Notes
Name:_____________________________
Date: _________________ Period:______
Fractions (1)
I. Simplification
A. Vocabulary

_________________________: to show; to put into words

_________________________: to make something simpler; to make something easier to understand

A fraction is in ________________________ ______________________ or ________________________
_____________________ when the numerator and the denominator cannot be divided by any other common
factors other than 1.
B. How to Simplify a Fraction
1) Find a factor that the numerator and denominator have in common.
2) Divide the numerator and denominator by that factor.
3) Keep dividing the numerator and denominator by common factors until you cannot divide anymore (and have a
remainder of 0).
Examples
Directions: Write each fraction in simplest form.
Ex)
8
12
Ex)
9
15
Ex)
6
8
Ex)
16
20
Ex)
28
35
Ex)
9
36
Ex)
28
35
Ex)
40
56
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II. Converting between Mixed Numbers & Improper Fractions (and vice versa)
A. Vocabulary

_______________________: to change into a different form

_______________________ _____________________: the sum of a whole number and a fraction

Here is an example of a mixed number:
1
3
2

_______________________
_____________________: a fraction where the numerator is the greater than the
denominator
Examples
Directions: Is this an improper fraction? Explain.
Ex)
11
5
Ex)
2
6
Ex)
1
6
Ex)
11
7
B. How to Convert an Improper Fraction to a Mixed Number
1) Divide the numerator by the denominator. (Hint: Ask yourself how many times the denominator goes into the
numerator).
2) That number will be your whole number, and the remainder will be the numerator of the new fraction.
3) Leave the denominator the same.
4) Simplify if possible.
Examples
Directions: Convert the following improper fractions into mixed numbers.
Ex)
5
2
Ex)
6
4
Ex)
Page 2
18
11
Ex)
44
20
Ex)
7
4
Ex)
17
15
Ex)
9
3
Ex)
19
6
C. How to Convert a Mixed Number to an Improper Fraction
1) Multiply the whole number by the denominator.
2) Add the product to the numerator.
3) Leave the denominator the same.
4) Simplify if possible.
Examples
Directions: Convert the following mixed numbers into improper fractions.
Ex) 2
3
4
Ex) 1
2
6
Ex) 2
1
8
Ex) 3
2
6
Ex) 4
6
7
Ex) 6
3
10
Ex) 4
6
7
Ex) 6
3
10
III. Adding/ Subtracting Fractions
A. Identifying Like and Unlike Denominators

___________________ denominators have denominators that are the ________________________.

___________________ denominators have denominators that are ___________________________.
Examples
Directions: Please identify whether you are working “like” or “unlike” denominators.
Ex)
1 2

3 4
Ex)
1 2

3 3
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B. Adding/ Subtracting Fractions with Like Denominators
1) Add/subtract the numerators
2) Keep the same denominator.
3) Write the answer in simplest form. If your answer is an improper fraction, please convert it to a mixed number.
Examples
Directions: Find each sum or difference. Write your answer as a mixed number if possible. Express your answer in lowest
terms.
Ex)
1 3
 =
8 8
Ex)
1 4
 =
7 7
Ex)
1 5
 =
9 9
Ex)
4 16
=

20 20
C. Adding/ Subtracting Fractions with Unlike Denominators
1) Find a multiple that both denominators share. This is your common denominator.
2) Multiply the numerator and denominator by the number you need to in order to get the common denominator. Do this
for each fraction.
3) Both denominators should be the same at this point.
4) Add/subtract the numerators.
5) Keep the same denominator.
6) Express your answer in lowest terms. If your answer is an improper fraction, then convert it to a mixed number.
Examples
Directions: Find each sum or difference. Write your answer as a mixed number if possible. Express your answer in
simplest form.
Ex)
2 4
 =
3 5
Ex)
4 1
 =
12 6
Ex)
1 3
 =
4 5
Ex)
4 2
 =
6 5
Ex)
1 1 1
  =
3 5 15
Ex)
1 2 1
  =
2 9 3
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