Division with whole-number remainders - Remainders using division facts
Theory
When a number does not divide evenly, use the multiplication fact just below it. That fact gives the quotient, and what is left over is the remainder — always smaller than the divisor.
To divide a number that will not share out evenly, use the multiplication fact just below it.
The quotient is how many whole groups fit. The remainder is the amount left over that is too small to make another group.
The remainder is always smaller than the divisor. If it is not, a bigger fact still fits.
Every division with a remainder can be checked by rebuilding the original number.
| Division | Fact used | Answer | Check |
|---|---|---|---|
| \(38\div5\) | \(7\times5=35\) | \(7\) r \(3\) | \(35+3=38\) |
| \(47\div6\) | \(7\times6=42\) | \(7\) r \(5\) | \(42+5=47\) |
| \(59\div7\) | \(8\times7=56\) | \(8\) r \(3\) | \(56+3=59\) |
How to find a remainder with a fact
- Find the largest multiple of the divisor that is not greater than the number.
- Read off the quotient from that multiplication fact.
- Subtract the multiple from the number to get the remainder.
- Check the remainder is smaller than the divisor.
Largest fact: \(7\times5=35\).
| \(38-35\) | \(=\) | \(3\) |
Answer: \(7\) remainder \(3\).
Largest fact: \(7\times6=42\).
| \(47-42\) | \(=\) | \(5\) |
Answer: \(7\) remainder \(5\).
| \(8\times7+3\) | \(=\) | \(59\) |
It rebuilds \(59\), so the answer is right.
Largest fact: \(5\times4=20\).
| \(23-20\) | \(=\) | \(3\) |
3 stickers are left over.
Common pitfalls
Frequently asked questions
How do you find a remainder using times tables?
Find the largest multiple of the divisor that is not greater than the number. That fact gives the quotient, and subtracting it from the number gives the remainder. For \(38\div5\), use \(7\times5=35\), so \(38-35=3\) is the remainder.
What is a remainder?
A remainder is the amount left over after making as many equal groups as possible. It is always smaller than the divisor.
Why must the remainder be smaller than the divisor?
If the remainder were as big as the divisor, another whole group would fit. So a remainder of 5 or more when dividing by 5 means the quotient should be one larger.
How do you check a division with a remainder?
Multiply the quotient by the divisor and add the remainder. If you get back the original number, the answer is correct. \(7\times5+3=38\).
What if the number divides evenly?
Then the remainder is 0 and the answer is a whole number with nothing left over.