Fractions Study Guide
Common Denominator: The denominator or bottom number is the same.
Least Common Multiple (LCM): To find the LCM, you skip count by the two
numbers and then you find the FIRST number that the have the same.
EX #1: 4, 6
4, 8, 12, 16, 20, 24, 28…
6, 12, 18, 24, 30…
12 is your LCM
EX #2: 10, 12
10, 20, 30, 40, 50, 60, 70…
12, 24, 36, 48, 60, 72…
60 is your LCM
Greatest Common Factor (GCF): To find the GCF, you need to find the
factors for each number.
EX #1: 4, 6
4 (1,2, 4)
6 (1, 2, 3, 6)
2 is your GCF
EX #2: 10, 12
10 (1, 2, 5, 10)
12 (1, 2, 3, 4, 6, 12)
2 is your GCF
Changing Improper to Mixed Number:
Ex. 1
Step 1: Divide the numerator by the
denominator.
Step 2: Write the whole number answer big to
the left, make your remainder the numerator
and the denominator will stay the same as
before.
9
2
9  2 = 4 r1
4
1
2
Ex. 2
11
3
11  3 = 3 r2
3
2
3
Simplest Form: The greatest common factor of the numerator and
denominator is 1.
Are you in simplest form? To find out if you are in simplest form, you factor
out both the numerator and the denominator.
EX #1:
4
6
4 (1,2, 4)
4
2

2
=
6
3
6 (1, 2, 3, 6)
EX #2:
10
12
10 (1, 2, 5, 10)
12 (1, 2, 3, 4, 6, 12)
10
5

2
=
12
6
Steps to Adding/Subtracting Fractions:
Step 1: Are the denominators the same?
Yes: Skip to step 5
No: STOP! Don’t add those fractions! Go to step 2
4
7
+
=
5
15
4
7
=
5
15
Step 2: Find the LCM of the denominators
5 – 5, 10, 15, 20, 25, 30, 35, 40, …
15 – 15, 30, 45, 60, 75
Step 3: Make the LCM the new denominator
15
+
15
=
15
-
15
=
Step 4: Create equivalent fractions (however you changed the
denominator, you need to change the numerator.)
X3
x1
12
7
+
=
15
15
X3
X3
x1
12
7
=
15
15
x1
X3
x1
Step 5: Add/Subt only the numerators
12
7
19
+
=
15 15
15
12 7
5
=
15 15
15
… Now check to make sure that it is not improper
AND
that it is in its simplest form.
Changing Improper Fractions: Divide the numerator by the denominator.
The answer is the whole number the remainder is the new numerator and
the denominator stays the same.
Is it in its Simplest Form? Find the greatest common factor (GCF). Once
you have found the GCF. Divide both the numerator and the denominator
by the GCF. If the GCF is 1, then the number is already in simplest form.
12
7
19
4
+
=
= 1
15
15 15
15
12 7
5
1
=
5 =
3
15 15
15
4 (1,2,4)
15 (1,3,5,15)
5 (1,5)
15 (1,3,5,15)