Name: ___________________________________________
Date: _____________________
Fractions Study Guide
 Fraction Vocabulary & Definitions
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Fraction- A part of a whole object or set of objects. Fractions represent a division
sentence. An object or set is divided into equal groups and each part or group is one
fraction of the whole.
Numerator- The top number in a fraction. It represents how many parts of the whole
are being talked about or used. For example the 3 in ¾ is the numerator. Of the four
equal parts a whole is divided into we are looking at/using 3 of them.
Denominator- The bottom number in a fraction. It represents how many parts there are
to the whole. For example the 4 in ¾ is the denominator, the whole is divided into four
equal parts.
Common Denominator- Denominators that are the same. Example: ¾ and ¼ both have 4
as the denominator and have common denominators.
Equivalent fractions- Fractions that name the same amount. Example: 2/4 and 4/8 are
both naming one half of an object or set.
Fraction of a Set- Part of a group of objects. For example ½ of a bag of candy or ¼ of the
books on a shelf.
Fraction of a Whole- Part of one object. For example ¼ of a cake or ½ of an apple are
both parts of one whole object.
Improper Fraction- A fraction where the numerator is GREATER than its denominator.
Example: 16/4.
Mixed Number- A whole number and a fraction. It represents a whole, and some parts.
Example: 2 ½.
 Equivalent Fractions
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Check if two fractions are equivalent by cross multiplying:
 Example 1:
2
4
4
8
4x4=16
2x8=16
*The answers are the same so they are equivalent.

Example 2:
3
4
5
8
4x5=20
3x8=24
*The answers are NOT the same so they are NOT equivalent.
 Ordering Fractions
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To order fractions with the same denominator from smallest to greatest:
 Look at the numerators. Order them from smallest to largest.
 The smaller the numerator the smaller the fraction.
 Example:
Biggest
Smallest
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3
9
5
9
8
9
To order fractions with the same numerator from smallest to greatest:
 Look at the denominators. Order them from largest to smallest.
 The larger denominators are the smallest fractions since the whole is being
broken into more pieces—each piece is smaller. (If you share a cake with 3
friends you get more than if you have to share that same cake with 10 friends).
 Example:
Biggest
Smallest
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2
9
2
9
2
6
2
4
2
3
To order fractions with different denominators and numerators:
 Find a common denominator for all fractions then compare numerators.
 Example:
2
6
1
4
1. Find a common denominator:
6, and 4 both go into 12 so 12 is the common denominator.
2. Convert fractions to twelfths.
2
6
=
4
12
1
4
3. Compare numerators.
4
12
>
3
12
=
3
12
 Adding/Subtracting Fractions
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When the denominators are the same you can add the numerators and keep the
denominators. THIS WILL BE ON TEST!
 Example 1:
2
4
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1
4
2 + 1=
4
3
4
1
4
2 - 1=
4
1
4
Example 2:
2
4
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When the denominators are NOT the same you must find a common (same)
denominator then add the numerators.
THERE WILL ONLY BE EXTRA CREDIT PROBLEMS LIKE THIS ON THE TEST!
 Example1:
2
4
+
1
3
Step 1: Find a common denominator.
4x3=12 so 4 and 3 are both factors of 12 and 12 is a common
denominator.
Step 2: Convert fractions to common denominator.
2
4
6
12
=
1
3
=
4
12
Step 3: Add numerators, keep the denominator.
6 + 4
6+4
=
12
12
12

=
10
12
Example 2:
2
4
-
1
3
Step 1: Find a common denominator.
4x3=12 so 4 and 3 are both factors of 12 and 12 is a common
denominator.
Step 2: Convert fractions to common denominator.
2
4
6
12
=
1
3
=
4
12
Step 3: Subtract the numerators, keep the denominator.
6 - 4
6-4
=
12
12
12
=
2
12
Practice Adding and Subtracting Fractions
with Common Denominators
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Practice Comparing Fractions
(You must find a common denominator BEFORE comparing!)
Practice Adding and Subtracting Fractions with Unlike Denominators
THIS WILL ONLY BE EXTRA CREDIT ON TEST
(You must find a common denominator BEFORE adding or subtracting!)