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Multiplication

Where this is used

When you have several groups that all hold the same number of things, counting one by one takes forever. Multiplication gets you the total in one step. It shows up in factories, in shops, and inside computer programs — it may be the most-used calculation there is.

Key points

Multiplication has a rectangle shape

3 × 4 means "4 groups of 3." Lay them out and you get a rectangle 3 tall and 4 wide. The number of squares in that rectangle is the answer. So multiplication is something you can actually see as a shape.

4 groups3 in each3 × 4 = 12 (count the squares)

Flipping it around gives the same answer

3 × 4 and 4 × 3 both come out to 12. Tip the rectangle on its side and the number of squares doesn't change. Once you know this, you only have to memorize about half of the times table.

344 × 3 = 12 (the same rectangle, just tipped over)

The times table is a map of multiplication

Learn the times table and 81 different calculations become instant. Even as an adult, this is the base that all mental math sits on. Here's a pattern: in the 9s, the tens digit and the ones digit of the answer always add up to 9 (18 → 1 + 8 = 9).

The 3s go up by 3 every time
0510152033×163×293×3123×4153×5183×6

Using it to work out prices

Buy 7 rolls at ¥120 each and you get 120 × 7 = ¥840. Shopping is mostly multiplication. If you can figure out roughly what the total should be before you reach the register, you'll notice when something rings up wrong.

How many rolls, and what you pay
02505007501000 yen1201 roll2402 rolls3603 rolls4804 rolls6005 rolls7206 rolls8407 rolls

Check yourself 5questions

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Q1 There are 4 boxes with 6 eggs in each box. How many eggs in all?

Q2 What is 7 × 8?

Q3 There are 5 rows of chairs with 8 chairs in each row. How many chairs in all?

Q4 You buy 7 rolls at ¥120 each. What do you pay?

Q5 Which one has the same answer as 3 × 4?

Jobs that use this

Every job uses this. The ones below are just where it shows up most.

Production line supervisor $55k
Event venue coordinator $42k
Programmer $110k

Production line supervisor$55k

If you know how many items the line makes in one minute, multiplication tells you how many it makes in 8 hours. Supervisors run that calculation every day to decide whether an order will ship on time.

Maths used: MultiplicationRate per unit

Event venue coordinator$42k

When planning how to lay out the seats, you multiply rows by seats per row to find how many people fit. Get one row wrong and dozens of people are left without a seat.

Maths used: MultiplicationArea

Programmer$110k

Inside a computer, the same calculation gets repeated tens of thousands of times. Time for one repeat × number of repeats tells a programmer how many seconds the program will take.

Maths used: MultiplicationComputational cost

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