1. 2-6 Solving Equations with Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 2-6 Solving Equations with Rational Numbers Warm Up Add or subtract. + 1 5 1 1 16 1 1. 5 10 2. 5 16 2 – 1 3. 4.8 + 3.6 4. 2.4 – 0.05 8.4 2.35 7 10 3838

3. 2-6 Solving Equations with Rational Numbers 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. 2-6 Solving Equations with Rational Numbers MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems… Sunshine State Standards

5. 2-6 Solving Equations with Rational Numbers m + 4.6 = 9 Use the Subtraction Property of Equality. Subtract 4.6 from both sides. 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. Remember! Additional Examples 1A: Solving Equations with Decimals Solve. 4.4 m = – 4.6 =

6. 2-6 Solving Equations with Rational Numbers 8.2p = –32.8 –4 p = Use the Division Property of Equality. Divide both sides by 8.2. –32.8 8.2 8.2p 8.2 = Additional Examples 1B: Solving Equations with Decimals Solve.

7. 2-6 Solving Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals x = 18 Use the Multiplication Property of Equality. Multiply both sides by 1.2. = 15 x 1.2 = 1.2 15 1.2 Solve.

8. 2-6 Solving Equations with Rational Numbers m + 9.1 = 3 Check It Out: Example 1A and 1B m + 9.1 = 3 –6.1 m = –9.1 Solve each equation. A. B. – 3.1p = 15.5 15.1 –3.1–3.1 = p –5 –5 p =

9. 2-6 Solving Equations with Rational Numbers 2727 = – 3737 n + Additional Example 2A: Solving Equations with Fractions n – + = – – 2727 3737 2727 2727 n = – 5757 Subtract from both sides. 2727 Solve.

10. 2-6 Solving Equations with Rational Numbers 1616 = 2323 y – Additional Example 2B: Solving Equations with Fractions Find a common denominator, 6. y = 5656 =y 4646 1616 + 1616 = 2323 – 1616 + 1616 + y Add to both sides. 1616 Solve.

11. 2-6 Solving Equations with Rational Numbers 5656 = 5858 x 6565 6565 5656 = 5858 x Simplify. Additional Example 2C: Solving Equations with Fractions Multiply by the reciprocal. x = 3434 3 4 Solve. 5656 Divide both sides by. 5656 = 5858 x ÷ 5656 5656 ÷

12. 2-6 Solving Equations with Rational Numbers 1313 = 5858 m – Check It Out: Example 2A Solve each equation. m – + = + 1313 5858 1313 1313 m = 23 24 m = + 8 24 15 24 m – = 5858 1313

13. 2-6 Solving Equations with Rational Numbers 3838 x = 6 19 Check It Out: Example 2B Solve each equation. = 6 19 3838 x ÷ 3838 3838 x = ÷ 3838 8383 3838 x = 8383 2 1 16 19 x =

14. 2-6 Solving Equations with Rational Numbers Write an equation: Total servings Amount needed for each dessert Amount of sugar Additional Example 3: Solving Word Problems Using Equations  = 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? 2323 2323 s 2323 2323  = 2

15. 2-6 Solving Equations with Rational Numbers Now solve the equation. Additional Example 3 Continued Mr. Rios can make 4 servings. 2323 = 2  s   3232 2323 3232 2323  = 2 s 2323 24 6, or 4 s = 8383 s =  3232 Multiply both sides by the reciprocal. Simplify. 2323 Divide both sides by. 2323 = 2 2323 s  ÷ 2323 2323 ÷

16. 2-6 Solving Equations with Rational Numbers Check It Out: Example 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 16 gallons of gasoline, how much gasoline can the tank in the minivan hold? 3535 2 1 = Amount of gas in van Three-fifths Amount of gas in car

17. 2-6 Solving Equations with Rational Numbers Check It Out: Example 3 Continued 3535 = x 33 2 = x 5353 x = 33 5 2 3 3535 = 33 2 x   ÷ 3535 3535 ÷ 1212 16 3535 = x 33 2 1 11 1 55 2, or = So, the tank in the minivan can hold gallons of gas. 27 1212 1212

18. 2-6 Solving Equations with Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. 2-6 Solving Equations with Rational Numbers Lesson Quiz: Part I Solve. 1. x – 23.3 = 17.8 2. j + = –14 3. 9y = 4. 1 15 y = x = 41.1 3535 2323 3434 j = – 15 5 12 d 4 =2 3838 1 2 d = 9

20. 2-6 Solving Equations with Rational Numbers 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? Lesson Quiz: Part II 5. 5 hours 2525

21. 2-6 Solving Equations with Rational Numbers 1. Solve. a – 36 = 44.9 A. a = 36.7 B. a = 49.2 C. a = 59.9 D. a = 80.9 Lesson Quiz for Student Response Systems

22. 2-6 Solving Equations with Rational Numbers 2. Solve. c + = –11 A. c = 12C. c = 11 B. c = –12D. c = 11 Lesson Quiz for Student Response Systems 11 20 4545 3434 3434 4545

23. 2-6 Solving Equations with Rational Numbers 3. Solve. 8e = A. e = 8C. e = B. e = 5D. e = Lesson Quiz for Student Response Systems 2323 1313 1 12 3 20 2323

24. 2-6 Solving Equations with Rational Numbers 4. Solve. = 3 A. h = 9C. h = 11 B. h = 10D. h = 12 Lesson Quiz for Student Response Systems 1212 1212 1212 1212 h3h3 5656