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Solving Equations: Decimals, Fractions, and Word Problems

This lesson covers solving equations involving decimals and fractions, as well as applying equations to real-world scenarios. Topics include addition and subtraction with decimals, multiplying and dividing with fractions, and solving word problems.

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Solving Equations: Decimals, Fractions, and Word Problems

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 1 1 5 1 1 16 Warm Up Add or subtract. 5 10 7 10 1. + 3 8 5 16 2. 2 – 1 3. 4.8 + 3.6 8.4 2.35 4. 2.4 – 0.05

  3. Coefficient The numerical factor of a term that contains a variable. coefficient 3x variable

  4. Sunshine State Standards MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems…

  5. – 4.6 = –4.6 = 4.4 m 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. Additional Examples 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 Use the Subtraction Property of Equality. Subtract 4.6 from both sides. m + 4.6 = 9

  6. –32.8 8.2 8.2p 8.2 = p = –4 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 Use the Division Property of Equality. Divide both sides by 8.2.

  7. x 1.2 = 15 x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. Use the Multiplication Property of Equality. Multiply both sides by 1.2. x = 18

  8. –9.1 –9.1 = –6.1 m 15.1 –3.1 –3.1 –3.1 p = p = –5 Check It Out: Example 1A and 1B Solve each equation. A. m + 9.1 = 3 m + 9.1 = 3 B. –3.1p = 15.5

  9. 2 7 27 2 7 3 7 27 n – + = – – Subtract from both sides. 5 7 n = – Additional Example 2A: Solving Equations with Fractions Solve. 3 7 2 7 n + = –

  10. 1 6 1 6 2 3 1 6 1 6 y – + + = Add to both sides. 4 6 1 6 y = + 5 6 y = Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = Find a common denominator, 6.

  11. 5 6 5 6 5 8 5 6 5 6 Divide both sides by . x ÷ = ÷ 5 8 6 5 5 6 6 5 = • x • 3 4 = x Additional Example 2C: Solving Equations with Fractions Solve. 5 8 5 6 x = 3 Multiply by the reciprocal. 4 Simplify.

  12. 1 3 5 8 5 8 13 13 13 m – + = + m – = 23 24 m = Check It Out: Example 2A Solve each equation. 5 8 1 3 m – = 15 24 8 24 m = +

  13. 3 8 3 8 3 8 6 19 6 19 3 8 6 19 8 3 = • = = ÷ x x x 16 19 = x Check It Out: Example 2B Solve each equation. 3 8 6 19 x = 3 8 ÷ 2 8 3 • 1

  14. 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? 2 3 2 3 2 3 2 3 = 2  s Additional Example 3: Solving Word Problems Using Equations Write an equation: Amount needed for each dessert Amount of sugar Total servings  =

  15. 2 3 2 3 2 3 s = 2  2 3 3 2 2 3 2 3 3 2 2 3 2 3 2 3 s s  ÷  = 2  ÷ = 2  Divide both sides by . 8 3 3 2  = s 24 6 , or 4 s = Additional Example 3 Continued Now solve the equation. Multiply both sides by the reciprocal. Simplify. Mr. Rios can make 4 servings.

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

  17. 3 5 3 5 33 2 3 5 x ÷ = ÷ 5 3 33 2 x = • • 1 2 16 33 • 5 2 • 3 x = 55 2 , or = Check It Out: Example 3 Continued 3 5 x = • 33 2 3 5 x = • 1 11 1 2 27 1 1 2 So, the tank in the minivan can hold gallons of gas. 27

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. 5 12 j = –15 1 y = 15 1 d = 9 2 Lesson Quiz: Part I Solve. 1.x – 23.3 = 17.8 x = 41.1 3 4 2 3 2.j + = –14 3 5 3. 9y = 3 8 d = 2 4. 4

  20. 2 5 Lesson Quiz: Part II Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5. 5 hours

  21. 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

  22. Lesson Quiz for Student Response Systems 2. Solve. c + = –11 A. c = 12 C.c = 11 B.c = –12 D.c = 11 3 4 4 5 4 5 11 20 11 20 3 4

  23. Lesson Quiz for Student Response Systems 3. Solve. 8e = A. e = 8 C.e = B.e = 5 D.e = 2 3 1 12 2 3 1 3 3 20

  24. Lesson Quiz for Student Response Systems 4. Solve. = 3 A. h = 9 C.h = 11 B.h = 10 D.h = 12 h3 5 6 1 2 1 2 1 2 1 2

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