How to Convert from Improper Fractions to Mixed Fractions (Mathematics Lesson)
Converting from Improper to Mixed FractionsImproper fractions can be converted to mixed fractions.
- An improper fraction (or top-heavy fraction) is a fraction where the top number is greater than (or equal to) the bottom number.
- A mixed fraction has a whole number and a fraction.
How to Convert from Improper to Mixed Fractions
An Example QuestionConvert the improper fraction below to a mixed fraction.
Express it as a quotient and a remainder.
5 ÷ 2 = 2 r 1Don't forget: If a number does not divide exactly into another, you get a quotient (2 in our example) and a remainder (1) that is left over.
r means remainder. See the Note.
Write the quotient (2) as the whole number part of the mixed fraction.
Write the remainder (1) as the numerator of the fraction part of the mixed fraction.
2 1/?The denominator of the original improper fraction (2) becomes the denominator of the fraction part of the mixed fraction.
2 1/2 (two and a half) is 5/2 (five-halves) written as a mixed fraction.
A Real Example of How to Convert from Improper to Mixed FractionsThe slider below shows another example of converting improper fractions to mixed fractions:
Here's a second test on converting improper fractions to mixed fractions.
Here's a third test on converting improper fractions to mixed fractions.
What Is a Remainder?A remainder is the amount left over after a division.
A number can often be divided exactly by another number. For example, 4 ÷ 2 = 2. This means 4 objects can be divided into 2 equal groups of 2:
However, try 5 ÷ 2. There are 2 equal groups of 2, but 1 is left over:
5 ÷ 2 = 2 with a remainder 1
5 ÷ 2 = 2 r 1.
2 is the quotient.
1 is the remainder.
How to Find the Quotient and Remainder with a CalculatorThis Note explains how to find Step 1 in our example.
Question: Find 5 ÷ 2, expressing the answer as a quotient and a remainder.
Using the on-screen calculator:
- Type 5 ÷ 2.
- Click the = button. The answer is 2.5.
The quotient is 2.
To find the remainder, start with 2.5 still showing in the calculator.
- Subtract the quotient.
Type - 2.
- Click the = button. The answer is 0.5.
- Multiply by the number you first divided by (2 in this example, as we are finding 5 ÷ 2).
Type × 2.
- Click the = button. The answer is 1. This is the remainder.
5 ÷ 2 = 2 r 1.