Title: Fractions Review
1Fractions 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
2This power point would not have been possible
without Monica Yuskaitis.
3Parts of a Fraction
3
numerator
denominator
4
By Monica Yuskaitis
4Parts of a Fraction
3
numerator
denominator
4
dividend
3
divisor
4
Which means34
By Monica Yuskaitis
5¾ 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
6Or 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
7How 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
8How many quarters are in a whole?
4
?
1/4 1/4 1/4 1/4
14 1/4
1 ¼ 4
By Monica Yuskaitis
94
1 4/4
1/4 1/4 1/4 1/4
14 1/4
1 ¼ 4
By Monica Yuskaitis
10How many quarters are in a half?
1/4
2
1/4
½ 1/4 2
Or 2 quarters equals ½ dollar.
By Monica Yuskaitis
11Equivalent 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
12Equivalent 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
13To Find Equivalent Fractions
 Multiply the numerator and the denominator by
the same number.  Or
1
3
3
x
3
3
9
By Monica Yuskaitis
14To Find Equivalent Fractions
 Divide the numerator and the denominator by the
same number.
4
4
1
12
4
3
By Monica Yuskaitis
15Adding Like Denominators
Only add the numerators
1/4
1/4
3
1
4
4
4
4
1/4
1/4
By Monica Yuskaitis
16Subtracting Like Denominators
Only subtract the numerators
1/4
1/4
4
1
3

4
4
4
1/4
1/4
By Monica Yuskaitis
17To Add or Subtract Fractions with Unlike
Denominators
 1/3 1/6 ?
 1/3 1/9 ?
 Rewrite each fraction using the least common
multiple.
18Common 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
19Shortcut 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
20To 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
21To 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
22Subtract these Fractions
Use the short cut to find the Least
Common Denominator (LCD).
1
2
1

8
By Monica Yuskaitis
23Mixed Numbers
 Mixed numbers are whole numbers and fractions
together.
1
3
1
1
1
½
2
By Monica Yuskaitis
24Shortcut 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
25Shortcut 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
26To 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
29To 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
30Try it!
1
2
3
5
31 Answer 1 9/10
 How did you do?
32When would you multiply a fraction by a fraction?
 Your family eats 1/8 of 1/2 of a leftover
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
34Multiplying Fractions
 When you multiply two fractions that are between
0 and 1 the product is smaller than both
fractions.
By Monica Yuskaitis
35Multiplying Fractions
½ x ¾ 3/8
Look at the diagram on the next slide to
understand why.
By Monica Yuskaitis
36Multiplying Fractions
½ x ¾ 3/8
½ of ¼ 1/8
¼
¼
¼
¼
1/8
1/8
1/8
By Monica Yuskaitis
37How 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
41When 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
43How 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
441
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
49Cross Simplifying
 Sometimes you can cross simplify before you
multiply instead of afterwards.
50Cross Simplifying
46
1
X
1
2
23
1 X 46
462 23
1
2 X 1
22 1
51When 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
52Multiplying 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
53Multiplying Fractions
1¼ x ½ 5/8
Look at the diagram on the next slide to
understand why.
By Monica Yuskaitis
54Multiplying 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
55How 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
61Dividing 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
62Dividing 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
632½ ¾ ?
 Answer There are 3 1/3 (¾s) in 2 ½.
64Dividing 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)
65Dividing 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
665 ¼ ¼
 In other words, there are 21 fourths in 5 1/4.
67Try it!
3 ¾ ¾ ?
68Answer 5In other words, there are 5 3/4s in 3
3/4.
69Credits
Monica Yuskaitis and Clipart from Microsoft
Clip Gallery located on the Internet at
http//cgl.microsoft.com/ clipgallerylive/default.
asp