Multiplication is a convenient way to describe equal groups. Division can share an amount equally or find how many equal groups fit into it. Drawing a small array of dots makes both operations easier to understand than memorising answers alone.
Use equal groups
Four groups of three counters contain 3 + 3 + 3 + 3 = 12 counters. This can be written as 4 × 3 = 12. An array with four rows and three columns shows the same total. Turning the array shows why 3 × 4 gives the same answer.
Multiplying a whole number by 1 leaves it unchanged. Multiplying it by 0 gives 0. These rules describe groups; they are not exceptions to remember without meaning.
Division and remainders
To calculate 12 ÷ 3, share 12 counters into three equal groups. Each group has four counters. When an amount does not divide exactly, a remainder is left. For whole-number division, the remainder must be smaller than the divisor.
- Check with: dividend = divisor × quotient + remainder.
- Division by zero is not defined.
- Division is not commutative: 12 ÷ 3 is different from 3 ÷ 12.
Put it into practice
A worked example
Share 23 stickers equally among five children. How many does each get?
- Five groups of four use 5 × 4 = 20 stickers.
- 23 − 20 = 3 stickers remain.
- Check: 5 × 4 + 3 = 23, and the remainder 3 is smaller than 5.
Answer: Four stickers each, with three stickers left over.
Try it yourself
Have a go before revealing the answer.
Find 7 × 6 using 5 × 6 and 2 × 6.
Show answer
30 + 12 = 42.
Answer: 30 + 12 = 42.
Find 29 ÷ 4 as a quotient and remainder.
Show answer
Quotient 7, remainder 1. Check: 4 × 7 + 1 = 29.
Answer: Quotient 7, remainder 1. Check: 4 × 7 + 1 = 29.
Watch out for these
- Make every group equal before using multiplication.
- A remainder equal to or larger than the divisor means another full group can be made.
Continue with official resources
Match these concept notes to your current textbook and syllabus. They are independent explanations, not official board publications.
