Improper fractions to mixed numerals
Theory
An improper fraction becomes a mixed numeral by grouping its parts into whole sets. Divide the numerator by the denominator: the quotient is the whole number, and the remainder becomes the new numerator over the same denominator.
An improper fraction has a numerator equal to or larger than its denominator, like \(\dfrac{11}{4}\).
Divide the top by the bottom. The quotient is the whole-number part.
The remainder becomes the new numerator, over the same denominator: \(\dfrac{11}{4}=2\dfrac{3}{4}\).
Divide the numerator by the denominator. The quotient is the whole part; the remainder is the new numerator.
| Improper | Divide | Mixed |
|---|---|---|
| \(\dfrac{11}{4}\) | \(11\div4=2\) r \(3\) | \(2\dfrac{3}{4}\) |
| \(\dfrac{7}{2}\) | \(7\div2=3\) r \(1\) | \(3\dfrac{1}{2}\) |
| \(\dfrac{12}{4}\) | \(12\div4=3\) r \(0\) | \(3\) |
How to change an improper fraction to a mixed numeral
- Divide the numerator by the denominator.
- Write the quotient as the whole number.
- Put the remainder over the same denominator as the fraction part.
\(11\div4=2\) remainder \(3\).
| \(\dfrac{11}{4}\) | \(=\) | \(2\dfrac{3}{4}\) |
\(7\div2=3\) remainder \(1\).
| \(\dfrac{7}{2}\) | \(=\) | \(3\dfrac{1}{2}\) |
\(8\div3=2\) remainder \(2\).
| \(\dfrac{8}{3}\) | \(=\) | \(2\dfrac{2}{3}\) |
\(12\div4=3\) with no remainder.
| \(\dfrac{12}{4}\) | \(=\) | \(3\) |
Common pitfalls
Frequently asked questions
How do you change an improper fraction to a mixed numeral?
Divide the numerator by the denominator. The quotient is the whole number and the remainder goes over the same denominator. \(\dfrac{11}{4}=2\dfrac{3}{4}\).
What happens to the remainder?
The remainder becomes the new numerator, written over the same denominator as the original fraction.
What if there is no remainder?
Then the fraction is a whole number. \(\dfrac{12}{4}=3\), because \(12\div4=3\) exactly.
Which number is the whole part?
The quotient, the answer to the division, is the whole-number part, not the remainder.