1. Pre-Algebra 3.6 Solving Equations with Rational Numbers

2. Multiply. + 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 Warm Up

3. Learn to solve equations with rational numbers.

4. m + 4.6 = 9 Subtract 4.6 from both sides. Once you have solved and 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! Solve. 4.4 m = – 4.6 = A. Example: Solving Equations with Decimals.

5. 8.2p = –32.8 –4 p = Divide both sides by 8.2 –32.8 8.2 8.2p 8.2 = Solve. B. Examples: Solving Equations with Decimals

6. = 15 Solve. x = 18 Multiply both sides by 1.2 x 1.2 = 1.2 15 1.2 C. Examples: Solving Equations with Decimals

7. m + 9.1 = 3 Subtract 9.1 from both sides. –6.1 m = –9.1 = Solve. A. B. 5.5b = 75.9 75.9 5.55.5 = b 13.8 b = Divide both sides by 5.5 Try This

8. = 90 y = 405 Multiply both sides by 4.5 y 4.5 = 4.5 90 4.5 Solve. C. Try This

9. 2727 = – 3737 n + n – + = – – 2727 3737 2727 2727 n = – 5757 Subtract from both sides. 2727 Solve. A. Examples: Solving Equations with Fractions

10. 1616 = 2323 y – Find a common denominator; 6. y = 5656 =y 4646 1616 + 1616 = 2323 – 1616 + 1616 + y Add to both sides. 1616 Solve. B. Simplify. Examples: Solving Equations with Fractions

11. 5656 = 5858 x 6565 6565 5656 = 5858 x Simplify. Multiply both sides by. 6565 x = 3434 3 4 Solve. C. Examples: Solving Equations with Fractions

12. 1919 = – 5959 n + n – + = – – 1919 5959 1919 1919 n = – 2323 Subtract from both sides. 1919 Simplify –. 6969 Solve. A. Try This

13. 1212 = 3434 y – Find a common denominator; 4. y = 1 1414 =y 3434 2424 + 1212 = 3434 – 1212 + 1212 + y Add to both sides. 1212 Solve. B. Simplify. Try This

14. 3838 = 6 19 x 8383 8383 3838 = 6 19 x Simplify. Multiply both sides by. 8383 x = 16 19 2 1 Solve. C. 3838 = 6 19 x Try This

15. Write an equation: Original amount of milk Milk for casserole Milk for cereal Convert fractions: 5252 2(2)+1 2 = 1212 2 = –= c 3434 5252 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? 1212 3434 –= Examples: Solving Word Problems Using Equations

16. Now solve the equation. 5252 – = c Mr. Rios has 3 cups of milk. 1414 5252 = c – + 5252 3434 + 5252 3434 13 4 1414 3, or c = 3434 c = + 10 4 Add to both sides. 5252 Find a common denominator, 4. Simplify. Examples Continued

17. Write an equation: Van’s gas tank Ratio of car’s tank to van’s tank Capacity of car’s tank = Convert decimal to a fraction: 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 15.5 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2323 15.5 = 15 = = 1 2 2 15(2)+1 31 2 = Try This

18. Simplify. 31 2 2323 = g Now solve the equation. 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 Try This

19. 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 5 =2 3838 1 2 d = 9 Lesson Quiz: Part 1

20. 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 1313 Lesson Quiz: Part 2