1. Fractions
Ms. Crusenberry
9-2013

2. Vocabulary Fraction – part of a whole number
Numerator – the number of parts that are used; the number above the fraction line
Denominator – the number of parts to the whole; the number below the fraction line

3. Write the fraction

4. Comparing Fractions
Cross Product – the answer obtained by multiplying the denominator of one fraction by the numerator of another aka cross multiplication Greater than > or Less than < multiply 2 x 5 first = > 4 multiply 3 x 3 last = 9

5. Practice

6. Answers 6 x 6 = 12 < 8 x 5 = 40 7 x 6 = 42 > 8 x 6 = 40

7. Simplifying Fractions
Simplest form – a fraction in which the numerator and denominator have no common factor greater than one
Simplify – to express in simplest form

8. Example
14 ÷ 2 = 7 16 ÷ 2 = 8 What is the greatest common factor? x 14 1 x 16 2 x 7 2 x 8 4 x 4 2 is the greatest common factor

9. Practice
4/18
12/42
27/81
13/39
80/120
55/121
12/15
45/50

10. Answers
2/9
2/7
1/3
2/3
5/11
4/5
9/10

11. Mixed Number/Improper Fractions
Mixed number – number composed of a whole number and a fraction ex. 1 ½
Improper fraction – fractions who numerators are equal to or greater than their denominators ex. 50/10

12. Renaming Mixed Numbers as Improper Fractions
Step 1 – multiple the whole number by the denominator
Step 2 – add the numerator
Step 3 – Write the answer over the denominator Ex. 3 ½ x =

13. Practice
2 ¾
8 3/7
5 ½
6 2/9
23 2/5
10 ¾

14. Answers
11/4
59/7
11/2
56/9
115/5
43/4

15. Renaming Improper Fractions as Mixed Numbers
Ex. 18/5 Step 1 – divide 18 by so, its 3 3/ **The number left is the new numerator and you always keep the denominator

16. Practice
32/6
61/4
235/4
79/5
19/2
80/8

17. Answers
5 1/3
15 ¼
5/ ¾
15 4/5
9 ½ 10

18. Writing Mixed Numbers in Simplest Form
3 2/4 - 2/4 simplifies to ½, so your answer is 3 ½
5 16/8 – 16/8 simplifies to 2, so you add that whole number to the one in the mixed number to get the answer 7
4 7/6 – 7/6 simplifies to 1 1/6 – so you add that whole number to the one in the mixed number to get the answer 5 1/6

19. Practice
6 5/15
17 13/10
7 6/3
6 4/3
10 25/6

20. Answers
6 1/3
18 3/10 9
7 1/3
14 1/6

21. Multiplying Fractions
Ex. 2/7 x 4/5 Step 1 – multiply the numerators 2 x 4 = 8 Step 2 – multiply the denominators 7 x 5 = 35 Answer is 8/35

22. Continued…
Ex. 6 x 4/7 Step 1 – make the whole number a 6 a fraction by putting it over 1 Step 2 – multiply the numerators 6 x 4 = 24 Step 3 – multiply the denominators 1 x 7 = 7 Answer is 24/7 (must make an improper fraction) = 3 3/7

23. Practice
2/3 x 4/5
4/7 x 3/6
11/13 x 26/33
5/11 x 4/6
6/7 x 5/12

24. Answers
8/15
2/7
286/429
10/33
5/12

25. Using Cross Simplification
Ex. 9 x Step 1 - Check the first numerator with the second denominator; simply if possible 3 goes into both so 9 becomes a 3 and the 15 becomes a 5 Step 2 – Check the first denominator with the second numerator; simply if possible 2 goes in to both so 10 becomes 5 and 14 becomes 7 New problem is now: 3 x 7 = 21 **This does not simplify any further

26. Practice
4/9 x 7/12
6/12 x 2/12
3/16 of 8/9
4/9 of 7/12
7/10 x 5/28

27. Answers
7/27
1/12
1/6
1/8

28. Multiplying Mixed Numbers
Ex. 2 ¾ x 1 ½ Step 1: You must change mixed numbers to improper fractions before you can multiply them. 2 ¾ = 11/4 and 1 ½ = 3/2, so 11 x 3 = **you must rename to a mixed number, so the answer is 4 1/8

29. Practice
Cross simplify the improper fractions if you can before multiplying them.
1 ½ x 2 3/5
2 1/6 x 2/3
5 1/3 x 2 ½
5/6 x 2 3/10
3 5/6 x 3/8

30. Answers
3 9/10
1 4/9
13 1/3
1 11/12
1 7/16

31. Dividing Fractions
Ex. 5/7 ÷ 4/5 Step 1 – keep the first fraction Step 2 – change the ÷ to x Step 3 – do the reciprocal of 4/5, which is 5/4 5/7 x 5/4 = 25/28

32. Practice
Cross simplify if you can after you do the steps but before you divide
2/7 ÷ 5/6
3/8 ÷ ¾
4/7 ÷ 5/7
2/3 ÷ 5/6
3/13 ÷ 5/6
9 ÷ 9/10

33. Answers
5/21
4/5
18/65 10

34. Dividing Mixed Numbers
Just like multiplying mixed numbers, you must change the mixed numbers to improper fractions before you do anything else
Once that is done, change the ÷ to x and then do the reciprocal of the last improper fraction

