You know division facts from fact families: $24 \div 4 = 6$ because $6 \times 4 = 24$. But what about $23 \div 4$? Some totals do not split evenly. The part left over is the remainder.
Key idea
To divide $23 \div 4$, find the biggest multiple of 4 that fits in 23: $5 \times 4 = 20$. The quotient is 5 and the remainder is $23 - 20 = 3$. Write $23 \div 4 = 5$ R 3. The remainder is always less than the divisor.
Why it works
Make groups of 4 from 23 counters. After 5 groups you have used 20, and 3 are left. If 4 or more were left, you could make another group, so you were not done yet. That is why a remainder must be smaller than the divisor.
Worked example: Find the quotient and remainder
Divide $23 \div 4$.
- Count by 4s: 4, 8, 12, 16, 20, 24. 24 is too big, so stop at $20 = 5 \times 4$.
- Left over: $23 - 20 = 3$.
- Check: $5 \times 4 + 3 = 23$.
Answer: $5$ R $3$
Worked example: Check a remainder
Is $47 \div 6 = 6$ R 11 correct?
- $6 \times 6 + 11 = 47$, so the numbers add up, but 11 is more than 6.
- 11 left over is enough for another group of 6: one more group, with $11 - 6 = 5$ left.
Answer: No. $47 \div 6 = 7$ R 5.
Common mistake
Stopping too early and leaving a remainder that is as big as the divisor or bigger, like 6 R 11 for $47 \div 6$. Always compare: if the remainder is not less than the divisor, make another group.