1. Lesson 2.4 Multiplying Rational Numbers (Fractions)
Day 1
Lesson 2.4 Multiplying Rational Numbers (Fractions)
Students will be able to multiply rational numbers.
core-instruction-5nbt

2. Worksheet: Multiplying and Dividing fractions and mixed numbers #1-10
Homework 11/1/2016
Worksheet: Multiplying and Dividing fractions and mixed numbers #1-10

3. Change mixed number into improper
(whole times the denominator) plus the numerator
4 5 7
(4)(7) = 28
28 +5 = 33
33 7

4. How do you change an integer into a fraction?
For example: 9 By adding a 1 in the denominator 9 1

5. RULES
Positive x Positive = Positive
Positive x Negative = Negative
Negative x Negative = Positive
Negative x Positive = Negative
An odd number of Negatives multiplied together gives a negative result.
An even number of Negatives multiplied together gives a positive result.

6. EXAMPLES: Positive x Positive = Positive x Negative =
Negative x Negative =
(-8) x (+9)
Negative x Positive =
(-4) x (-2) x (-3)
Odd number of Negatives =
(-1) x (-9) x (-3) x (-2)
Even number of Negatives =

7. = + 40 = Positive = - 42 = Negative = + 12 = Positive = - 72
(8) x (+5)
Positive x Positive
(+7) x (-6)
Positive x Negative
(-4) x (-3)
Negative x Negative
(-8) x (+9)
Negative x Positive
(-4) x (-2) x (-3)
Odd number of Negatives
(-1) x (-9) x (-3) x (-2)
Even number of Negatives
= + 40
= Positive
= - 42
= Negative
= + 12
= Positive
= - 72
= Negative
= - 24
= Negative
= + 54
= Positive

8. Multiply Fractions & Mixed Numbers
Change any mixed #s into improper fractions.
When multiplying fractions, they do NOT need to have a common denominator.
Figure out the sign. Negative answer or positive answer?
Multiply numerators.
Multiply denominators.
Simplify. (You can also simplify before you multiply.)

9. YouTube

10. EXAMPLES 3 5 3 5 x = 2 5 -3 4 x = -4 7 -3 8 x =

11. EXAMPLES 3 5 3 5 9 25 x =
POSITIVE x POSITIVE = POSITIVE 2 5 -3 4 x = -4 7 -3 8 x =

12. EXAMPLES 3 5 3 5 9 25 x = 2 5 -3 4 -6 20
POSITIVE x NEGATIVE = NEGATIVE x = -4 7 -3 8 x =

13. EXAMPLES 3 5 3 5 9 25 x = 2 5 -3 4 -6 20 x =
NEGATIVE x NEGATIVE = POSITIVE -4 7 -3 8 12 56 x =

14. MORE EXAMPLES -4 -5 -3 6 x = 2 5
(2) 2 = -2 3 -3 4 -3 -2 x x =

15. MORE EXAMPLES
-12 30 -4 -5 -3 6 x = 2 5
(-2) 2 = -2 3 -3 4 -3 -2 x x =

16. -4 -5 -3 6 -12 30 -2 5 2 5 (-2) -2 3 -3 4 -3 -2 MORE EXAMPLES 2
ODD Number of Negatives = Negative = x =
Reduced to LOWEST TERMS 2 5
(-2) 2 = -2 3 -3 4 -3 -2 x x =

17. -2 5 -4 -5 -3 6 2 5 12 5 -2 1 -2 -2 3 -3 4 -3 -2 MORE EXAMPLES 2 x =
CHANGE MIXED TO AN IMPROPER FRACTION 2 5 12 5 -2 1 -2 2 x = x = -2 3 -3 4 -3 -2 x x =

18. -2 5 -4 -5 -3 6 2 5 12 5 -2 1 -24 5 (-2) -2 3 -3 4 -3 -2 MORE EXAMPLES= 2 5 12 5 -2 1
-24 5
(-2) 2 = x = = -2 3 -3 4 -3 -2 x x =

19. MORE EXAMPLES -2 5 -4 -5 -3 6 x =
Change back to mixed and reduce fraction 2 5 12 5 -2 1
-24 5 4 5
(-2) 2 -4 = x = =
Positive x Negative = Negative -2 3 -3 4 -3 -2 x x =

20. -2 5 -4 -5 -3 6 2 5 -2 1 4 5 -2 3 -3 4 -3 -2 18 24 MORE EXAMPLES 2 -5= 2 5 -2 1 4 5 2 -5 x = -2 3 -3 4 -3 -2 18 24 x x =

21. -2 5 -4 -5 -3 6 2 5 -3 4 4 5 -2 3 -3 4 -3 -2 18 24 3 4 MORE EXAMPLES 2= 2 5 -3 4
EVEN Number of Negatives = Positive 4 5 2 -1 x =
Reduce to LOWEST TERMS -2 3 -3 4 -3 -2 18 24 3 4 x x = =

22. TRY THESE -4 5 3 7 = x -5 8 3 -7 -2 -4 x x = 1 6 3 7 -1 x =

23. TRY THESE -4 5 3 7
-12 35 = x -5 8 3 -7 -2 -4 x x = 1 6 3 7 -1 x =

24. TRY THESE -4 5 3 7
-12 35 = x -5 8 3 -7 -2 -4 30
224 15
112 x x = = 1 6 3 7 -1 x =

25. TRY THESE -4 5 3 7
-12 35 = x -5 8 3 -7 -2 -4 30
224 15
112 x x = = 1 6 3 7 1 6
-10 7
-10 42 -5 21 -1 x = x = =

26. Mixed Numbers
To multiply mixed numbers, convert them to improper fractions first. 1

27. Try These: Multiply
Multiply the following fractions and mixed numbers:

28. Solutions: Multiply

29. Solutions (alternative): Multiply
Note: Problems 1, 2 and 4 could have been simplified before multiplying. 1 2 2 1 1 2 1 3 1 3

30. Lesson 2.4 Dividing Rational Numbers (Fractions)
Day 2
Lesson 2.4 Dividing Rational Numbers (Fractions)
Students will be able to divide rational numbers.

