When we put things into equal groups, we are working with the ideas of multiplication and division.
Multiplication — Repeated Addition
- Multiplication helps us add the same number many times quickly.
- 3 x 4 = 12 means 3 groups of 4, or 4 + 4 + 4 = 12.
Division — Sharing Equally
- Division means splitting a total into equal groups.
- 12 / 4 = 3 means 12 shared into 4 equal groups gives 3 in each group.
- We can also think of it as: how many groups of 4 can we make from 12?
Important Terms
- Dividend — the total number to be divided.
- Divisor — the number we divide by.
- Quotient — the answer (result of division).
- Remainder — the amount left over when division is not exact.
Relationship: Division and Multiplication
If a x b = c, then c / a = b and c / b = a.
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There are 5 baskets. Each basket has 6 apples. How many apples in all?
5 x 6 = 30 apples
24 children are divided into groups of 6. How many groups?
24 / 6 = 4 groups
35 mangoes are shared equally among 8 children. How many does each child get, and how many are left over?
35 / 8 = 4 remainder 3. Each child gets 4 mangoes, and 3 mangoes are left over.
A box holds 9 chocolates. Ritu buys 7 boxes. How many chocolates in all?
7 x 9 = 63 chocolates
56 students sit in rows of 7. How many rows are there?
56 / 7 = 8 rows
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Common mistakes
- Confusing the quotient and remainder — the quotient is what each person/group gets; the remainder is what is left over.
- Writing 0 as the remainder when division is exact — this is correct! When 20 / 4 = 5, the remainder is 0.
Summary
Multiplication and division are opposite operations. Division splits a total into equal groups. Always check: quotient x divisor + remainder = dividend.