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Arithmetic Study Guide for the
ACCUPLACER Assessment Test


  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)


is 3 parts have a dot out of 4

  Proper fraction: the top number is less than the bottom number.

  Improper fraction: the top number is equal to or is larger than the bottom number.

  Mixed Number: a whole number is written next to a proper fraction.

  Common Denominator: is a number that can be divided evenly by all of the denominators in the problem

The common denominator for these
fractions will be 12. It also happens to
be least common denominator


Step 1: Find a number that goes evenly into the numerator and the denominator of the fraction. With the
fraction to the left, the number that will go in evenly is 8.



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.


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.

Adding and Subtracting Fractions With Different Bottom Numbers

Step 1: Need to find the common denominator for all fractions
Step 2: Then go ahead and add or subtract the fractions.

*Remember to change improper fractions to a mixed number.

Multiplying Fractions

Multiply the numerators across. Then multiply the
denominators across. Make sure the product is in lowest terms.

Multiplying with Mixed Numbers

Step 1: Change every mixed fraction to an improper fraction.

Step 2: The multiply across.

Step 3: Then, change the improper fraction to a mixed number in lowest terms

Dividing Fractions


The fraction that is right of the division sign will need to be turned upside down by writing the numerator in the
denominator and the denominator in the numerator. Then follow the rules for multiplying fractions.

1. Change to an improper fraction. 
2. Change 42/16 to a mixed number.