solution. Check It Out: Example 2 Continued 8 1
  22. 22. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Lesson Quiz Solve each equation. Write the answer in simplest form. 1. 3x = 2. x = 4 3. x = 14 4. = 9 5. Rebecca used 3 pt of paint to paint of the trim in her bedroom. How many pints will Rebecca use for the trim in the entire bedroom? 1 8 __ 1 4 __ 3 7 __ y 7 __ 1 4 __ x = 161 24 __x = 98 3 __ 2 3 __x = or 32 y = 63 12

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