Name: ____________________________Date: ___________________________
Class: Developing College Math Skills
Objective: We will change improper fractions to whole or mixed numbers, change mixed
numbers to improper fractions, add fractions, find common denominators, and estimate answers
by completing pages 19-30.
Changing Improper Fractions to Whole or Mixed Numbers
*(NIDO): Divide: Numerator IN Denominator OUT
Example 1: Change 8/8 to a whole number.
Example 2: Change 20/4 to a whole number
*When there is a remainder, write a fraction with the remainder over the denominator. The
result is a mixed number.
Example 3: Change 21/9 to a mixed number
Step 1: Divide 21 by 9
Step 2: Write the remainder over the denominator
Step 3: Reduce
Example 4: A kitchen counter is 90 inches long.
Find the length of the counter in feet. (1 foot=12 inches)
Step 1: Write the problem as an improper fraction.
(Divide 90 inches by the number of inches in one foot)
Step 2: Divide 90 by 12.
Step 3: Reduce
Changing Mixed Numbers to Improper Fractions
Example: Change 2 ¼ to an improper fraction.
Step 1: Multiply the denominator 4 by the whole number 2.
Step 2: Add the numerator 1, to 8.
Step 3: Write the total, 9, over the denominator, 4.
Notes 19-30 --Adding Fractions, Finding Common Denominators, Estimating Page 1 of 3
Adding Fractions with the Same Denominators
The answer to an addition problem is called the sum or total. Tip: To add fractions, write the
problem vertically, with fractions one under the other.
To add fractions with the same denominators, add the numerators, and put the total over the
denominator.
Example 1: 2/7 + 3/7=
Step 1: add the numerators 2+3
Step 2: put the total over the denominator, 7
Example 2: 5/12 + 1/12=
Step 1: add the numerators
Step 2: put the total over the denominator, 12
Step 3: reduce the answer
*If the total of an addition problem is an improper fraction, change the improper fraction to a
mixed number.
Example 3: 5/8 + 7/8
Step 1: add the fractions
Step 2: change the improper fraction to a mixed number
Step 3: reduce
Example 4:
8 3/8
3 7/8
+ 5 5/8
Adding Fractions with Different Denominators
*When the fractions in an addition problem do not have the same denominators, rewrite the
problem so that each fraction has the same denominator, called a common denominator.
*The smallest number that can be divided evenly by all the denominators in a problem is called
the lowest common denominator or LCD.
Example: 3/5 + 4/15
Step 1: Since 5 divides evenly into 15, the LCD is 15.
Step 2: Raise 3/5 to higher terms
Step 3: Add the new fractions
Notes 19-30 --Adding Fractions, Finding Common Denominators, Estimating Page 2 of 3
Finding a Common Denominator
Here are two ways of finding a common denominator when the largest denominator in an
addition problem doesn’t work.
1. Multiply the denominators together
2. Go through the multiplication table of the largest denominator.
Example 1: 2/5 + ¾
Step 1: Multiply the denominators.
Step 2: Raise each fraction to 20ths
Step 3: Add the new fractions
Step 4: Change the answer to a mixed number.
Example 2: 2/3 + 5/6 + ¾
Step 1: Go through the multiplication table of the 6’s.
6x1=6 (6 cannot be divided by 4)
6x2=12 (12 can be divided by 3 and 4)
Step 2: Raise each fraction to 12ths
Step 3: Add the new fractions
Step 4: Change the answer to a mixed number and reduce.
Example 3: Add and reduce
9 3/8
3 5/ 6
+ 4 1/3
Notes 19-30 --Adding Fractions, Finding Common Denominators, Estimating Page 3 of 3