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. So \(539 \div 4 = 134 \text{ r } 3 = 134\tfrac{3}{4}\). This Year 5 maths page shows how to write the answer as a mixed number, how to simplify the fraction, and when a fraction makes sense (lengths, amounts) and when it does not (people, buses).
The remainder is part of one more group. If \(3\) are left when dividing by \(4\), that is \(3\) out of the \(4\) needed, or \(\dfrac{3}{4}\) of a group.
The answer is a mixed number: the quotient (whole number part) followed by the fraction \(\dfrac{\text{remainder}}{\text{divisor}}\).
Write the fraction in simplest form by dividing the top and bottom by the same number: \(\dfrac{2}{4} = \dfrac{1}{2}\), \(\dfrac{3}{6} = \dfrac{1}{2}\).
Fractions make sense for things that can be split, such as lengths, money or liquids. They do not make sense for people or vehicles.
Turning a remainder into a fraction:
Writing the remainder as a fraction
- Divide with short division to find the quotient and remainder.
- Write the remainder over the divisor.
- Simplify the fraction if possible.
- Write the answer as a mixed number.
| \(\text{H: }5 \div 4\) | \(=\) | \(1 \text{ r } 1\) |
| \(\text{T: }13 \div 4\) | \(=\) | \(3 \text{ r } 1\) |
| \(\text{O: }19 \div 4\) | \(=\) | \(4 \text{ r } 3\) |
\(134 \text{ r } 3 = 134\dfrac{3}{4}\).
| \(\text{H: }4 \div 3\) | \(=\) | \(1 \text{ r } 1\) |
| \(\text{T: }11 \div 3\) | \(=\) | \(3 \text{ r } 2\) |
| \(\text{O: }22 \div 3\) | \(=\) | \(7 \text{ r } 1\) |
\(137\dfrac{1}{3}\).
| \(\text{H: }5 \div 4\) | \(=\) | \(1 \text{ r } 1\) |
| \(\text{T: }12 \div 4\) | \(=\) | \(3\) |
| \(\text{O: }6 \div 4\) | \(=\) | \(1 \text{ r } 2\) |
\(131\dfrac{2}{4} = 131\dfrac{1}{2}\).
| \(\text{T: }37 \div 6\) | \(=\) | \(6 \text{ r } 1\) |
| \(\text{O: }15 \div 6\) | \(=\) | \(2 \text{ r } 3\) |
\(62\dfrac{3}{6} = 62\dfrac{1}{2}\).
| \(\text{T: }24 \div 9\) | \(=\) | \(2 \text{ r } 6\) |
| \(\text{O: }65 \div 9\) | \(=\) | \(7 \text{ r } 2\) |
\(27\dfrac{2}{9}\). The fraction \(\dfrac{2}{9}\) cannot be simplified.
| \(\text{T: }23 \div 7\) | \(=\) | \(3 \text{ r } 2\) |
| \(\text{O: }20 \div 7\) | \(=\) | \(2 \text{ r } 6\) |
Each piece is \(32\dfrac{6}{7}\) cm long.
| \(\text{T: }30 \div 8\) | \(=\) | \(3 \text{ r } 6\) |
| \(\text{O: }60 \div 8\) | \(=\) | \(7 \text{ r } 4\) |
You cannot have half a minibus. \(37\) are full and \(4\) students are left, so \(38\) minibuses are needed.
Common pitfalls
Frequently asked questions
How do you write a remainder as a fraction?
Put the remainder over the divisor. \(539 \div 4 = 134 \text{ r } 3\), which is \(134\dfrac{3}{4}\).
What is a mixed number?
A whole number and a fraction together, such as \(137\dfrac{1}{3}\).
How do you simplify the fraction?
Divide the top and bottom by the same number. \(\dfrac{3}{6} = \dfrac{1}{2}\), so \(62\dfrac{3}{6} = 62\dfrac{1}{2}\).
When should you not use a fraction?
When the things cannot be split, such as people or buses. Then round the answer up or down to suit the question.
Can the fraction be more than one whole?
No. The remainder is always smaller than the divisor, so the fraction is always less than one.