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Page 133 #14-26 ANSWERS

Page 133 #14-26 ANSWERS. Student Learning Goal Chart. Lesson Reflections. Pre-Algebra Learning Goal Students will understand rational and real numbers. Students will understand rational and real numbers by being able to do the following:.

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Page 133 #14-26 ANSWERS

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  1. Page 133 #14-26 ANSWERS

  2. Student Learning Goal Chart Lesson Reflections

  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)

  5. Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers.

  6. Pre-Algebra HW Page 124 #33-64 all

  7. 3-3 Multiplying Rational Numbers Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  8. 3-3 Multiplying Rational Numbers 15 17 7 8 5 3 43 20 3 8 Pre-Algebra Warm Up Write each number as an improper fraction. 1 2 7 1. 3. 2. 2 3 1 3 5 8 2 3 4. 5. 6 5 3 8

  9. Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57

  10. Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers.

  11. Multiplication Repeated addition 1 3 • 1 3 1 4 1 4 1 4 3 4 = = 3 = + + 4 4 4 Kendall invited 36 people to a party. She needs to triple the recipe for a dip, or multiply the amount of each ingredient by 3. Remember that multiplication by a whole number can be written as repeated addition. Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator.

  12. RULES FOR MULTIPLYING TWO RATIONAL NUMBERS If the signs of the factors are the same, the product is positive. (+) • (+) = (+) or (–) • (–) = (+) If the signs of the factors are different, the product is negative. (+)•(–)=(–)or(–)•(+)=(–)

  13. Helpful Hint To write as a mixed number, divide: 12 5 –8 • 6 7 = 12 = 2 R2 –48 7 5 = 2 5 = 2 6 7 –6 = Additional Example 1A: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. 6 7 A. –8 Multiply Simplify

  14. 16 3 1 3 5(3) + 1 3 5 = = 16 3 = 2 32 3 = 2 3 = 10 Additional Example 1B: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. 1 3 B. 5 2 Multiply Simplify

  15. –3 • 5 8 = –15 8 = 7 8 –1 = Try This: Example 1A Multiply. Write the answer in simplest form. 5 8 –3 A. Multiply Simplify

  16. 2 5 9(5) + 2 5 47 5 47 5 9 = = 4 = 188 5 = 3 5 = 37 Try This: Example 1B Multiply. Write the answer in simplest form. 2 5 9 4 B. Multiply Simplify

  17. 6 15 35 23 = • = • 2 3 3 5 • A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators. If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator.

  18. = 2 5 = Helpful Hint A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. To simplify the product, rearrange the six green squares into the first two columns. You can see that this is . 2 5 6 15

  19. 1(6) 8(7) = 3 1(6) 8(7) = 4 3 28 = Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 6 7 1 8 A. Multiply numerators. Multiply denominators. Look for common factors: 2. Simplest form

  20. –2(9) 3(2) = –1 –2(9) 3(2) 3 = 1 1 –3 = Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. 2 3 9 2 B. – Multiply numerators. Multiply denominators. Look for common factors: 2, 3. Simplest form

  21. 1 2 3 7 31 1 = 4 7 2 31(1) 7(2) = 31 14 3 14 = or 2 Additional Example 2C: Multiplying Fractions Multiply. Write the answer in simplest form. 1 2 3 7 C. 4 Write as an improper fraction. Multiply numerators. Multiply denominators. 31 ÷ 14 = 2 R3

  22. 3(5) 5(8) = 1 3(5) 5(8) = 1 3 8 = Try This: Example 2A Multiply. Write the answer in simplest form. 5 8 3 5 A. Multiply numerators. Multiply denominators. Look for common factors: 5. Simplest form

  23. –7(4) 8(7) = –1 –7(4) 8(7) 1 = 1 2 1 2 = – Try This: Example 2B Multiply. Write the answer in simplest form. 4 7 7 8 B. – Multiply numerators. Multiply denominators. Look for common factors: 4, 7. Simplest form

  24. 7 9 3 5 13 7 = 2 5 9 13(7) 5(9) = 91 45 1 45 = or 2 Try This: Example 2C Multiply. Write the answer in simplest form. 7 9 3 5 C. 2 Write as an improper fraction. Multiply numerators. Multiply denominators. 91 ÷ 45 = 2 R 1

  25. Additional Example 3: Multiplying Decimals Multiply. A. 2(–0.51) Product is negative with 2 decimal places. 2 • (–0.51) = –1.02 (–0.4)(–3.75) B. Product is positive with 3 decimal places. (–0.4) • (–3.75) = 1.500 00 = 1.5 You can drop the zeros after the decimal point.

  26. Try This: Example 3 Multiply. A. 3.1 (0.28) 3.1 • (0.28) = 0.868 Product is positive with 3 decimal places. (–0.4)(–2.53) B. Product is positive with 3 decimal places. (–0.4) • (–2.53) = 1.012

  27. 1 8 Evaluate –3 x for the value of x. 18 18 –3 x –3 (5) –25 8 = = (5) –125 8 = 5 8 = –15 Additional Example 4A: Evaluating Expressions with Rational Numbers A. x = 5 Substitute 5 for x. Write as an improper fraction. –125 ÷ 8 = –15 R5

  28. 1 8 Evaluate –3 x for the value of x. 18 –3 x 18 2 7 27 = –3 Substitute for x. 27 –25 8 = –25 • 2 = 8 • 7 25 28 = – Additional Example 4B: Evaluating Expressions with Rational Numbers Continued 2 B. x = 7 Write as an improper fraction. 1 Look for common factors: 2. 4

  29. 3 5 Evaluate –5 y for the value of y. 35 –5 y 6 7 Substitute for x. 67 35 = –5 67 –28 5 = –28 • 6 = 5 • 7 24 5 45 = – , or – 4 Try This: Example 4A 67 A. y = Write as an improper fraction. –4 Look for common factors: 7. 1

  30. 3 5 Evaluate –5 y for the value of y. 35 –5 y 35 = –5 (3) –28 5 (3) = –84 5 = 4 5 = –16 Try This: Example 4B B. y = 3 Substitute 3 for y. Write as an improper fraction. –84 ÷ 5 = –16 R4

  31. 2 7 1 5 12 – Lesson Quiz: Part 1 Multiply. 1 7 9 1. 5 8 2 3 – 2. 3. –0.47(2.2) –1.034 1 2 45 4.Evaluate 2 (x) for x = . 2

  32. 1 3 Lesson Quiz: Part 2 5. Teri is shopping for new shoes. Her mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for off. How much money does Teri need to buy the shoes? $10

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