1. Ch 4 Sec 3: Slide #1 Columbus State Community College Chapter 4 Section 3 Multiplying and Dividing Signed Fractions

2. Ch 4 Sec 3: Slide #2 Multiplying and Dividing Signed Fractions 1.Multiply signed fractions. 2.Multiply fractions that involve variables. 3.Divide signed fractions. 4.Divide fractions that involve variables. 5.Solve application problems involving multiplying and dividing fractions.

3. Ch 4 Sec 3: Slide #3 “ of ” NOTE When used with fractions, the word of indicates multiplication. For example, 1 3 1 4 ofmeans 1 3 1 4

4. Ch 4 Sec 3: Slide #4 Multiplying Fractions If a, b, c, and d are numbers (but b and d are not 0), then a b c d a c b d =

5. Ch 4 Sec 3: Slide #5 3 4 5 7 –– Multiplying Signed Fractions Multiply. (a) EXAMPLE 1 Multiplying Signed Fractions 3 5 4 7 = 15 28 = 3 4 5 7 –– The product of two negative numbers is positive. The answer is in lowest terms because 15 and 28 have no common factor other than 1.

6. Ch 4 Sec 3: Slide #6 Multiplying Signed Fractions Multiply. (b) EXAMPLE 1 Multiplying Signed Fractions 1 2 3 5 1 2 3 5 1 3 2 5 = 3 10 = The answer is in lowest terms because 3 and 10 have no common factor other than 1.

7. Ch 4 Sec 3: Slide #7 1 1 1 1 1 1 Using Prime Factorization to Multiply Fractions EXAMPLE 2 Using Prime Factorization to Multiply Fractions Multiplying a positive number times a negative number gives a negative product. (a) 6 7 14 18 – 6 7 14 18 – 2 3 2 7 7 2 3 3 = – 2 3 = –

8. Ch 4 Sec 3: Slide #8 111 111 Using Prime Factorization to Multiply Fractions EXAMPLE 2 Using Prime Factorization to Multiply Fractions (b) 5 9 27 35 of 5 9 27 35 5 3 3 3 3 3 5 7 = 3 7 =

9. Ch 4 Sec 3: Slide #9 Entering Fractions on the TI 30 XIIS c A b

10. Ch 4 Sec 3: Slide #10 Entering Fractions on the TI 30 Xa c a b

11. Ch 4 Sec 3: Slide #11 c A b c A b c A b Whole Number Numerator Denominator bcA If there is no whole number, leave this step out. Method used for entering proper and improper fractions Entering Fractions on the TI 30 XIIS and the TI 30 Xa

12. Ch 4 Sec 3: Slide #12 c A b 84 120 10 7 84120 = Entering Fractions on the TI 30 XIIS and the TI 30 Xa

13. Ch 4 Sec 3: Slide #13 = = c A b 2848 28 48 12 7 (-) Entering Fractions on the TI 30 XIIS and the TI 30 Xa c A b 2848 12 7 + – TI 30 XIIS TI 30 Xa

14. Ch 4 Sec 3: Slide #14 1 1 Multiplying a Fraction and an Integer EXAMPLE 3 Multiplying a Fraction and an Integer Find 2 3 of 45. 2 3 45 1 2 3 3 5 3 1 = 30 1 = =

15. Ch 4 Sec 3: Slide #15 1 11 1 Multiplying Fractions with Variables EXAMPLE 4 Multiplying Fractions with Variables (a) 2 2 m m n n n 3 5 5 2 2 3 m n n n n = m n = 4 m 2 n 3 5 15 12 m n 4 4 m 2 n 3 5 15 12 m n 4 1 1 1 1 1 1 1 1 1 1 1 1

16. Ch 4 Sec 3: Slide #16 1 1 1 1 1 1 1 1 1 1 5 a 2 2 3 b b 2 3 b 5 7 a = 5 a 6 b 12 b 2 35 a Multiplying Fractions with Variables EXAMPLE 4 Multiplying Fractions with Variables 2 b 7 = (b) 5 a 6 b 12 b 2 35 a

17. Ch 4 Sec 3: Slide #17 Reciprocal of a Fraction Two numbers are reciprocals of each other if their product is 1. The reciprocal of the fraction is because Reciprocal of a Fraction a b b a a b b a 1 1 1 1 =1= 1 1 a b b a =

18. Ch 4 Sec 3: Slide #18 Reciprocals Find the reciprocal of each number. 1. 2. 3. NumberReciprocalReason 4 7 2 9 9 2 7 4 8 1 8 4 7 7 4 28 ==1 = 2 9 9 2 18 =1 8 1 1 8 8 8 ==1

19. Ch 4 Sec 3: Slide #19 Reciprocal NOTE Every number has a reciprocal except 0. Why not 0? 0 (reciprocal) ≠ 1 Put any number here. When you multiply it by 0, you get 0, never 1.

20. Ch 4 Sec 3: Slide #20 Dividing Fractions If a, b, c, and d are numbers (but b, c, and d are not 0), then we have the following. a b c d ÷ a b d c = In other words, change division to multiplying by the reciprocal of the divisor.

21. Ch 4 Sec 3: Slide #21 1 4 3 1 Dividing Signed Fractions EXAMPLE 5 Dividing Signed Fractions (a) 3 4 = – 2 5 ÷ 8 15 – 2 5 ÷ 8 – = 2 5 15 8 – ReciprocalsChange division to multiplication

22. Ch 4 Sec 3: Slide #22 5 ÷ 1 4 Dividing Signed Fractions EXAMPLE 5 Dividing Signed Fractions 20 = (b)5 ÷ 1 4 = 5 1 4 1 ReciprocalsChange division to multiplication

23. Ch 4 Sec 3: Slide #23 Dividing Signed Fractions EXAMPLE 5 Dividing Signed Fractions (c)0 ÷ 4 9 Division by zero is undefined.

24. Ch 4 Sec 3: Slide #24 11 11 1 1 a2a2 b3b3 2 b 2 a Dividing Fractions with Variables EXAMPLE 6 Dividing Fractions with Variables a a 2 b b b b b a = (a) a2a2 b3b3 ÷ a 2 b 2 = 2a2a b

25. Ch 4 Sec 3: Slide #25 Dividing Fractions with Variables EXAMPLE 6 Dividing Fractions with Variables 11 11 1 1 n3n3 6 1 n4n4 n n n 1 2 3 n n n n = (b) n3n3 6 ÷ n4n4 = 1 6n6n

26. Ch 4 Sec 3: Slide #26 Indicator Words Indicator Words for Multiplication Indicator Words for Division product double triple times twice of (when of follows a fraction) per each goes into divided by divided into divided equally

27. Ch 4 Sec 3: Slide #27 EXAMPLE 7 Using Indicator Words – Solving Applications (a)Alberto will spend of his paycheck on his bills. If Alberto receives a paycheck for $480, how much will he spend on his bills? 1 6 1 6 of 480= 1 6 480 1 =80 Alberto will spend $80 on his bills. 80 1 Using Indicator Words to Solve Application Problems

28. Ch 4 Sec 3: Slide #28 EXAMPLE 7 Using a Sketch – Solving Applications (b)Bina purchased a spool containing 36 yd of ribbon. She wants to make awards for a banquet. If each award requires yd of ribbon, how many awards can she make? 2 3 2 3 36 ÷ = 36 1 3 2 =54 Bina can make 54 awards. 18 1 36 yd of ribbon 2 3 yd Using a Sketch to Solve Application Problems

29. Ch 4 Sec 3: Slide #29 Multiplying and Dividing Signed Fractions Chapter 4 Section 3 – Completed Written by John T. Wallace