MOD and DIV Gym
Drilling the two operators students trip on: DIV, integer division that gives the whole-number quotient, and MOD, the remainder left over, with worked examples and their everyday uses.
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Free interactive practice on the steps that lose marks under exam pressure.
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Dividing two ways
When a computer divides whole numbers it can give two useful answers. DIV tells you how many whole times one number fits into another, and MOD tells you what is left over. These two come up constantly in programming, and they are easy to mix up. This module drills them with worked examples until they are automatic.
Division vocabulary
Learn these four terms before you do the sums.
DIV against MOD
The two operators answer different questions about the same division.
Whole part and leftover
A top answer treats one division as two answers. Work out how many whole times the divisor fits to get the DIV result, then see what is left to get the MOD result. A quick check ties them together: the DIV result times the divisor, plus the MOD result, gets you back to the start. Testing a number MOD 2 tells you at once whether it is even.
Match the term
- DIV
- MOD
- quotient
- remainder
- gives the whole-number result of a division
- gives only what is left over
- how many whole times one number fits another
- the amount that does not divide evenly
What is 17 MOD 5?
What does 17 MOD 5 give?
- 2
- 3
- 12
- 0
Which are correct?
Select the TWO statements that are correct.
- 10 DIV 3 gives 3.
- 10 MOD 3 gives 1.
- 10 DIV 3 gives 1.
- 10 MOD 3 gives 3.
Work out a remainder
Put the steps of working out 17 MOD 5 by hand in order, earliest first.
- See how many whole times 5 fits into 17
- That whole number is 3, the DIV result
- Multiply 3 by 5 to get 15
- Subtract 15 from 17 to get the remainder 2
Complete the facts
Integer division DIV gives the whole-number _____. The amount left over is found with _____. 17 DIV 5 gives _____. 17 MOD 5 gives _____. To test whether a number is even, check that the number MOD 2 gives _____.
Integer division
Work out 17 DIV 5. This is how many whole times 5 fits into 17. What is the answer?
The remainder
Work out 17 MOD 5. This is the remainder after 5 fits into 17 three times. What is the answer?
Spot the correct results
Tap the TWO results that are correct.
- 17 DIV 5 is 3
- 17 MOD 5 is 2
- 17 DIV 5 is 2
- 17 MOD 5 is 3
DIV or MOD?
Read each task and choose the operator that solves it.
- You want to test whether a number is even. Which operator helps?
- 17 sweets are shared into bags of 5. How many FULL bags are there?
- 17 sweets are shared into bags of 5. How many sweets are LEFT OVER?
Explain the operators
Explain what the DIV and MOD operators do and give a worked example of each.
- Explain what DIV returns, with an example
- Explain what MOD returns, with an example
- Give one real use of MOD, such as testing for even numbers