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Fractions Review
Name:______________________________________
Equivalent Fractions: to create equivalent fractions, just multiply the numerator (top) and the
denominator (bottom) by the same number. WHY?
Example:
1 3 3 1
  ,  
3 3 9 3
,
1
 
3
All three of these answers and one third are equivalent
fractions!
Try: Write three equivalent fractions for each of the fractions below.
1
4
2
5
3
8
Reducing Fractions: You should reduce all fraction answers as much as possible. Reducing fractions
means that the top and the bottom don’t share any factors. One way to do this is to completely factor the
top and bottom then cross off any matches.
Example:
6 3 2

because there is a 2 on the top and the bottom we can cancel it out. WHY?
10 5  2
We’re left with
3
6
which is the reduced form of
. After you do this for awhile you can start to see a
5
10
shortcut of just dividing the top and bottom of the fraction by their shared factor.
Try to reduce the following fractions. If you need to list all the factors, do it then cross off any matches.
8
10
30
35
24
90
40
72
Challenge:
2940
3150
Fractions Review
Name:______________________________________
Mixed Fractions vs. Improper Fractions: Both of these fractions are seen in math. You should be
able to between the two, however, improper fractions are typically more useful and easiest to deal with.
So we’re going to focus on how to change mixed fractions to improper ones.
What we mean by mixed fraction: a mixed fraction is a whole number and a fraction together—like
2 12 . It
means you have 2 wholes and an additional half.
What we mean by improper fraction: an improper fraction is a fraction where the numerator is larger than
the denominator. For example,
15
.
2
It is typically easier to do the four arithmetic operations (adding, subtracting, multiplying, and dividing) with
improper fractions. So, how do you changed mixed fractions to improper ones?
Multiply the denominator by the whole number, then add the numerator. The answer is your numerator
and the denominator is what it was in the mixed number.
Example: Change
2 12 to an improper fraction. Denominator = 2, Whole number = 2, Numerator = 1.
5
2 x 2 = 4, 4+1 = 5, so 2 12 
2
Try to convert the following mixed fractions to improper fractions:
2 163
6 52
**For the rest of this review, we’ll assume that you should change any mixed fractions to improper
fractions before you do any operations.**
Multiplying Fractions: This is the easiest operation to do with fractions. You just multiply the two
numerators together and the two denominators together. You should also reduce your final answer.
Examples:
2 4
2 4
8
 

Can we reduce? What if you aren’t sure, what can you do?
3 15 3 15 45
2 18 36
 
Can we reduce?
9 4 36
Try to multiply the following fractions:
4 5

21 12
6 3

7 8
Sometimes we can take a shortcut if you have larger numbers:
3 21

7 17
Fractions Review
Name:______________________________________
Dividing Fractions: Dividing is also not that bad because you don’t need to have common
denominators. You just need to know that dividing by a number is the same thing as multiplying by the
reciprocal. (An easy example to think about is asking how many halves are there in 4? Is the same as
doing 4 times 2. One half and 2 are reciprocals.) Any time you are doing a division problem that has
fractions in it, just change it to a multiplication problem, then it’s not that bad.
Example:
5
6
5

3 9
3 4 12
   
Can we reduce this answer?
5 4
5 9 45
5
6
5
1
5 1
  
6 5
Try dividing the following fractions:
2
3
3
8
5 10

7 11
Common Denominators: Now that we’ve dealt with the “easy” operations to do with fractions we need
to talk about why adding and subtracting are harder—they require that the fractions being added or
subtracted have common (the same) denominators. Why? We already know how to find equivalent
fractions, now we need to focus on how to pick the denominator we want to be the “common” one.
Example: What common denominator should we use to be able to compare
2
3
and ? Looking at the
3
4
denominators of the fractions, you need to ask yourself what number has factors of 3 and 4? 12 has both
3 and 4 as a factor. (What if you don’t find the smallest common denominator? That’s ok, you’ll just have
more reducing to do at the end.) So we’re going to make equivalent fractions for each that have 12 as a
denominator:
2
, what do we need to multiply the denominator by to get 12? Remember that to get an equivalent
3
2 4 8
fraction we have to multiply the top and the bottom by the same number. So,  
. Is it ok that it’s
3 4 12
For
not reduced right now? YES!!!
3
, what do we need to multiply the denominator by to get 12? Remember that to get an equivalent
4
3 3 9
fraction we have to multiply the top and the bottom by the same number. So,  
.
4 3 12
For
Try to make the following pairs of fractions have common denominators. (Do not reduce your answers!)
1
2
and
4
5
5
3
and
12
4
Fractions Review
Name:______________________________________
Adding Fractions: When we want to add fractions, we are really trying to add pieces of whole numbers
together. We need the pieces to be of the same size to be able to put them together in a meaningful way.
That’s why we need to make sure that before we add fractions together, we have common denominators.
2 3
 . First we need them to have common denominators. We just
3 4
8 9
 .
did that on the previous page. Once we change them to have common denominators we have
12 12
17
So we have 8 12ths and 9 12ths, how many total 12ths do we have?
.
12
Examples: Let’s say we want to do
You do NOT add the denominators!
Now, let’s try
7 1
 . First, what common denominator should we use? What number has 8 and 6 as a
8 6
factor? 48 has both as a factor, but you might know that 24 also has both as a factor. It’s fine to use
either one, but using the smaller one means less reducing later. Change both fractions so they have 24
as a denominator:
21 4
25

. Now add the numerators to get an answer of
. Can you reduce?
24 24
24
Subtracting Fractions: Just like adding fractions, subtracting fractions requires that you have common
denominators. Once you have common denominators, simply subtract the numerators and place that
result over the common denominator.
Example:
5 7

First we need a common denominator. What number has factors of 6 and 10? 60
6 10
does. Anything smaller? 30 also does—we can use either as long as you make sure you reduce your
5
we need to multiply the top and bottom by 5,
6
25
7
21
making it
. To change
we need to multiply the top and bottom by 3, making it
.
10
30
30
25 21
 . How many 30ths are there if we take 25 of them and subtract 21?
So, now the problem is
30 30
4
2
There are
left after the subtraction. Can we reduce? YES! What is the final answer?
.
15
30
answer as much as possible. We’ll use 30. To change
Try to find the most reduced answer possible for the following problems:
7
9

15 20
4 5

21 12
9 7

20 15
1 2

4 7