Math Core

Imagine 4 plates with 3 cookies on each plate. You could add $3 + 3 + 3 + 3$ . But there is a faster way to say it and write it. That way is called multiplication.

What are equal groups?

Groups are equal when every group has the same number of things.

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Here there are 4 groups with 3 cookies in each group. Every group has 3, so the groups are equal.

These groups are not equal:

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One group has 2, one has 4 and one has 1. You can only multiply when the groups are equal.

From adding to multiplying

To find the total cookies, you can add the groups:

3 + 3 + 3 + 3 = 12

Adding the same number again and again is called repeated addition. Multiplication is a short way to write it:

4 \times 3 = 12

Read it as "4 times 3 equals 12" or "4 groups of 3 is 12."

Definition

Multiplication

Multiplication finds the total when you have equal groups.

\text{number of groups} \times \text{number in each group} = \text{total}

The numbers you multiply are called factors. The answer is called the product.

In $4 \times 3 = 12$ , the factors are 4 and 3. The product is 12.

Skip counting

You can also find the total by skip counting. Count by the number in each group, one group at a time.

For 4 groups of 3, count by threes: 3, 6, 9, 12. You said 4 numbers, one for each group.

Worked example: Stars in boxes

There are 5 boxes. Each box has 2 stars. How many stars are there?

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There are 5 groups of 2. Write $5 \times 2$ .

Skip count by twos: 2, 4, 6, 8, 10.

$5 \times 2 = 10$ . There are 10 stars.

Worked example: Write it two ways

Write $6 + 6 + 6$ as a multiplication. Then find the product.

The number 6 is added 3 times. That is 3 groups of 6, so write $3 \times 6$ .

Skip count by sixes: 6, 12, 18.

$3 \times 6 = 18$ .

Worked example: A word problem

A pet shop has 4 fish tanks. There are 5 fish in each tank. How many fish are there in all?

Number of groups: 4 tanks
Number in each group: 5 fish

$4 \times 5$ . Skip count by fives: 5, 10, 15, 20.

There are 20 fish.

Common mistake

Don't mix up the two numbers. The first factor tells how many groups. The second factor tells how many are in each group. "4 tanks with 5 fish each" is $4 \times 5$ : 4 groups of 5.

Tip

Check with repeated addition. For $4 \times 5$ , add $5 + 5 + 5 + 5 = 20$ . Same answer!

Practice

Practice 1

How many apples are there?

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Type a number.

Practice 2

Which picture shows equal groups?

Practice 3

Which multiplication means the same as $2 + 2 + 2 + 2 + 2 + 2$ ?

Practice 4

What is $3 \times 4$ ?

Type a number.

Practice 5

In $7 \times 5 = 35$ , how many groups are there?

Type a number.

Practice 6

Maya has 6 bags. She puts 5 marbles in each bag. How many marbles does she use?

Type a number.

Practice 7

A spider has 8 legs. How many legs do 2 spiders have?

Type a number.

Practice 8

Leo has 20 stickers. He puts them into equal groups of 5. How many groups does he make?

Type a number.