35. Example
3 ½ ÷ 2 ½ - change to improper 7/2 ÷ 5/2 – change the sign and use reciprocal 7/2 x 2/5 – cross simplify if possible then multiply 7/1 x 1/5 = 7/5 (this is improper so fix it by changing it to a mixed number) Answer is 1 2/5

36. Practice
2 ¾ ÷ 5/6
1 1/3 ÷ ¼
2 2/7 ÷ 2 2/7
7 ½ ÷ 6 2/3
5 2/5 ÷ 1 1/5

37. Answers
3 3/10
5 1/3 1
1 1/8
4 ½

38. Adding Fractions with Like Denominators
Ex. 2/7 + 4/7 = 6/7 Step 1 – add the numerators Step 2 – carry over the denominator Step 3 – simplify if needed Ex. 2 4/ /5 = 8 7/5 = 9 2/5 Step 1 – add the whole numbers Step 2 – add the numerators Step 3 – carry over the denominator Step 4 – simply if needed

39. Practice 5/8 + 3/8 5/11 + 4/11 2 5/16 + 5 1/16 3 2/19 + 4 3/19
4 17/20 + 3/20

40. Answers 1
9/11
7 3/8
7 5/19 5

41. Subtracting with Like Denominators
You do these problems the exact same way as you did the addition, except you are subtracting the numbers Ex. 4/7 – 2/7 = 2/ /12 – 5 5/12 = 8 6/12 = 8 ½

42. Practice 7/8 – 3/8 11/12 – 1/12 25 4/5 – 6 3/5 13 3/13 – 2/13
19 19/21 – 5 5/21

43. Answers
5/6
19 1/5
13 1/13
14 2/3

44. Adding with Unlike Denominators
Common denominators – common multiples of two or more denominators
Least common denominator (LCD) – smallest denominator that is a multiple of two denominators

45. How to Solve these Problems
Step 1 – find the least common multiple of the denominators
Step 2 – use 12 as a new denominator
Step 3 – raise the fractions to higher terms
Step 4 – add the fractions, simplify if needed

46. Example
find the LCD (the smallest number that both 6 and will go into) 6 x 1 = 6 4 x 1 = 4 6 x 2 = x 2 = x 3 = 12
goes into 12 twice so 2 x 1 = 2; 4 goes into three times so 3 x 3 = 9
Answer is 11/12

47. Practice
2/7 + ¾
3/8 + 2/3
2/9 + 2/3
1/8 + 2/5
5/12 + 2/3

48. Answers
5/7
1 1/24
8/9
21/40
1 1/12

49. Subtraction with Unlike Denominators
Use solve the problems the exact same way as you did the addition problems except you are subtracting

50. Practice
8/9 – 1/3
2/3 – 2/5
2/3 – 2/7
4/5 – 1/3
7/10 – 1/2

51. Answers
5/9
4/15
8/21
7/15
1/5

52. Addition/Subtraction of Mixed Numbers
You will do these the exact same way with the exception of whether you add or subtract.
Step 1 – change all mixed numbers to improper fraction
Step 2 – find the LCD
Step 3 – add or subtract
Step 4 – simplify/rename into a mixed number

53. Example of Addition
6 3/ /3 45/7 + 10/3 – cross simplify when you can 15/7 + 10/1 – find the LCD (it is 7) 15/7 + 70/7 – add the numerators/carry denominator 85/7 – rename into a mixed number = 12 1/7

54. Example of Subtraction
18 5/ /8 113/6 – 19/8 – cross simplify when you can 113/6 – 19/8 – find the LCD (it is 24) 452/24 – 57/24 – subtract the numerators/carry denominator 395/24 – rename into a mixed number = 16 11/24

55. Practice
5 1/ /6
5 3/8 + ¼
2 3/ /10
11 5/8 + 13
2 1/ / /3

56. Answers
9 ½
5 5/8
8 27/40
24 5/8
7 5/8

57. Practice
5 6/7 – 4 2/3
10 9/10 – 3/20
9 5/6 – 3
8 15/16 – 2 ¼
5 2/3 – 2 2/5

58. Answers
1 4/21
10 ¾
6 5/6
6 11/16
3 4/15

59. Subtracting with Renaming
Step 1 – Rename the whole number as a mixed fraction Ex: 15 = 14 8/ /8 is equal to 1, so 1 plus = 15

60. Example – when missing the top fraction
/ / /8 13 5/8 Step 1 – rename 16 to an improper fraction of 15 8/8. I chose 8/8 because it is the denominator of the mixed number that determines this. Step 2 – perform the subtraction

61. Example – when you have numerators you cannot subtract
16 2/8 + 8/ / / /8 13 7/8 Step 1 – rename 16 to an improper fraction of 15 8/8. I chose 8/8 because it is the denominator of the fractions. Step 2 – add the 8/8 to the 2/8 to get 10/8 Step 3 – perform the subtraction

62. Example – when you have different denominators
15 2/7 = 15 6/ /21 = 14 27/21
4 8/ / /21
10 19/21
Step 1 – carry the whole numbers and then find LCD
Step rename 15 to an improper fraction
of 14 21/21. I chose 21/21 because it is the denominator of the fractions.
Step 2 – add the 21/21 to the 6/21 to get 27/21
Step 3 – perform the subtraction