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3-6. Solving Equations with Rational Numbers. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 3-6. Solving Equations with Rational Numbers. 1. 1. 5. 1. 1. 16. Course 3. Warm Up Add or subtract. 5 10. 7 10. 1. +. 3 8. 5 16. 2. 2 – 1 . 3. 4.8 + 3.6 .

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3-6

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  1. 3-6 Solving Equations with Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 3-6 Solving Equations with Rational Numbers 1 1 5 1 1 16 Course 3 Warm Up Add or subtract. 5 10 7 10 1. + 3 8 5 16 2. 2 – 1 3. 4.8 + 3.6 8.4 2.35 4. 2.4 – 0.05

  3. 3-6 Solving Equations with Rational Numbers Course 3 Problem of the Day A computer word is made of strings of 0’s and 1’s. How many different words can be formed using 8 characters? (An example is 01010101.) 256

  4. 3-6 Solving Equations with Rational Numbers Course 3 Learn to solve equations with rational numbers.

  5. 3-6 Solving Equations with Rational Numbers – 4.6 = –4.6 = 4.4 m Remember! Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. Course 3 Additional Example 1A: Solving Equations with Decimals. Solve. m + 4.6 = 9 A. m + 4.6 = 9 Subtract 4.6 from both sides.

  6. 3-6 Solving Equations with Rational Numbers –32.8 8.2 8.2p 8.2 = p = –4 Course 3 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 B. Divide both sides by 8.2

  7. 3-6 Solving Equations with Rational Numbers x 1.2 = 1.2 •15 1.2 • Course 3 Additional Examples 1C: Solving Equations with Decimals Solve. x 1.2 C. = 15 Multiply both sides by 1.2 x = 18

  8. 3-6 Solving Equations with Rational Numbers 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Course 3 Try This: Example 1A & 1B Solve. A. m + 9.1 = 3 m + 9.1 = 3 Subtract 9.1 from both sides. B. 5.5b = 75.9 Divide both sides by 5.5

  9. 3-6 Solving Equations with Rational Numbers y 4.5 = 4.5 •90 4.5 • Course 3 Try This: Examples 1C Solve. y 4.5 = 90 C. Multiply both sides by 4.5 y = 405

  10. 3-6 Solving Equations with Rational Numbers 2 7 Subtract from both sides. 5 7 n = – 27 2 7 3 7 27 n – + = – – Course 3 Additional Examples 2A: Solving Equations with Fractions Solve. 3 7 2 7 A. n + = –

  11. 3-6 Solving Equations with Rational Numbers 1 6 Add to both sides. 1 6 1 6 2 3 1 6 y – + + = 4 6 1 6 y = + 5 6 y = Course 3 Additional Examples 2B: Solving Equations with Fractions Solve. 1 6 2 3 B. y – = Find a common denominator; 6. Simplify.

  12. 3-6 Solving Equations with Rational Numbers 6 5 Multiply both sides by . 5 8 6 5 5 6 6 5 = • x • 3 4 = x Course 3 Additional Examples 2C: Solving Equations with Fractions Solve. 5 8 5 6 C. x = 3 4 Simplify.

  13. 3-6 Solving Equations with Rational Numbers 1 9 Subtract from both sides. 19 6 9 1 9 5 9 19 2 3 n – + = – – Simplify – . n = – Course 3 Try This: Example 2A Solve. 5 9 1 9 A. n + = –

  14. 3-6 Solving Equations with Rational Numbers 1 2 Add to both sides. 1 2 1 2 3 4 1 2 y – + + = 3 4 2 4 y = + 1 4 y = 1 Course 3 Try This: Example 2B Solve. 1 2 3 4 B. – = y Find a common denominator; 4. Simplify.

  15. 3-6 Solving Equations with Rational Numbers 6 19 3 8 x = 6 19 8 3 3 8 8 3 x = • • 8 3 Multiply both sides by . 16 19 = x Course 3 Try This: Examples 2C Solve. 6 19 3 8 x C. = 2 1 Simplify.

  16. 3-6 Solving Equations with Rational Numbers 1 2 Mr. Rios wants to prepare a casserole that requires 2 cups of milk. If he makes the casserole, he will have only cup of milk left for his breakfast cereal. How much milk does Mr. Rios have? 3 4 2(2)+1 2 1 2 5 2 = = 2 5 2 3 4 Course 3 Additional Examples 3: Solving Word Problems Using Equations Convert fractions: Write an equation: Milk for cereal Original amount of milk Milk for casserole – = – = c

  17. 3-6 Solving Equations with Rational Numbers 5 2 5 2 3 4 5 2 5 2 c – Add to both sides. + = + 3 4 10 4 c = + 1 4 13 4 , or 3 c = 1 4 Mr. Rios has 3 cups of milk. Course 3 Additional Examples 3 Continued Now solve the equation. 5 2 3 4 c = – Find a common denominator, 4. Simplify.

  18. 3-6 Solving Equations with Rational Numbers 2 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 15.5 gallons of gasoline, how much gasoline can the tank in the minivan hold? 15(2)+1 31 1 15.5 = 15 = = 2 2 2 2 3 31 2 Course 3 Try This: Examples 3 Convert decimal to a fraction: Write an equation: Capacity of car’s tank Van’s gas tank Ratio of car’s tank to van’s tank • = g • =

  19. 3-6 Solving Equations with Rational Numbers 3 2 3 2 2 3 31 2 Multiply both sides by . g = • • • 3 2 93 4 g = 1 4 g = 23 1 4 The van’s gas tank holds 23 gallons of gasoline. Course 3 Try This: Examples 3 Continued Now solve the equation. 31 2 2 3 g = • Simplify.

  20. 3-6 Solving Equations with Rational Numbers 5 12 j = –15 1 y = 15 1 d = 9 2 Course 3 Lesson Quiz: Part 1 Solve. 1.x – 23.3 = 17.8 x = 41.1 3 4 2 3 2.j + = –14 3 5 3. 9y = 3 8 d = 2 4. 4

  21. 3-6 Solving Equations with Rational Numbers 1 3 Course 3 Lesson Quiz: Part 2 Tamara had 6 bags of mulch for her garden. Each bag contained 8 lb of mulch. What was the total weight of the mulch? 5. 50 lb

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