1. 2-4 Multiplying Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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

3. 2-4 Multiplying Rational Numbers Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57

4. 2-4 Multiplying Rational Numbers MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems… Sunshine State Standards

5. 2-4 Multiplying Rational Numbers 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. 1414 3434 1414 ++ = Repeated addition 1414 3 3 4 = = Multiplication 3 1 4 1 4

6. 2-4 Multiplying Rational Numbers

7. 2-4 Multiplying Rational Numbers –8 6767 Multiply. Write the answer in simplest form. Multiply. Simplify. –48 7 –6 6767 –8 6 7 To write as a mixed number, divide: Helpful Hint –48 7 –48 7 = –6 R6 6767 = –6 Additional Example 1A: Multiplying a Fraction and an Integer

8. 2-4 Multiplying Rational Numbers 2 1313 Multiply. Simplify. 10 2323 16 3 2 32 3 5 5(3) + 1 3 = = 1313 5 16 3 Multiply. Write the answer in simplest form. Additional Example 1B: Multiplying a Fraction and an Integer

9. 2-4 Multiplying Rational Numbers Multiply. Write each answer in simplest form. 5858 –3 Check It Out: Example 1A –3 5 8 –15 8 –1 7878, or 5858 –3

10. 2-4 Multiplying Rational Numbers 4 3434 6 Check It Out: Example 1B Multiply. Write each answer in simplest form. 4 6 4 + 3 4 = 4 27 4 4 4 27 = = 27 4 3434 6

11. 2-4 Multiplying Rational Numbers A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Caution!

12. 2-4 Multiplying Rational Numbers 1(6) 8(7) Multiply. Write the answer in simplest form. 6767 Simplify. 3 28 1818 1(6) 8(7) Multiply numerators. Multiply denominators. Look for common factors: 2. 3 4 Additional Example 2A: Multiplying Fractions

13. 2-4 Multiplying Rational Numbers –2(9) 3(2) 3 1 Simplify. –3 Multiply numerators. Multiply denominators. Look for common factors: 2, 3. 9292 2323 – 1 –1–1 Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form.

14. 2-4 Multiplying Rational Numbers Multiply. Write each answer in simplest form. 5858 3535 Check It Out: Example 2A 3838 3(5) 5(8) 5858 3535

15. 2-4 Multiplying Rational Numbers 3535 7 12 Multiply. Write each answer in simplest form. Check It Out: Example 2B – 7 20 – 3535 7 12 – 7 (– 3) 12 5 –1 4

16. 2-4 Multiplying Rational Numbers Multiply. Product is negative with 2 decimal places. 2 (–0.51) = –1.02 B. (–0.4)(–3.75) Product is positive with 3 decimal places. (–0.4) (–3.75) = 1.500 You can drop the zeros after the decimal point. = 1.5 Additional Example 3: Multiplying Decimals A. 2(–0.51) 00

17. 2-4 Multiplying Rational Numbers 3.1 (0.28) Multiply. Check It Out: Example 3A 3.1 ×0.28 248 620 0.868

18. 2-4 Multiplying Rational Numbers – 0.003 (– 2.6) Multiply. Check It Out: Example 3B × –0.003 –2.6 18 60 0.0078

19. 2-4 Multiplying Rational Numbers Joy completes of her painting each day. How much of her painting does she complete in a 7-day week? 1 20 Additional Example 4: Application = (7) 1 20 Multiply. 1 7 20 1 = 7 20 Joy completes of her painting in a 7-day week. 7 20

20. 2-4 Multiplying Rational Numbers Check It Out: Example 4 3 10 Ken completes of his work each day. How much work does he complete in 2 days? (2) 3 10 Ken completes of his work in 2 days. 5757 = 3 10 2121 3 2 10 1 = = 6 10 = 3535

21. 2-4 Multiplying Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

22. 2-4 Multiplying Rational Numbers 4. Evaluate 2 (x) for x =. 1. Lesson Quiz Multiply. –1.034 2. 5858 2323 – 1717 9 3. –0.47(2.2) 1212 2 4545 – 5 12 1 2727 Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week? 5. 8989 6 miles 2929

23. 2-4 Multiplying Rational Numbers 1. Multiply. 8 A. 1C. 2 B. 1D. 8 Lesson Quiz for Student Response Systems 2525 3535 4545 1515 1515

24. 2-4 Multiplying Rational Numbers 2. Multiply. – A. –C. – B. –D. – Lesson Quiz for Student Response Systems 7 12 5 12 7 18 5 18 7979 3434

25. 2-4 Multiplying Rational Numbers 3. Multiply. –0.39(3.2) A. –1.238 B. –1.248 C. –1.428 D. –1.842 Lesson Quiz for Student Response Systems

26. 2-4 Multiplying Rational Numbers 4. Sam cycles mile each day. What is the total distance that Sam cycles in 5 days? A. 7 milesC. 6 miles B. 6 milesD. 4 miles Lesson Quiz for Student Response Systems 7878 3838 3838 7878