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Mixed Fractions

Mixed and Improper Fractions

Mixed fractions and improper fractions are ways to show a value of one or greater.

Mixed fractions and improper fractions can be used to show the same value. Look at the rectangles below.

As an improper fraction, there are 4 equal parts in one whole, and 5 parts are shaded.

The same value can be written as a mixed fraction. The whole number part is the number of full rectangles that are shaded. There is one full rectangle. The fraction part tells the fraction for the partially shaded rectangle. There is one part of the 4 equal parts colored. The fraction part is 1/4.

Definitions

mixed fraction: A number made of two parts: a whole number and a proper fraction. Example: 2 1/3

Renaming Improper Fractions

Any improper fraction can be renamed as a mixed fraction using division.

Write 9/2 as a mixed fraction.

Step 1: Divide the numerator by the denominator.

9 ÷ 2 = 4 remainder 1

Step 2: Write the mixed fraction. The remainder is the numerator of the fraction part. The denominator stays the same as it is in the original improper fraction.

Test-Taking Hint

Some multiple choice questions can be solved by eliminating choices that are obviously incorrect.



Renaming Mixed Fractions

Any mixed fraction can be renamed as an improper fraction.

Write 4 3/5 as an improper fraction.

Step 1: The numerator of the improper fraction is found by multiplying the whole number by the denominator, then adding the numerator from the mixed fraction.

(4 × 5) + 3 = 23

Step 2: Write the improper fraction. The denominator is the same as the denominator in the fraction part of the mixed fraction.

Test-Taking Hint

An answer in a multiple choice problem might look correct if you go too quickly. Often the wrong answers listed are ones you would find if you made a common error.