1. Pre-Algebra 3-6 Solving Equations with Rational Numbers 3-6 Solving Equations with Rational Numbers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 3-6 Solving Equations with Rational Numbers Warm Up Add or subtract. + 1 5 1 1 16 1 Pre-Algebra 3-6 Solving Equations with Rational Numbers 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. Pre-Algebra 3-6 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 8 characters? (An example is 01010101.) 256

4. Pre-Algebra 3-6 Solving Equations with Rational Numbers Learn to solve equations with rational numbers.

5. Pre-Algebra 3-6 Solving Equations with Rational Numbers m + 4.6 = 9 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 Example 1A: Solving Equations with Decimals. Solve. 4.4 m = – 4.6 = A.

6. Pre-Algebra 3-6 Solving Equations with Rational Numbers 8.2p = –32.8 –4 p = Divide both sides by 8.2 –32.8 8.2 8.2p 8.2 = Additional Examples 1B: Solving Equations with Decimals Solve. B.

7. Pre-Algebra 3-6 Solving Equations with Rational Numbers = 15 Additional Examples 1C: Solving Equations with Decimals Solve. x = 18 Multiply both sides by 1.2 x 1.2 = 1.2 15 1.2 C.

8. Pre-Algebra 3-6 Solving Equations with Rational Numbers m + 9.1 = 3 Subtract 9.1 from both sides. Try This: Example 1A & 1B –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

9. Pre-Algebra 3-6 Solving Equations with Rational Numbers = 90 Try This: Examples 1C y = 405 Multiply both sides by 4.5 y 4.5 = 4.5 90 4.5 Solve. C.

10. Pre-Algebra 3-6 Solving Equations with Rational Numbers 2727 = – 3737 n + Additional Examples 2A: Solving Equations with Fractions n – + = – – 2727 3737 2727 2727 n = – 5757 Subtract from both sides. 2727 Solve. A.

11. Pre-Algebra 3-6 Solving Equations with Rational Numbers 1616 = 2323 y – Additional Examples 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. B. Simplify.

12. Pre-Algebra 3-6 Solving Equations with Rational Numbers 5656 = 5858 x 6565 6565 5656 = 5858 x Simplify. Additional Examples 2C: Solving Equations with Fractions Multiply both sides by. 6565 x = 3434 3 4 Solve. C.

13. Pre-Algebra 3-6 Solving Equations with Rational Numbers 1919 = – 5959 n + Try This: Example 2A n – + = – – 1919 5959 1919 1919 n = – 2323 Subtract from both sides. 1919 Simplify –. 6969 Solve. A.

14. Pre-Algebra 3-6 Solving Equations with Rational Numbers 1212 = 3434 y – Try This: Example 2B Find a common denominator; 4. y = 1 1414 =y 3434 2424 + 1212 = 3434 – 1212 + 1212 + y Add to both sides. 1212 Solve. B. Simplify.

15. Pre-Algebra 3-6 Solving Equations with Rational Numbers 3838 = 6 19 x 8383 8383 3838 = 6 19 x Simplify. Try This: Examples 2C Multiply both sides by. 8383 x = 16 19 2 1 Solve. C. 3838 = 6 19 x

16. Pre-Algebra 3-6 Solving Equations with Rational Numbers Write an equation: Original amount of milk Milk for casserole Milk for cereal Convert fractions: Additional Examples 3: Solving Word Problems Using Equations 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 –=

17. Pre-Algebra 3-6 Solving Equations with Rational Numbers Now solve the equation. Additional Examples 3 Continued 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.

18. Pre-Algebra 3-6 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 = Convert decimal to a fraction: Try This: Examples 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 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 =

19. Pre-Algebra 3-6 Solving Equations with Rational Numbers Simplify. 31 2 2323 = g Now solve the equation. Try This: Examples 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

20. Pre-Algebra 3-6 Solving Equations with Rational Numbers Lesson Quiz: Part 1 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

21. Pre-Algebra 3-6 Solving Equations with Rational Numbers Tamara had 6 bags of mulch for her garden. Each bag contained 8 lb of mulch. What was the total weight of the mulch? Lesson Quiz: Part 2 5. 50 lb 1313