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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 Yuskaitis
This power point would not
have been possible without
Monica Yuskaitis.
Parts of a Fraction
3 = numerator
4 = denominator
3
= dividend
4
= divisor
Which means…3÷4
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.
¾ looks like
Or 75% of the whole
1/4
1/4
1/4
If the rectangle is 1 foot high,
then each section is 0.25 ft.
How much of 4 is 3?
 To
find how big a portion you
have, divide the numerator by the
denominator.
3÷4 = 0.75
or 75%
So ¾ = 75%
How many quarters are in a whole?
4
1= 4/4
1/4 1/4
1/4 1/4
1÷4 = 1/4
1÷ ¼ = 4
How many quarters are in a half?
½ ÷1/4 = 2
1/4
1/4
2
Or: 2 quarters equals ½ dollar.
Equivalent Fractions
Name the same amount but have
different numerators and
denominators.
 Or: Half a dollar = 2 quarters.

1
2
1 = 2
2
4
1
4
1
4
Equivalent Fraction Models
¼=2/8
1/8
1/4
1/4
1/8
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
4
=
6
8
To Find Equivalent Fractions

Multiply the numerator and the
denominator by the same number.
1 x 3
3
=
3
3
9

Or…
To Find Equivalent Fractions

Divide the numerator and the
denominator by the same
number.
4 ÷ 4
1
=
12
4
3
Adding Like Denominators
Only add the numerators
3 + 1
4
=
4
4
4
1/4 1/4
1/4 1/4
Subtracting Like Denominators
Only subtract the numerators
4 - 1
3
=
4
4
4
1/4 1/4
1/4 1/4
To Add or Subtract Fractions
with Unlike Denominators:
 1/3

+ 1/6 = ?
1/3 + 1/9 = ?
 Rewrite
each fraction using the
least common multiple.
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
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
+ 9
3 will divide evenly into 9,
so 9 is your LCD or LCM.
To Add or Subtract Fractions
With Unlike Denominators

Rewrite the fractions using the least
common denominator or least
common multiple.
1 =
5
1 =
+10

To Add or Subtract Fractions
With Unlike Denominators
Now just add the numerators.
1x 2 =
5 x 2 = 10
1
1
+10
10
10
Remember when
adding fractions
you never add the
denominators.
Subtract these Fractions
1
2
1
- 8
Use the short
cut to find the
Least Common
Denominator
(LCD).
Mixed Numbers

Mixed numbers are whole
numbers and fractions together.
1
3 2 =
½
1
1
1
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 or LCM.
1
3 2
1
+ 1 8
2 will divide evenly into 8,
so 8 is your LCD or LCM.
To Add Mixed Numbers With
Unlike Denominators

Find the multiples of each
denominator.
1
3
4 = 4, 8, 12, 16, 20, 30
1
1
+ 10 = 10, 20, 30, 40, 50

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
3
4 x 5 =20
1
1
+ 10
20
Ask yourself what
you multiply 4 by
to get 20.
To Subtract Two Mixed Numbers
with Unlike Denominators
 Borrow 1 whole. Rename. Add to
what you already had, then
subtract.
1
/2 1 = 5 20 = 25
- 1
20
4
8
4
= 20
10
+
20
answer=
20
8
20
17
20
Try it!
3
- 1
-
1
2
3
5
Answer= ?
Answer= 1 9/10
How did you do?
When 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
1/ *
8
½=?
 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 or 1/12 x 1/2
Multiplying Fractions

When you multiply two fractions that are
between 0 and 1 the product is smaller
than both fractions.
½x¾=
3/
8
Look at the diagram on the
next slide to understand why.
Multiplying Fractions
½ x ¾ = 3/8
½ of ¼ = 1/8
¼
¼
¼
1/8
1/8
1/8
¼
How to Find a Fraction of a
Fraction:

When you see a fraction problem
with the word “of”, multiply.
1 of
4
x
2
9

Multiply your numerators straight
across.
1 x 4 = 4
2
9

Then multiply your denominators
straight across.
1 x 4 = 4
2
9 18

Simplify your answer. In this
case we reduce.
1 x 4 = 4 ÷ 2= 2
2
9 18 ÷ 2 9
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.
2x¾

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
How to Find the Fraction of
a Whole Number

The first thing to remember is “of”
means multiply in mathematics.
=
X
of
(times)
 Multiply.
1 of
46
x
2
 Change
your whole number to a
fraction by adding a one underneath.
1 x 46
2
1
 Multiply
across.
your numerators straight
1 x 46 = 46
2
1
 Multiply
across.
your denominators straight
1 x 46 = 46
2
1
2

Simplify your answer. In this case
we change an improper fraction to a
mixed number or a whole number.
23
1 x 46 = 46 2)46
2
1
2
Cross Simplifying:

Sometimes you can cross simplify before
you multiply instead of afterwards.
1 X 46 =
1
2
1 X 46
46÷2= 23
2 X 1 2÷2 = 1
=
23
1
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
Multiplying Fractions

When you multiply a positive mixed
number by a fraction between 0 and 1 the
product is less than the mixed number.
1¼ x ½ =
5/
8
Look at the diagram on the
next slide to understand why.
Multiplying Fractions
½ of ¼= 1/8
1¼ x ½ = 5/8
¼
¼
¼
¼
1/8
1/8
1/8
1/8
¼
¼
¼
¼
1/8
How to Find a Fraction of a
Mixed Number

The first thing to remember is “of”
means multiply in mathematics.
=
of
X
(times)
 When
you see a fraction problem
with the word “of” in it, you multiply.
1 of
4
x
3
2
9
 First
change the mixed number to
an improper fraction.
27 + 4
+
x
1 x 3 4 31
2 27 9 9

Then multiply the numerators
straight across.
1 x 31 = 31
2
9
 Next
multiply the denominators
straight across.
1 x 31 = 31
2
9 18
 Lastly
simplify your answer. In this
case change the improper fraction to
a mixed number.
13
18
1
1 x 31 = 31 18)31
2 9 18
18
13
Dividing Mixed Numbers
2½ ÷ ¾ = ?
½ of ¼ = 1/8
¼
1/4
1/4
1/4
1/4
¼
¼
1/4
1/4
1/4
1/4
¼
¼
2½ ÷ ¾ = ?
Answer= There are 3 1/3 (¾’s)
in 2 ½.
Dividing Mixed Numbers and
Fractions

Multiply the first number by the reciprocal
of the second number. (To find the
reciprocal flip it!)
5 ¼ ÷ ¼ = ? (The reciprocal is 4/1…)
Change 5 ¼ into an improper fraction:
5 = 20/4
20/4 + ¼ = 21/4
21/4 * 4/1 = 84/4 Simplify: 21
Try it!
3¾÷¾=?
Answer= 5
Credits
Monica Yuskaitis
and
Clipart from “Microsoft Clip
Gallery” located on the Internet
at http://cgl.microsoft.com/
clipgallerylive/default.asp