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Pre-Algebra: Solving Equations with Rational Numbers

This lesson covers solving equations involving rational numbers in Pre-Algebra, including decimals and fractions. Students will learn methods and practice solving equations step by step.

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Pre-Algebra: Solving Equations with Rational Numbers

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  1. Page 129 #24-57 ANSWERS

  2. Student Learning Goal Chart Lesson Reflections 3-1, 3-2, 3-3, 3-4, 3-5, 3-6

  3. Pre-Algebra Learning GoalStudents will understand rational and real numbers.

  4. Students will understand rational and real numbers by being able to do the following: • Learn to write rational numbers in equivalent forms (3.1) • Learn to add and subtract decimals and rational numbers with like denominators (3.2) • Learn to add and subtract fractions with unlike denominators (3.5) • Learn to multiply fractions, decimals, and mixed numbers (3.3) • Learn to divide fractions and decimals (3.4) • Learn to solve equations with rational numbers (3.6)

  5. Today’s Learning Goal Assignment Learn to solve equations with rational numbers.

  6. Pre-Algebra HW Page 138 #14-26 all

  7. 3-6 Solving Equations with Rational Numbers Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  8. 3-6 Solving Equations with Rational Numbers 1 1 5 1 1 16 Pre-Algebra Warm Up Multiply. 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

  9. 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

  10. Today’s Learning Goal Assignment Learn to solve equations with rational numbers.

  11. – 4.6 = –4.6 = 4.4 m Remember! 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. Additional Example 1A: Solving Equations with Decimals. Solve. m + 4.6 = 9 A. m + 4.6 = 9 Subtract 4.6 from both sides.

  12. –32.8 8.2 8.2p 8.2 = p = –4 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 B. Divide both sides by 8.2

  13. x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. x 1.2 C. = 15 Multiply both sides by 1.2 x = 18

  14. 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Try This: Example 1A & 1B Solve. A. m + 9.1 = 3 m + 9.1 = 3 Subtract 9.1 from both sides. B. 5.5b = 75.9 Divide both sides by 5.5

  15. y 4.5 = 4.5 •90 4.5 • Try This: Examples 1C Solve. y 4.5 = 90 C. Multiply both sides by 4.5 y = 405

  16. 2 7 Subtract from both sides. 5 7 n = – 27 2 7 3 7 27 n – + = – – Additional Examples 2A: Solving Equations with Fractions Solve. 3 7 2 7 A. n + = –

  17. 1 6 Add to both sides. 1 6 1 6 2 3 1 6 y – + + = 4 6 1 6 y = + 5 6 y = Additional Examples 2B: Solving Equations with Fractions Solve. 1 6 2 3 B. y – = Find a common denominator; 6. Simplify.

  18. 6 5 Multiply both sides by . 5 8 6 5 5 6 6 5 = • x • 3 4 = x Additional Examples 2C: Solving Equations with Fractions Solve. 5 8 5 6 C. x = 3 4 Simplify.

  19. 1 9 Subtract from both sides. 19 6 9 1 9 5 9 19 2 3 n – + = – – Simplify – . n = – Try This: Example 2A Solve. 5 9 1 9 A. n + = –

  20. 1 2 Add to both sides. 1 2 1 2 3 4 1 2 y – + + = 3 4 2 4 y = + 1 4 y = 1 Try This: Example 2B Solve. 1 2 3 4 B. – = y Find a common denominator; 4. Simplify.

  21. 6 19 3 8 x = 6 19 8 3 3 8 8 3 x = • • 8 3 Multiply both sides by . 16 19 = x Try This: Examples 2C Solve. 6 19 3 8 x C. = 2 1 Simplify.

  22. 1 2 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? 3 4 2(2)+1 2 1 2 5 2 = = 2 5 2 3 4 Additional Examples 3: Solving Word Problems Using Equations Convert fractions: Write an equation: Milk for cereal Original amount of milk Milk for casserole – = – = c

  23. 5 2 5 2 3 4 5 2 5 2 c – Add to both sides. + = + 3 4 10 4 c = + 1 4 13 4 , or 3 c = 1 4 Mr. Rios has 3 cups of milk. Additional Examples 3 Continued Now solve the equation. 5 2 3 4 c = – Find a common denominator, 4. Simplify.

  24. 2 3 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? 15(2)+1 31 1 15.5 = 15 = = 2 2 2 2 3 31 2 Try This: Examples 3 Convert decimal to a fraction: Write an equation: Capacity of car’s tank Van’s gas tank Ratio of car’s tank to van’s tank • = g • =

  25. 3 2 3 2 2 3 31 2 Multiply both sides by . g = • • • 3 2 93 4 g = 1 4 g = 23 1 4 The van’s gas tank holds 23 gallons of gasoline. Try This: Examples 3 Continued Now solve the equation. 31 2 2 3 g = • Simplify.

  26. 5 12 j = –15 1 y = 15 1 d = 9 2 Lesson Quiz: Part 1 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. 5

  27. 1 3 Lesson Quiz: Part 2 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

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