How to Convert from Improper Fractions to Mixed Fractions

How to Convert from Improper Fractions to Mixed Fractions

Improper 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

Question

Convert the improper fraction below to a mixed fraction.

Step-by-Step:

1

Divide the top number (called the numerator) of the fraction by the bottom number (called the denominator).

Express it as a quotient and a remainder.

5 ÷ 2 = 2 r 1

Don'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.

2

Use the answer from Step 1...

2 r 1

to write the mixed fraction.

Write the quotient (2) as the whole number part of the mixed fraction.

3

Use the answer from Step 1...

2 r 1

to write the mixed fraction.

Write the remainder (1) as the numerator of the fraction part of the mixed fraction.

4

Find the denominator of the fraction.

2 1/?

The denominator of the original improper fraction (2) becomes the denominator of the fraction part of the mixed fraction.

5

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).

Answer:

2 1/2 (two and a half) is 5/2 (five-halves) written as a mixed fraction.

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The slider below shows another real example of converting improper fractions to mixed fractions.

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See Also

What is an improper fraction? What is a mixed fraction? What is a whole number? What is a fraction? What is a mixed fraction? What is a numerator? What is a denominator? Simplifying fractions