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Mixed Numbers & Improper Fractions

Mixed numbers consist of a whole number and a fraction, for example two and a half (2 ½). An improper fraction is a fraction whose top number (numerator) is bigger than its bottom number (denominator). For example, five halves (5/2) is an improper fraction. Sometimes, to work with fractions, you have to convert a mixed number into an improper fraction, or vice versa, and this section explains how to do so.

Converting Between Mixed Numbers and Improper Fractions

Converting Between Mixed Numbers and Improper Fractions Video transcript - RTF

Examples & Activity


Click on the titles below to view each example.

Convert 11 over 6 to a mixed number.

Line 1: Divide the denominator into the numerator. Remember that 11 over 6 means 11 divided by 6.

Line 2: Divide 6 into 11 and identify the quotient as 1, the divisor as 6 and the remainder as 5.

Line 3: Write the mixed number as the quotient followed by the remainder over the divisor, so the mixed number is 1 and 5 over 6.

Convert 4 and 2 over 3 to an improper fraction.

Line 1: In the numerator, multiply the whole number by the denominator, and add to the original numerator, so the numerator becomes 4 times 3 plus 2. The denominator does not change so it stays as 3.

Line 2: Simplify the numerator so the improper fraction is 14 over 3.


Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet


Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window