Division: Sharing and Grouping: Class 3 Study Guide
Division means splitting into equal parts. If you know your tables, you can divide.
Division is shown by the sign ÷. If 12 sweets are shared equally among 3 children, each child gets 4 sweets: 12 ÷ 3 = 4. The number being divided (12) is the dividend, the number we divide by (3) is the divisor, and the answer (4) is the quotient.
Division is the opposite of multiplication. Since 3 × 4 = 12, we know 12 ÷ 3 = 4 and 12 ÷ 4 = 3. Every multiplication table is also a division table in reverse.
Sharing and grouping
In sharing, you know how many groups and find how many in each: 20 mangoes shared among 4 baskets gives 5 in each. In grouping, you know the size of each group and find how many groups: 20 mangoes in baskets of 5 gives 4 baskets. Both are 20 ÷ 4 or 20 ÷ 5 depending on the story.
| Story | Type | Sum |
|---|---|---|
| 20 mangoes shared by 4 baskets | Sharing | 20 ÷ 4 = 5 |
| 20 mangoes packed 5 per basket | Grouping | 20 ÷ 5 = 4 |
Division by repeated subtraction
You can also divide by taking away the same number again and again. For 15 ÷ 3, subtract 3 repeatedly: 15 − 3 = 12, 12 − 3 = 9, 9 − 3 = 6, 6 − 3 = 3, 3 − 3 = 0. We subtracted 3 five times, so 15 ÷ 3 = 5.
Remainders
Sometimes things cannot be shared equally. 17 ÷ 5: 5 × 3 = 15, which leaves 2. So 17 ÷ 5 = 3 remainder 2. The remainder is always smaller than the divisor. You can check: (3 × 5) + 2 = 17.
5 × 3 = 15 is just below 17.
17 − 15 = 2.
3 remainder 2.
5 × 3 + 2 = 17.
Common mistakes
Students sometimes divide the smaller number by the larger, which gives a different problem. Keep the total first. Others forget to check that the remainder is smaller than the divisor. If it is not, the quotient can be bigger. Finally, division by 0 is not possible because nothing can be shared among zero groups.
Check your understanding: model answers
1. 24 ÷ 6 = 4 pencils each. 2. 29 ÷ 4 = 7 remainder 1. Check: (7 × 4) + 1 = 29. 3. For example: 18 sweets are packed in bags of 3. How many bags? 18 ÷ 3 = 6.
✨ Key Takeaways
- Division shares a total equally or finds how many equal groups.
- Division is the reverse of multiplication.
- A remainder is what is left over and is smaller than the divisor.
- Check division by multiplying and adding the remainder.
💬 Questions for Discussion & Reflection
- Share 24 pencils among 6 students. How many each?
- Find 29 ÷ 4 and check your answer.
- Make up a grouping story for 18 ÷ 3.