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Fractions Review

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Fractions Review: How to add, subtract, multiply and divide fractions and mixed numbers Compiled and adapted by Lauren McCluskey from several power points by Monica ... – PowerPoint PPT presentation

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Title: Fractions Review


1
Fractions Review
  • How to add, subtract, multiply and divide
    fractions and mixed numbers

Compiled and adapted by Lauren McCluskey from
several power points by Monica Yuskaitis
2
This power point would not have been possible
without Monica Yuskaitis.
3
Parts of a Fraction
3
numerator
denominator
4
By Monica Yuskaitis
4
Parts of a Fraction
3
numerator
denominator
4
dividend
3
divisor
4
Which means34
By Monica Yuskaitis
5
¾ looks like
Or 75 of the whole
1/4
1/4
1/4
If you think about money, ¾ of a dollar equals
0.75 or 75 cents.
By Monica Yuskaitis
6
Or ¾ might look like
1/4
0.25ft.
1/4
0.25ft
75 of the whole
1/4
0.25ft
0.25ft
If the rectangle is 1 foot high, then each
section is 0.25 ft.
By Monica Yuskaitis
7
How much of 4 is 3?
  • To find how big a portion you have, divide the
    numerator by the denominator.
  • 34 0.75
  • or 75
  • So ¾ 75

8
How many quarters are in a whole?
4
?
1/4 1/4 1/4 1/4
14 1/4
1 ¼ 4
By Monica Yuskaitis
9
4
1 4/4
1/4 1/4 1/4 1/4
14 1/4
1 ¼ 4
By Monica Yuskaitis
10
How many quarters are in a half?
1/4
2
1/4
½ 1/4 2
Or 2 quarters equals ½ dollar.
By Monica Yuskaitis
11
Equivalent Fractions
  • Name the same amount but have different
    numerators and denominators.
  • Or Half a dollar 2 quarters.

1
2
1
1

4
2
4
2
1
4
By Monica Yuskaitis
12
Equivalent Fraction Models
¼2/8
1/8
1/8
1/4
1/4
1/8
1/8
1/8
1/4
1/8
1/4
1/8
So if you have 3 times as much, you have
3
6

4
8
By M.Yuskaitis
13
To Find Equivalent Fractions
  • Multiply the numerator and the denominator by
    the same number.
  • Or

1
3
3
x

3
3
9
By Monica Yuskaitis
14
To Find Equivalent Fractions
  • Divide the numerator and the denominator by the
    same number.

4
4
1


12
4
3
By Monica Yuskaitis
15
Adding Like Denominators
Only add the numerators
1/4
1/4
3
1
4


4
4
4
1/4
1/4
By Monica Yuskaitis
16
Subtracting Like Denominators
Only subtract the numerators
1/4
1/4
4
1
3
-

4
4
4
1/4
1/4
By Monica Yuskaitis
17
To Add or Subtract Fractions with Unlike
Denominators
  • 1/3 1/6 ?
  • 1/3 1/9 ?
  • Rewrite each fraction using the least common
    multiple.

18
Common Multiple
  • A number that is a multiple of two or more
    numbers.

Some multiples of 3 6 6, 12, 18, 24, 30, 36,
42
By Monica Yuskaitis
19
Shortcut for Finding the Least Common Denominator
or Least Common Multiple
Check to see if the smaller denominator divides
evenly into the larger denominator.
1
3
1
3 will divide evenly into 9, so 9 is your LCD or
LCM.

9
By Monica Yuskaitis
20
To Add or Subtract Fractions With Unlike
Denominators
  • Rewrite the fractions using the least common
    denominator or least common multiple.

1

5
1


10
By Monica Yuskaitis
21
To Add or Subtract Fractions With Unlike
Denominators
  • Now just add the numerators.

1
x 2
5
10
x 2
Remember when adding fractions you never add the
denominators.
1
1

10
10
10
By Monica Yuskaitis
22
Subtract these Fractions
Use the short cut to find the Least
Common Denominator (LCD).
1
2
1
-
8
By Monica Yuskaitis
23
Mixed Numbers
  • Mixed numbers are whole numbers and fractions
    together.

1
3
1
1
1
½

2
By Monica Yuskaitis
24
Shortcut for Finding the Least Common Denominator
Check to see if the smaller denominator divides
evenly into the larger denominator. If it does,
use the larger denominator for your LCD.
By Monica Yuskaitis
25
Shortcut for Finding the Least Common Denominator
2 will divide evenly into 8, so 8 is your LCD or
LCM.
1
3
2
1
1

8
By Monica Yuskaitis
26
To Add Mixed Numbers With Unlike Denominators
  • Find the multiples of each denominator.

1
3
4, 8, 12, 16, 20, 30
4
1
1

10, 20, 30, 40, 50
10
By Monica Yuskaitis
27
  • Compare the lists of multiples. Circle the
    common multiples between the two lists.

1
3
4, 8, 12, 16, 20, 24
4
1
1
10, 20, 30, 40, 50

10
By Monica Yuskaitis
28
  • Find the equivalent fractions for 1/4 1/10
    with 20 as the denominator.

Ask yourself what you multiply 4 by to get 20.
1
3
4
20
x 5
1
1

10
20
By Monica Yuskaitis
29
To Subtract Two Mixed Numbers with Unlike
Denominators
  • Borrow 1 whole. Rename. Add to what you already
    had, then subtract.
  • 2
  • answer

/
1
1
20
5
25



20
20
20
4
-
8
1
8
4

20
10
20
17
20
30
Try it!
1
  • 3
  • - 1
  • Answer ?

2
3
5
31
  • Answer 1 9/10
  • How did you do?

