Multiplication Basics

For Elementary Students

What is Multiplication?

Multiplication is a fast way to add the same number many times.

Think about it like this: Instead of counting 2 + 2 + 2 + 2 + 2, you can just say 5 × 2! Much faster!

Multiplication Means "Groups Of"

Example: 3 × 4 means "3 groups of 4"

Imagine 3 bags, each with 4 candies:

Bag 1: 🍬 🍬 🍬 🍬
Bag 2: 🍬 🍬 🍬 🍬
Bag 3: 🍬 🍬 🍬 🍬

Count them all: 4 + 4 + 4 = 12

So 3 × 4 = 12!

Another Way to Think About It

Example: 4 × 3 means "4 groups of 3"

Now imagine 4 bags, each with 3 candies:

Bag 1: 🍬 🍬 🍬
Bag 2: 🍬 🍬 🍬
Bag 3: 🍬 🍬 🍬
Bag 4: 🍬 🍬 🍬

Count: 3 + 3 + 3 + 3 = 12

So 4 × 3 = 12 too!

Both give the same answer!

Reading Multiplication

5 × 3 = 15

We read this as:

• "5 times 3 equals 15"
• OR "5 groups of 3 equals 15"

The Multiplication Symbol

You might see multiplication written different ways:

• 3 × 4 (times sign)
• 3 · 4 (dot)
• 3(4) (numbers next to each other)

They all mean the same thing: 3 times 4.

Skip Counting Is Multiplication!

When you skip count, you're actually multiplying!

Example: Count by 5s: 5, 10, 15, 20, 25

That's the same as:

• 1 × 5 = 5
• 2 × 5 = 10
• 3 × 5 = 15
• 4 × 5 = 20
• 5 × 5 = 25

Multiplication with Your Fingers

Example: 4 × 3 = ?

Hold up 3 fingers, 4 times (or 4 fingers, 3 times):

Count all the fingers: 12!

For Junior High Students

Multiplication Vocabulary

• Factors: The numbers you multiply (3 and 4 in 3 × 4)
• Product: The answer (12 in 3 × 4 = 12)

Example: 6 × 7 = 42

• Factors: 6 and 7
• Product: 42

Multiplication as Repeated Addition

Multiplication is a shortcut for adding the same number multiple times.

Example: 5 × 3 = ?

Long way: 3 + 3 + 3 + 3 + 3 = 15

Short way: 5 × 3 = 15

Why it works: You're adding 3 five times!

Properties of Multiplication

Commutative Property: Order doesn't matter

• 3 × 5 = 15
• 5 × 3 = 15

Both equal 15! You can multiply in any order.

Why? 3 groups of 5 is the same total as 5 groups of 3.

Identity Property: Multiplying by 1

Any number times 1 equals that same number.

• 7 × 1 = 7
• 1 × 25 = 25

Why? One group of 7 is just 7!

Zero Property: Multiplying by 0

Any number times 0 equals 0.

• 9 × 0 = 0
• 0 × 1000 = 0

Why? If you have zero groups, you have nothing!

Arrays Show Multiplication

An array is objects arranged in rows and columns.

Example: 4 × 3 (4 rows, 3 in each row)

⭐ ⭐ ⭐
⭐ ⭐ ⭐
⭐ ⭐ ⭐
⭐ ⭐ ⭐

Count them: 12 stars

So 4 × 3 = 12

OR you can see it as 3 columns of 4: 3 × 4 = 12 (same answer!)

Multiplication Tables (Times Tables)

Learning multiplication facts makes math faster!

The 2s table (counting by 2s):

• 2 × 1 = 2
• 2 × 2 = 4
• 2 × 3 = 6
• 2 × 4 = 8
• 2 × 5 = 10

The 5s table (counting by 5s):

• 5 × 1 = 5
• 5 × 2 = 10
• 5 × 3 = 15
• 5 × 4 = 20
• 5 × 5 = 25

The 10s table (easiest!):

• 10 × 1 = 10
• 10 × 2 = 20
• 10 × 3 = 30
• 10 × 4 = 40

Tip: To multiply by 10, just add a zero!

Strategies for Learning Multiplication

Doubles: Numbers multiplied by 2

• 2 × 6 = 12 (6 + 6)
• 2 × 8 = 16 (8 + 8)

Fives end in 0 or 5:

• 5 × 2 = 10
• 5 × 3 = 15
• 5 × 4 = 20
• 5 × 5 = 25

Nines trick: Use your fingers!

For 9 × 4:

• Hold up 10 fingers
• Put down the 4th finger
• Left side (3 fingers) = tens → 3
• Right side (6 fingers) = ones → 6
• Answer: 36

Real-Life Uses

Shopping: "3 shirts at $12 each. Total cost?"

• 3 × $12 = $36

Cooking: "Recipe needs 2 cups per batch. Making 4 batches?"

• 4 × 2 = 8 cups

Arrays: "Classroom has 5 rows with 6 desks each. Total desks?"

• 5 × 6 = 30 desks

Time: "7 days in a week. How many days in 4 weeks?"

• 4 × 7 = 28 days

Checking Your Answer

Use division to check multiplication!

If 5 × 6 = 30, then:

• 30 ÷ 5 = 6 ✓
• 30 ÷ 6 = 5 ✓

Both work, so 30 is correct!

Practice