Jupiter2U School
Chapter 04

4. Multiplication, Division & Times Tables

Primary

Multiplication is fast repeated addition; division is fair sharing or grouping. Knowing your times tables turns slow counting into an instant answer.

At a glance
Core ideaMultiplication is fast repeated addition; division is fair sharing or grouping.
Key termArray: rows and columns of dots that picture a multiplication fact.
You can…Recall the times tables and divide with a remainder.
Watch out3 × 4 = 4 × 3, but division is not reversible — 12 ÷ 3 ≠ 3 ÷ 12.
01 · Theory

Repeated addition and equal sharing

Multiplication (×): 4 × 3 means 4 groups of 3, the same as 3 + 3 + 3 + 3 = 12. An array — rows and columns of dots — is a picture of a multiplication fact. The times tables from 1 to 10 are simply these results memorised, so you don't have to add them up every time.

Division (÷): 12 ÷ 3 asks "how many groups of 3 fit into 12?" — the answer is 4. Multiplication and division undo each other: since 4 × 3 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3. Sometimes sharing doesn't come out even, leaving a remainder: 13 ÷ 4 = 3 remainder 1.

02 · Explanation

Why times tables and arrays help

Knowing your times tables by heart is like knowing how to spell common words — it frees your brain to focus on the harder parts of a problem instead of re-adding the same numbers every time. Every later topic in math, from fractions to algebra, leans on quick multiplication.

An array also reveals a neat fact: 3 rows of 4 dots has exactly the same total as 4 rows of 3 dots — just turn the picture on its side. That is why 3 × 4 = 4 × 3, always.

Step 1DivideHow many whole times does the divisor go into the current digits?
Step 2MultiplyMultiply that quotient digit back by the divisor.
Step 3SubtractTake the product away to leave the remainder so far.
Step 4Bring downCarry down the next digit beside that remainder.
Step 5RepeatLoop until no digits remain; whatever is left is the remainder.
03 · Practical

Worked example: arrays and sharing with a remainder

Problem A — multiplication

A farmer plants apple trees in 6 rows of 8 trees each. How many trees in total?

  1. This is 6 groups of 8: 6 × 8.
  2. Using the times table (or 6 × 8 = 6 × 10 − 6 × 2 = 60 − 12): 48.
Problem B — division with a remainder

23 cookies are shared equally among 5 friends. How many does each friend get, and how many are left over?

  1. 23 ÷ 5: 5 goes into 23 four whole times, since 5 × 4 = 20.
  2. Left over: 23 − 20 = 3.
  3. Each friend gets 4 cookies, with 3 cookies left over.
04 · Q&A

Test your understanding

What is 7 × 8?

56. A handy trick: 7 × 8 = 7 × 10 − 7 × 2 = 70 − 14 = 56.

Why is 3 × 4 the same as 4 × 3?

Because of the array picture: 3 rows of 4 dots has the same total dots as 4 rows of 3 dots — just rotate it. This is called the commutative property of multiplication.

If 9 × 6 = 54, what are 54 ÷ 9 and 54 ÷ 6?

54 ÷ 9 = 6 and 54 ÷ 6 = 9. Multiplication and division facts travel together in the same fact family, just like addition and subtraction do.

What does a remainder mean?

It's the amount left over after making as many equal, whole groups as possible — always smaller than the number you divided by. In 13 ÷ 4, the remainder 1 means one item couldn't join a full group of 4.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Repeated additionArraysTimes tablesEqual sharingRemaindersFact familiesMultiplication and Division
Infographic

The key facts, visualised

a x b
b groups of a added together
Array
Rows and columns show a product
Divide
Split into equal groups
Remainder
What is left over after sharing
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1What is 6 x 4?

  1. 6 x 4 means four groups of 6
  2. Add 6 + 6 + 6 + 6 = 24
  3. Or use the times table: 6 x 4 = 24

Example 2Share 17 sweets among 5 children equally.

  1. 5 x 3 = 15, so each child gets 3
  2. 17 - 15 = 2 left over
  3. Each gets 3 with remainder 2
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Work out 7 x 8.
From the times table, 7 x 8 = 56.
2Draw an array for 3 x 5. How many dots?
3 rows of 5 dots make 15 dots.
3Divide 24 by 6.
6 fits into 24 exactly 4 times, so 24 / 6 = 4.
4What is 29 divided by 4?
4 x 7 = 28 with 1 left over, so 7 remainder 1.
5Write the fact family for 3, 4, 12.
3x4=12, 4x3=12, 12/4=3, 12/3=4.
6Nine boxes hold 6 pencils each. How many pencils?
9 x 6 = 54 pencils.