32
When would you multiply a fraction by a fraction?
  • Your family eats 1/8 of 1/2 of a left-over
    wedding cake.
  • 1/8 of 1/2 or 1/8 x 1/2

By Monica Yuskaitis
33
  • Jose had already read 1/2 of his novel. Today
    he read 1/12 of the 1/2 left. How much of the
    book has he read?
  • 1/12 of 1/2 1/24
  • or
  • 1/12 x 1/2 1/24

By Monica Yuskaitis
34
Multiplying Fractions
  • When you multiply two fractions that are between
    0 and 1 the product is smaller than both
    fractions.

By Monica Yuskaitis
35
Multiplying Fractions
½ x ¾ 3/8
Look at the diagram on the next slide to
understand why.
By Monica Yuskaitis
36
Multiplying Fractions
½ x ¾ 3/8
½ of ¼ 1/8
¼
¼
¼
¼
1/8
1/8
1/8
By Monica Yuskaitis
37
How to Find a Fraction of a Fraction
  • When you see a fraction problem with the word
    of, multiply.

1
4
x
of
2
9
By Monica Yuskaitis
38
  • Multiply your numerators straight across.

x 4
1
4

9
2
By Monica Yuskaitis
39
  • Then multiply your denominators straight across.

x 4
1
4

9
2
18
By Monica Yuskaitis
40
  • Simplify your answer. In this case we reduce.

x 4
1
4
2
2



9
2
18
2
9

By Monica Yuskaitis
41
When would you multiply a fraction and a whole
number?
  • You walk a 4 mile route halfway.
  • ½ of 4 or ½ x 4
  • You walk a ¾ mile route twice.
  • 2 x ¾

By Monica Yuskaitis
42
  • A 12 ticket to the magic show is on sale for 2/3
    of the original price.
  • 2/3 of 12 or 2/3 x 12

By Monica Yuskaitis
43
How to Find the Fraction of a Whole Number
  • The first thing to remember is of means
    multiply in mathematics.

of

X (times)
By M. Yuskaitis
44
  • Multiply.

1
x
of 46
2
By Monica Yuskaitis
45
  • Change your whole number to a fraction by adding
    a one underneath.

1
x 46
2
1
By Monica Yuskaitis
46
  • Multiply your numerators straight across.

x 46
1
46

1
2
By Monica Yuskaitis
47
  • Multiply your denominators straight across.

x 46
1
46

1
2
2
By Monica Yuskaitis
48
  • Simplify your answer. In this case we change an
    improper fraction to a mixed number or a whole
    number.

23
x 46
1
46
2)

46
1
2
2
By Monica Yuskaitis
49
Cross Simplifying
  • Sometimes you can cross simplify before you
    multiply instead of afterwards.

50
Cross Simplifying

46
1

X
1
2
23
1 X 46
462 23

1
2 X 1
22 1
51
When would you multiply a mixed number by a
fraction?
  • In a car race, the track is 2 ¼ miles long. If
    the car breaks down ½ way through the course, how
    far did you go?
  • 1/2 of 2 1/4 or 1/2 x 2 1/4

By Monica Yuskaitis
52
Multiplying Fractions
  • When you multiply a positive mixed number by a
    fraction between 0 and 1 the product is less than
    the mixed number.

By Monica Yuskaitis
53
Multiplying Fractions
1¼ x ½ 5/8
Look at the diagram on the next slide to
understand why.
By Monica Yuskaitis
54
Multiplying Fractions
1¼ x ½ 5/8
½ of ¼ 1/8
¼
¼
¼
¼
1/8
1/8
1/8
1/8
¼
¼
¼
¼
1/8
By Monica Yuskaitis
55
How to Find a Fraction of a Mixed Number
  • The first thing to remember is of means
    multiply in mathematics.

X (times)
of

By M. Yuskaitis
56
  • When you see a fraction problem with the word
    of in it, you multiply.

1
4
x
of
3
2
9
By Monica Yuskaitis
57
  • First change the mixed number to an improper
    fraction.

27 4
1
4
31

x
3
2
9
9
x
27
By Monica Yuskaitis
58
  • Then multiply the numerators straight across.

1
31
31
x

2
9
By Monica Yuskaitis
59
  • Next multiply the denominators straight across.

1
31
31
x

2
9
18
By Monica Yuskaitis
60
  • Lastly simplify your answer. In this case change
    the improper fraction to a mixed number.

13
1
18
1
31
31
18)
31
x

2
9
18
18
13
By Monica Yuskaitis
61
Dividing Mixed Numbers
2½ ¾ ?
  • Ask yourself How many 3/4s are there in 2 1/2?

1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
Graphics By M.Yuskaitis
62
Dividing Mixed Numbers
2½ ¾ ?
½ of ¼ 1/8
¼
¼
¼
¼
1/4
1/4
¼
1/4
1/4
1/4
1/4
1/4
1/4
Graphics By M.Yuskaitis
63
2½ ¾ ?
  • Answer There are 3 1/3 (¾s) in 2 ½.

64
Dividing Mixed Numbers and Fractions
  • Multiply the first number by the reciprocal of
    the second number. (To find the reciprocal flip
    it!)
  • (The reciprocal of 1/4 is 4/1)

65
Dividing Mixed Numbers and Fractions
5 ¼ ¼ ? 1) Change 5 ¼ into an improper
fraction 5 1/4 21/4 2)Multiply 21/4 4/1
84/4 3) Simplify 84/4 21
66
5 ¼ ¼
  • In other words, there are 21 fourths in 5 1/4.

67
Try it!
3 ¾ ¾ ?
68
Answer 5In other words, there are 5 3/4s in 3
3/4.
69
Credits
Monica Yuskaitis and Clipart from Microsoft
Clip Gallery located on the Internet at
http//cgl.microsoft.com/ clipgallerylive/default.
asp
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