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2-7

2-7. Solving Equations with Rational Numbers. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 1. 1. 5. 1. 1. 16. 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. Problem of the Day

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2-7

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  1. 2-7 Solving Equations with Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 1 1 5 1 1 16 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. 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 3 characters? (An example is 010.) 8

  4. Learn to solve equations with rational numbers.

  5. – 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. Additional Examples 1A: Solving Equations with Decimals. Solve. m + 4.6 = 9 m + 4.6 = 9 Subtract 4.6 from both sides.

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

  7. x 1.2 = 15 x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. Multiply both sides by 1.2 x = 18

  8. 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Check It Out: 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. y 4.5 = 4.5 •90 4.5 • Check It Out: Example 1C Solve. y 4.5 = 90 C. Multiply both sides by 4.5 y = 405

  10. 5 7 n = – 2 7 27 2 7 3 7 27 n – + = – – Subtract from both sides. Additional Example 2A: Solving Equations with Fractions Solve. 3 7 2 7 n + = –

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

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

  13. 1 9 Subtract from both sides. 19 6 9 1 9 5 9 19 2 3 n – + = – – Simplify – . n = – Check It Out: Example 2A Solve. 5 9 1 9 n + = –

  14. 1 2 Add to both sides. 1 2 1 2 3 4 1 2 y – + + = 3 4 2 4 y = + 1 4 y = 1 Check It Out: Example 2B Solve. 1 2 3 4 – = y Find a common denominator; 4. Simplify.

  15. 6 19 3 8 x = 6 19 3 8 x = 6 19 8 3 3 8 8 3 x = • • 8 3 Multiply both sides by . 16 19 = x Check It Out: Example 2C Solve. 2 1 Simplify.

  16. Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving of the dessert has tablespoon of sugar, how many servings can he make for the party? 2 3 2 3 2 3 2 3 = 2  s Additional Example 3: Solving Word Problems Using Equations Write an equation: Amount needed for each dessert Amount of sugar Total servings  =

  17. 3 2 2 3 2 3 s = 2  2 3 3 2 2 3 3 2 s Multiply both sides by .   = 2  8 3 3 2  = s 24 6 , or 4 s = Additional Example 3 Continued Now solve the equation. Simplify. Mr. Rios can make 4 servings.

  18. 2 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold gallons of gasoline, how much gasoline can the tank in the minivan hold? 31 2 2 3 31 2 Check It Out: Example 3 Write an equation: Capacity of car’s tank Van’s gas tank Ratio of car’s tank to van’s tank • = g • =

  19. 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. Check It Out: Example 3 Continued Now solve the equation. 31 2 2 3 g = • Simplify.

  20. 5 12 j = –15 1 y = 15 1 d = 9 2 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. 2 5 Lesson Quiz: Part II Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5. 5 hours

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