Fraction Notes
Finding a Fractional Part of a Whole
Whole ÷ denominator x numerator
Example : ¾ of 200 = 200 ÷ 4 x 3 = 150
Finding Equivalent Fractions
Two strategies
1. Multiply the numerator and denominator by the same number
1 1𝑥3 3
=
=
2 2𝑥3 6
2. Divide the numerator and denominator by the same number (must be a factor of both)
5
5 ÷5
1
=
=
25
25 ÷5
5
Writing Fractions in Simplest Form
Find the GCF (greatest common factor) of the numerator and denominator. Divide the
numerator and denominator by the same number.
Comparing and Ordering Fractions
1. Find the LCM (least common multiple) of the denominators.
2. Multiply your numerator and denominator of each fraction by the number needed to get
the denominators to be the LCM
3. Now use the new numerators to compare or order fractions.
Example: Order the following fractions from least to greatest.
3 2 7
, ,
The LCM of 5, 3, and 15 is 30.
5 3 15
3 𝑥6
5𝑥6
18 2 𝑥 10
3 𝑥 10
= 30
20 7 𝑥 2 14
=
15 𝑥 2 30
= 30
7
3 2
so the order is 15 , 5 , 3
Finding Fractions in Between Fractions
1. Make equivalent fractions with common denominators.
2. Scale up the numerator and denominator by multiplying by one more than the number of
fractions needed.
Example: Find two fractions between ¼ and 3/8
2
3
Change fractions to and
8
8
6
9
Scale up by 3 since 3 is 1 more than the 2 fractions we need. Now we have 24 and 24 .
7
8
So two fractions in between would be 24 and 24 .