ACCUPLACER
Arithmetic & Elementary Algebra
Study Guide
Arithmetic
Fractions
Terms
Numerator:
Which tells how many parts you have (the number on top) 3
Denominator:
Which tells how many parts in the whole (the number on the bottom) 4
Example:
= 3/4 is 3 parts have a dot out of 4
Ex: Proper fraction: the top number is less than the bottom number.
Ex: Improper fraction: the top number is equal to or is larger than the bottom number.
1
,Ex: Mixed Number: a whole number is written next to a proper fraction.
2
,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.
Reducing Fractions to Lowest Terms
Example: 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.
Changing Mixed Numbers to Improper Fractions
Example: Change to an improper fraction.
Step 1: Multiply the denominator by the whole number. 2 X 4 = 8
Step 2: Add the result to the numerator. 8 + 3 = 11
Step 3: Place the total over the denominator.
3
, Adding and Subtracting Fractions With Different Bottom Numbers
*Remember to change improper fractions to a mixed number.
Multiplying Fractions
4
Arithmetic & Elementary Algebra
Study Guide
Arithmetic
Fractions
Terms
Numerator:
Which tells how many parts you have (the number on top) 3
Denominator:
Which tells how many parts in the whole (the number on the bottom) 4
Example:
= 3/4 is 3 parts have a dot out of 4
Ex: Proper fraction: the top number is less than the bottom number.
Ex: Improper fraction: the top number is equal to or is larger than the bottom number.
1
,Ex: Mixed Number: a whole number is written next to a proper fraction.
2
,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.
Reducing Fractions to Lowest Terms
Example: 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.
Changing Mixed Numbers to Improper Fractions
Example: Change to an improper fraction.
Step 1: Multiply the denominator by the whole number. 2 X 4 = 8
Step 2: Add the result to the numerator. 8 + 3 = 11
Step 3: Place the total over the denominator.
3
, Adding and Subtracting Fractions With Different Bottom Numbers
*Remember to change improper fractions to a mixed number.
Multiplying Fractions
4
