6.7 Changing Improper Fractions to Mixed Numbers

You learned earlier that the value of an improper faction must be equal to or greater than 1. Fractions such as 4/4 , 5/4 , 6/4 , etc., are improper fractions.

5/4 > 1 4/4 = 1 5/4 = 1 and ¼, which is written 1 ¼ 5/4 > 1 4/4 = 1 5/4 = 1 and ¼, which is written 1 ¼ . This is called a mixed number. It is made up of two parts: 1= whole number ¼ = proper fraction

Improper Fractions to Mixed Numbers An improper fraction can be changed into a mixed number either by using the method just shown (drawing) or by dividing. Recall that the line separationg the 5 and 4 means that the numerator is being divided by the denominator:

Example Write 6/4 as a mixed number.

Solution Problem Step 1 Step 2 Step 3 6/4 = ? Set up the Division: the denominator into the numerator: Divide. Write the remainder as the numerator and the divisor as the denominator of a fraction in its simplest form:

Another example: Write 32/5 as a mixed number:

Now let’s Reverse! Change 2 ½ into an improper fraction.

Solution Problem Step 1 Step 2 Step 3 2 ½ = ? Multiply the whole number by the denominator. Add the numerator to the product. Keep the same denominator Add the numerators

Another Example… Change 4 and 2/3 into an improper fraction.