Divide by a one-digit divisor (short division) - With a fractional remainder
Theory
A remainder can be written as a fraction: the remainder over the divisor. Added to the quotient it makes a mixed number, such as \(106\dfrac{1}{4}\). Simplify the fraction where possible.
A remainder does not have to be left whole. It can be written as a fraction to make a mixed number.
The remainder becomes the numerator and the divisor becomes the denominator.
Add this fraction to the whole-number quotient, and simplify the fraction if it has a common factor.
Do the short division, then turn the remainder into a fraction.
| Division | Quotient | Remainder | Mixed number |
|---|---|---|---|
| \(425\div4\) | \(106\) | \(1\) | \(106\dfrac{1}{4}\) |
| \(617\div3\) | \(205\) | \(2\) | \(205\dfrac{2}{3}\) |
| \(350\div4\) | \(87\) | \(2\) | \(87\dfrac{1}{2}\) |
How to write a remainder as a fraction
- Divide to find the whole-number quotient and the remainder.
- Write the remainder over the divisor as a fraction.
- Join the fraction to the quotient to make a mixed number.
- Simplify the fraction if it has a common factor.
\(617\div3=205\) r \(2\).
| \(617 \div 3\) | \(=\) | \(205\dfrac{2}{3}\) |
\(425\div4=106\) r \(1\).
| \(425 \div 4\) | \(=\) | \(106\dfrac{1}{4}\) |
\(350\div4=87\) r \(2\), and \(\dfrac{2}{4}=\dfrac{1}{2}\).
| \(350 \div 4\) | \(=\) | \(87\dfrac{1}{2}\) |
| \(293 \div 5\) | \(=\) | \(58\dfrac{3}{5}\) |
Each piece is \(58\dfrac{3}{5}\) cm.
Common pitfalls
Frequently asked questions
How do you write a remainder as a fraction?
Put the remainder over the divisor. For \(425\div4=106\) remainder \(1\), the fraction is \(\dfrac{1}{4}\), so the answer is \(106\dfrac{1}{4}\).
Which number goes on top of the fraction?
The remainder goes on top as the numerator, and the divisor goes underneath as the denominator.
Do you simplify the fraction?
Yes, if it has a common factor. \(87\dfrac{2}{4}\) simplifies to \(87\dfrac{1}{2}\).
What is a mixed number?
A whole number written together with a proper fraction, such as \(106\dfrac{1}{4}\). It combines the quotient and the fractional remainder.
When is the answer just a whole number?
When the remainder is \(0\). Then there is no fraction to add and the answer is the quotient on its own.