Division with Remainder
When b does not divide a exactly, a = bq + r with 0 ≤ r < b.
Key idea
When b does not divide a exactly, a = bq + r with 0 ≤ r < b.
In depth
When the groups do not fit evenly, what is left over is the remainder. The relation is dividend = divisor × quotient + remainder, with remainder smaller than divisor.
Worked example
47 ÷ 5: 5 × 9 = 45, remainder 2. So 47 = 5×9 + 2.
Formula
Real-world uses
- Packing 23 cookies into boxes of 5 (4 boxes and 3 left over)
- Scheduling rounds in a tournament
Common mistake
A remainder equal to or larger than the divisor means you can still fit another group.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Division with Remainder?
When b does not divide a exactly, a = bq + r with 0 ≤ r < b. It is a topic at the beginner level in Arithmetic & Number Sense.
What is the formula for Division with Remainder?
The key formula is a = bq + r.
Where is Division with Remainder used in real life?
Real-world examples: Packing 23 cookies into boxes of 5 (4 boxes and 3 left over); Scheduling rounds in a tournament.
What should I learn before Division with Remainder?
Make sure you are comfortable with Division, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Division with Remainder?
A remainder equal to or larger than the divisor means you can still fit another group.
How can I practise Division with Remainder?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Division with Remainder?
Move on to Fact Families next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Place Value – The value of a digit depends on its position: ones, tens, hundreds and so on.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.