2 6 Solving Equations with Rational Numbers Warm

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

2 -6 Solving Equations with Rational Numbers Warm Up Add or subtract. 1. 5 7 + 10 10 11 5 3 5 2. 2 – 1 8 16 11 16 3. 4. 8 + 3. 6 8. 4 4. 2. 4 – 0. 05 2. 35

2 -6 Solving Equations with Rational Numbers Coefficient The numerical factor of a term that contains a variable. coefficient 3 x � variable

2 -6 Solving Equations with Rational Numbers Sunshine State Standards MA. 8. A. 6. 4 Perform operations on real numbers (including…rational numbers…)…using real-world problems…

2 -6 Solving Equations with Rational Numbers Additional Examples 1 A: Solving Equations with Decimals Solve. m + 4. 6 = 9 – 4. 6 = – 4. 6 m = 4. 4 Use the Subtraction Property of Equality. Subtract 4. 6 from both sides. 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.

2 -6 Solving Equations with Rational Numbers Additional Examples 1 B: Solving Equations with Decimals Solve. 8. 2 p = – 32. 8 8. 2 p = – 4 Use the Division Property of Equality. Divide both sides by 8. 2.

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

2 -6 Solving Equations with Rational Numbers Check It Out: Example 1 A and 1 B Solve each equation. A. m + 9. 1 = 3 – 9. 1 = – 6. 1 m B. – 3. 1 p = 15. 5 15. 1 – 3. 1 p = – 5

2 -6 Solving Equations with Rational Numbers Additional Example 2 A: Solving Equations with Fractions Solve. 3 2 n+ =– 7 7 2 2 3 2 n– + =– – 7 7 n=– 5 7 2 Subtract from both sides. 7

2 -6 Solving Equations with Rational Numbers Additional Example 2 B: Solving Equations with Fractions Solve. 1 2 y– = 6 3 1 y 1 2 1 + – = + 6 6 3 6 4 1 y= + 6 6 5 y= 6 1 Add to both sides. 6 Find a common denominator, 6.

2 -6 Solving Equations with Rational Numbers Additional Example 2 C: Solving Equations with Fractions Solve. 5 5 x = 8 6 5 5 5 x÷ 5 = ÷ 6 8 6 6 5 63 • x= 8 • 5 6 5 4 3 x = 4 Divide both sides by 5. 6 Multiply by the reciprocal. Simplify.

2 -6 Solving Equations with Rational Numbers Check It Out: Example 2 A Solve each equation. 1 5 = 3 8 5 1 m– = 8 3 1 5 1 1 m– + = + 3 8 3 3 15 8 m= + 24 24 23 m= 24 m–

2 -6 Solving Equations with Rational Numbers Check It Out: Example 2 B Solve each equation. 3 6 x= 8 19 6 3 3 = x÷ ÷ 19 8 8 62 3 8 x • = • 8 3 19 x = 16 19 3 8 8 1 3

2 -6 Solving Equations with Rational Numbers Additional Example 3: Solving Word Problems Using Equations Mr. Rios wants to prepare a dessert, but only 2 has 2 3 tablespoons of sugar. If each serving 2 of the dessert has 3 tablespoon of sugar, how many servings can he make for the party? Write an equation: Total servings s Amount needed for each dessert 2 3 = = Amount of sugar 2 23

2 -6 Solving Equations with Rational Numbers Additional Example 3 Continued Now solve the equation. s 2 = 22 3 3 2 s ÷ 3 2 2 2 = 2 ÷ 3 3 3 Divide both sides by 2. 3 2 3 s 3 2 = 2 3 2 Multiply both sides by the 8 3 reciprocal. s= 3 2 24 s = 6 , or 4 Simplify. Mr. Rios can make 4 servings.

2 -6 Solving Equations with Rational Numbers Check It Out: Example 3 3 Rick’s car holds 5 the amount of gasoline as his 1 wife’s van. If the car’s gas tank can hold 16 2 gallons of gasoline, how much gasoline can the tank in the minivan hold? Amount of gas in van • Three-fifths = Amount of gas in car

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

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

2 -6 Solving Equations with Rational Numbers Lesson Quiz: Part I Solve. 1. x – 23. 3 = 17. 8 x = 41. 1 3 2 2. j + = – 14 4 3 5 j = – 15 12 3. 9 y = 3 5 y= 1 15 d = 23 4. 4 8 1 d=9 2

2 -6 Solving Equations with Rational Numbers Lesson Quiz: Part II 2 5. Tamara can mow 5 acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5 hours

2 -6 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 1. Solve. a – 36 = 44. 9 A. a = 36. 7 B. a = 49. 2 C. a = 59. 9 D. a = 80. 9

2 -6 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 2. Solve. c + 3 = – 11 4 4 5 A. c = 12 11 20 C. c = 11 4 5 B. c = – 12 11 20 D. c = 113 4

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

2 -6 Solving Equations with Rational Numbers Lesson Quiz for Student Response Systems 4. Solve. h = 35 3 6 A. h = 9 1 2 C. h = 11 1 2 B. h = 10 1 2 D. h = 12 1 2