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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.

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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. Learn to solve equations with rational numbers.

  4. – 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.

  5. –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

  6. 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

  7. 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

  8. 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

  9. 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 + = –

  10. 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.

  11. 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.

  12. 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 + = –

  13. 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.

  14. 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.

  15. 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

  16. 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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