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Arithmetic Study Guide for the ACCUPLACER (CPT) Fractions
Terms
→ Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) → Example:
=
3 4
3 4
is 3 parts have a dot out of 4
Proper fraction: the top number is less than the bottom number. Ex:
1 7 9 , , 3 10 19 3 9 8 , , 2 4 8 3 2 1 , 2 , 10 4 5 2 9 12 8 12 6 12
Improper fraction: the top number is equal to or is larger than the bottom number. Ex:
Mixed Number: a whole number is written next to a proper fraction. Ex: 1
Common Denominator: is a number that can be divided evenly by all of the denominators in the problem Ex:
3 → 12 → 4 2 → 12 → 3 1 → 12 → 2
Reducing Fractions to Lowest Terms Example: 48 8 6 Step 1: Find a number that goes evenly into the numerator and the denominator of the fraction. With the ÷ = 64 8 8 fraction to the left, the number that will go in evenly is 8.
The common denominator for these fractions will be 12. It also happens to be least common denominator.
6 2 3 ÷ = 8 2 4
Step 2: Check to see whether another number goes evenly into both the numerator and denominator. Stop when there are no more numbers that can go into the fraction. In the example, the fraction can be reduced further by dividing it by 2.
Changing Mixed Numbers to Improper Fractions Example: Change 2 2x4=8 8 + 3 = 11
3 to an improper fraction. 4
Step 1: Multiply the denominator by the whole number. Step 2: Add the result to the numerator. Step 3: Place the total over the denominator.
11 4
12/22/00 This document is used with permission granted by Aims Community College, Greeley, Colorado.
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Arithmetic Study Guide for the ACCUPLACER (CPT)
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Adding and Subtracting Fractions With Different Bottom Numbers Example 1:
3 2 + = 4 3 3 3 9 × = 4 3 12 2 4 8 × = 3 4 12

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