Name ______________________________
Homeroom __________________________
Fraction Review
A fraction can be read as a division statement.
This fraction can be read “three divided by four”.
3
4
Equivalent Fractions: You can make an equivalent fraction by multiplying or
dividing
the numerator and the denominator of a fraction by the same number.
Example
2x2 =4
3x2
6
Example
12 ÷ 6 = 2
18 ÷ 6
3
so 2
3
is equivalent to 4
6
so 2
3
is equivalent to 12
18
Simplifying fractions: A fraction is in simplest form if the numerator and
denominator have no common factors other than 1. The fraction is as small as you can
make it.
Example:
1)
2)
3)
8
12
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
1x8
2x4
1x12 2x6 3x4
GCF = 4
To simplify you need to find the Greatest Common Factor (GCF) of 8 and 12.
Then divide your fraction (the numerator and the denominator) by the GCF.
8÷ 4 = 2
12 ÷ 4 = 3
8
written in simplest form is 2
12
3
Comparing fractions:
When you compare fractions you need to use the symbol >, <, or =.
You have 2 strategies to choose from.
Strategy #1 - Find the Least common multiple (LCM) of all the denominators
Then, change all the denominators to the same number (the LCM)
Finally, you are able to compare the numerators.
Example: Compare
5
2
6
3
← Denominators are different so we need to make them the same.
6: 6, 12, 18, 24
List the multiples of 3: 3, 6, 9, 12,
List the multiples of
The least common multiple (LCM) is 6
Now change the denominators to 6 (the LCM).
5
6
← denominator is already 6
To change the denominator we must
multiply the numerator and denominator
by the same number.
5
6
Now compare
2
3
x2
x2
= 4
6
← now we have the same denominator
4
6
Strategy #2 - Cross multiply. Remember to Multiply the Butterfly.
15
Example:
5
6
>
12
2
3
Ordering fractions
Put fractions in order from least to greatest OR greatest to least. Be careful and read
the directions carefully.
Order 2 , 3 , and 7
3
4
from least to greatest.
12
Strategy #1 - Use a number line
Numbers on a number line are ordered from least to greatest.
Think about benchmark fractions (½, ⅓, ¼ ).
2/3
3/4
<------------------------------------------------------------------------------------->
0
1
2
3
4
5
6
7
8
9
10
11
12
12
12
12
12
12
12
12
12
12
12
12
12
Strategy # 2 - Use Least common multiple (LCM)
You need to change the denominators to the same number. Remember to change the
denominators you need to find the LCM.
2
3
7
Multiples of 3:
Multiples of 4:
3, 6, 9, 12
4, 8, 12, 16
Multiples of 12: 12, 24
LCM = 12
3
4
12
↓
↓
↓
8
12
9
12
7
12
Mixed Numbers:
A mixed number has a whole number and a fraction.
2
1
2
A mixed number can be changed into an improper fraction.
Example:
2
1
2
Multiply the denominator of the fraction by the whole number
2x2=4
Then add that product (4) to the numerator 4 + 1 = 5
The sum is our new numerator and the denominator remains the same (2)
2
1
2
=
5
2
Improper Fractions:
When the numerator of a fraction is larger than the denominator, that fraction is
improper. You can change an improper fraction to a mixed number by dividing the
numerator by the denominator.
Remember that fractions can be read as a division statement.
Example:
12
8
=
12
8
1 48
It can be read as “12 divided by 8”.
Adding and Subtracting Fractions:
We you add OR subtract fractions the denominators must be the same.
If the denominators are the same, you only add or subtract the numerators. The
denominators stay the same.
Example: 1
6
+ 4 = 5
6
6
7
8
-
4
8
= 3
8
If the denominators are different, you must first change the denominators to the same
number, and then add the numerators.
Example: 1
6
+ 2 =
3
2
3
1
6
7 8
x2
= 4
6
+ 4 =
6
5
6
x2
1 =
2
1 x4 = 4
2 x4
8
7
8
-
4
8
= 3
8
Adding Mixed Numbers:
When you add mixed numbers, add the whole numbers then add the fractions. If the
sum includes an improper fraction, you must change it to a mixed number.
2¼
6 3/4
+ 3 2/4
+ 2 3/4
___________
_____________
5
¾
8
6/4
4/4 = 1
=
9
2/4
8+1=9