Mixed numerals to improper fractions
Theory
A mixed numeral becomes an improper fraction by counting how many equal parts it holds. Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
A mixed numeral is a whole number and a fraction together, like \(1\dfrac{3}{4}\).
Each whole holds a full set of parts, so multiply the whole number by the denominator to count them.
Add the numerator to include the extra parts, and keep the same denominator: \(1\dfrac{3}{4}=\dfrac{7}{4}\).
Multiply the whole by the denominator, then add the numerator over the same denominator.
| Mixed | Whole times denominator, plus numerator | Improper |
|---|---|---|
| \(1\dfrac{1}{2}\) | \(1\times2+1=3\) | \(\dfrac{3}{2}\) |
| \(1\dfrac{3}{4}\) | \(1\times4+3=7\) | \(\dfrac{7}{4}\) |
| \(2\dfrac{1}{3}\) | \(2\times3+1=7\) | \(\dfrac{7}{3}\) |
How to change a mixed numeral to an improper fraction
- Multiply the whole number by the denominator.
- Add the numerator to that total.
- Write the total over the same denominator.
| \(1\dfrac{1}{2}\) | \(=\) | \(\dfrac{1\times2+1}{2}\) |
| \(=\) | \(\dfrac{3}{2}\) |
| \(1\dfrac{3}{4}\) | \(=\) | \(\dfrac{1\times4+3}{4}\) |
| \(=\) | \(\dfrac{7}{4}\) |
| \(2\dfrac{1}{3}\) | \(=\) | \(\dfrac{2\times3+1}{3}\) |
| \(=\) | \(\dfrac{7}{3}\) |
| \(2\dfrac{3}{4}\) | \(=\) | \(\dfrac{2\times4+3}{4}\) |
| \(=\) | \(\dfrac{11}{4}\) |
Common pitfalls
Frequently asked questions
How do you change a mixed numeral to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. \(1\dfrac{3}{4}=\dfrac{7}{4}\).
What is an improper fraction?
An improper fraction has a numerator equal to or larger than its denominator, such as \(\dfrac{7}{4}\). It is worth one whole or more.
Does the denominator change?
No. The denominator stays the same throughout; only the numerator is rebuilt from the whole number and the fraction part.
Why multiply the whole number by the denominator?
Each whole holds a full set of parts. Multiplying counts how many of those parts the whole numbers are worth.