Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 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 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 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 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 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 8.2p = –32.8 8.2 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 1C: 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 1A and 1B Solve each equation. A. m + 9.1 = 3 m + 9.1 = 3 –9.1 –9.1 = –6.1 m B. – 3.1p = 15.5 15.1 –3.1 p = –3.1 –3.1 p = –5 2-6 Solving Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions Solve. 3 2 n+ =– 7 7 2 2 3 2 n– + =– – 7 7 7 7 n=– 5 7 2 Subtract from both sides. 7 2-6 Solving Equations with Rational Numbers Additional Example 2B: 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 2C: Solving Equations with Fractions Solve. 5 5x = 8 6 5 5 5x÷5 ÷ = 6 8 6 6 5 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 2A 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 2B Solve each equation. 3 6 x= 8 19 3 6 x= 8 19 6 3 ÷3 ÷3 = x 8 8 19 8 62 8 3 8 x • = • 1 8 3 19 3 x = 16 19 2-6 Solving Equations with Rational Numbers Additional Example 3: Solving Word Problems Using Equations Mr. Rios wants to prepare a dessert, but only has 2 2 tablespoons of sugar. If each serving 3 of the dessert has 2 tablespoon of sugar, how 3 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 s 2 2 2 2 ÷ = 2 ÷ 3 3 3 3 Divide both sides by 2 . 3 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 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. 9y = 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. 8e = 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