1. 1-5 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. 1-5 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. 1-5 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. 1-5 Solving Equations with Rational Numbers Learn to solve equations with rational numbers.

5. 1-5 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. 1-5 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. 1-5 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. 1-5 Solving Equations with Rational Numbers m + 9.1 = 3 Use the Subtraction Property of Equality. Subtract 9.1 from both sides. Check It Out: Example 1A & 1B –6.1 m = –9.1 = Solve. A. B. 5.5b = 75.9 75.9 5.55.5 = b 13.8 b = Use the Division Property of Equality. Divide both sides by 5.5

9. 1-5 Solving Equations with Rational Numbers = 90 Check It Out: Example 1C y = 405 Use the Multiplication Property of Equality. Multiply both sides by 4.5 y 4.5 = 4.5 90 4.5 Solve. C.

10. 1-5 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.

11. 1-5 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. Simplify.

12. 1-5 Solving Equations with Rational Numbers 5656 = 5858 x 6565 6565 5656 = 5858 x Simplify. Additional Example 2C: Solving Equations with Fractions Multiply both sides by. 6565 x = 3434 3 4 Solve.

13. 1-5 Solving Equations with Rational Numbers 1919 = – 5959 n + Check It Out: Example 2A n – + = – – 1919 5959 1919 1919 n = – 2323 Subtract from both sides. 1919 Simplify –. 6969 Solve.

14. 1-5 Solving Equations with Rational Numbers 1212 = 3434 y – Check It Out: Example 2B Find a common denominator; 4. y = 1 1414 =y 3434 2424 + 1212 = 3434 – 1212 + 1212 + y Add to both sides. 1212 Solve. Simplify.

15. 1-5 Solving Equations with Rational Numbers 3838 = 6 19 x 8383 8383 Simplify. Check It Out: Example 2C Multiply both sides by. 8383 x = 16 19 3838 = 6 19 x 2 1 Solve.

16. 1-5 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

17. 1-5 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. 3232 Simplify.

18. 1-5 Solving Equations with Rational Numbers Write an equation: Van’s gas tank Ratio of car’s tank to van’s tank Capacity of car’s tank = Check It Out: Example 3 g 31 2 2323 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? 2323 2 31 =

19. 1-5 Solving Equations with Rational Numbers Simplify. 31 2 2323 = g Now solve the equation. Check It Out: Example 3 Continued The van’s gas tank holds 23 gallons of gasoline. 1414 31 2 2323 = g 3232 3232 g = 93 4 1414 g = 23 Multiply both sides by. 3232