Multiplication as equal groups and arrays

Read 4 × 3 as 4 groups of 3, count arrays of rows by multiplying, and turn a fact round when the other order is easier.

Equal groups and the × sign

When every group has the same number of things, you can count them with multiplication. 4 × 3 is read "4 groups of 3" or "4 times 3". The first number says how many groups there are; the second says how many are in each group.

You can find 4 × 3 by adding 3 four times, 3 + 3 + 3 + 3 = 12, or by counting by 3s: 3, 6, 9, 12. The answer to a multiplication is called the product.

Arrays

An array is things set out in equal rows. 3 rows of 5 is 3 × 5: each row is one group.

Arrays are everywhere: egg cartons, windows, seats in a hall, a bar of chocolate. To count one, multiply the number of rows by the number in each row instead of counting every one.

Turning it round

Turn an array on its side and the rows become columns. 3 rows of 5 becomes 5 rows of 3, and nothing is added or taken away. So 3 × 5 = 5 × 3: you can multiply two numbers in either order.

This halves the facts to learn: if you know 2 × 9 = 18, you also know 9 × 2 = 18. Pick whichever order is easier to count.

Two more facts are worth knowing. Any number times 1 is itself: 7 × 1 = 7, seven groups of 1. Any number times 0 is 0: 6 × 0 = 0, six groups with nothing in them.

Try it yourself

Work each one on paper first, then open the answer to check.

1. Write 6 groups of 4 as a multiplication, then find the product.

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   6 × 4 = 24.

2. A tray has 4 rows of 7 cupcakes. How many cupcakes are there?

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   4 × 7 = 28 cupcakes.

3. Which is the same as 5 + 5 + 5: 3 × 5 or 5 × 5?

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   3 × 5. There are three 5s.

4. If 8 × 3 = 24, what is 3 × 8?

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   24. Turning the numbers round does not change the product.

5. What is 9 × 0?

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   0. Nine groups of nothing is nothing.