31. Warm-Up #29 (11/2/16) -4 5 3 7 -5 8 3 -7 -2 -4 1 6 3 7 -1 = x x x = x

32. Homework (11/2/16)
Multiplying and Dividing Fractions and Mixed Numbers #11-20

33. Homework Solutions −5 12 6. -10 14 15 4 5 7. 3 17 20 7 9 8. −11 1 4
−5 6
−6 7
8. −11 1 4

34. RULES
Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Negative = Positive
Negative ÷ Positive = Negative
An odd number of Negatives divided together gives a negative result.
An even number of Negatives divided together gives a positive result.

35. Divide Fractions & Mixed Numbers
Change any mixed #s into improper fractions.
When dividing fractions, they do NOT need to have a common denominator.
Figure out the sign. Negative answer or positive answer?
To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction. Keep-Change-Change.
Simplify. (You can also simplify before you multiply.)

36. To find the reciprocal of a fraction, exchange the numerator and the denominator.

37. Dividing Fractions
Change Operation.
Flip 2nd Fraction.

38. Dividing Fractions
Finish the problem by following the rules for multiplying fractions.

39. Youtube

40. Try These: Divide
Divide the following fractions & mixed numbers:

41. Solutions: Divide

42. Additional Example 1A: Dividing Fractions
Divide. Write the answer in simplest form.
5 11
1 2 A. ÷
5 11 ÷
1 2
5 11 •
2 1 =
Multiply by the reciprocal.
5 11 •
2 1 =
No common factors.
10 11 =
Simplest form

43. Stand Quietly

44. Lesson 2.4 Multiplying Rational Numbers (Decimals)
Day 3
Lesson 2.4 Multiplying Rational Numbers (Decimals)
Students will be able to multiplying rational numbers.

45. Warm-Up #30 (11/3/16)
Divide the following fractions & mixed numbers:

46. Homework (11/3/16)
Worksheet: Multiplying Decimals Front page

47. Homework Solutions −4 35 16. −1 5 27 −2 5 17. 10 19 1 1 20 18. −1 12
7 16
15. −9 10
16. −1 5 27
−1 12
20. −

48. Steps
Determine the sign of your answer. Negative answer or positive answer?
Multiply numbers as normal.
Count the spaces behind each decimal.
Place the decimal based on the total decimal values.

49. YouTube

50. Multiplying Decimal Numbers
1 place
+ 2 places
7.6
0.24
304
+ 1520
1824
3 places
1.824
–1.824
Different signs = negative.

51. Multiplying Decimal Numbers
1 place
+ 1 places
6.6
0.5
330
2 places
3.30
Same signs = positive.
3.30

52. Lesson 2.4 Dividing Rational Numbers (Decimals)
Day 4
Lesson 2.4 Dividing Rational Numbers (Decimals)
Students will be able to divide rational numbers.

53. Worksheet: Multiplying Decimals Back page
Homework 11/4/16
Worksheet: Multiplying Decimals Back page

54. YouTube

55. Different ways to write division
−4÷13  − 

56. Division Involving 0
Undefined
Undefined
Indeterminate

57. Division Involving 0 Undefined. Indeterminate. What times 0 equals 3?

58. Steps Determine the sign. Negative answer or positive answer
No need to have the sign when divide
Change the division into a fraction
Look at the denominator. If it is a whole number, then you can continue dividing. If it is not a whole number, then multiply both numerator and the denominator by the decimal value of the denominator so you can divide by a whole number.
Rewrite the new fraction
But the new fraction into the division house D N

59. 1.32
0.4
1.32
0.4 10
13.2 4 = =
1 decimal place
1 zero

60. Additional Example 1: Dividing Decimals
Find ÷ 0.24.
0.384
0.24
0.384 ÷ 0.24 =
100
38.4 24 =
38.4 24 =
Divide. =
1.6

61. Check It Out: Example 2
Find ÷ 0.25.
0.585
0.25
0.585 ÷ 0.25 =
100
58.5 25 =
58.5 25 =
Divide. =
2.34

62. Dividing Decimal Numbers
Move the decimal point in the divisor so it is an integer.
Move the decimal point in the dividend the same number of places.
Place the decimal in the quotient directly above the new decimal point in the dividend.

63. Dividing Decimal Numbers 44.64 ÷ (3.6)
Same signs = positive.
12.4

64. Copyright © 2011 Pearson Education, Inc.
Divide
14.7 ÷ (0.03) a)
49 b) 49 c)
490 d)
490
Copyright © 2011 Pearson Education, Inc.
1.4

65. Copyright © 2011 Pearson Education, Inc.
Divide
14.7 ÷ (0.03) a)
49 b) 49 c)
490 d)
490
Copyright © 2011 Pearson Education, Inc.
1.4