Division Basics

For Elementary Students

What is Division?

Division means sharing or splitting things into equal groups.

Think about it like this: Imagine you have 12 cookies and want to share them equally with 3 friends. How many cookies does each friend get? That's division!

Division Means Sharing

Example: 12 ÷ 3 = 4

This means: "If you have 12 cookies and share them equally among 3 friends, each friend gets 4 cookies."

Friend 1: 🍪 🍪 🍪 🍪
Friend 2: 🍪 🍪 🍪 🍪
Friend 3: 🍪 🍪 🍪 🍪

Division Means Making Groups

You can also think of division as making groups!

Example: 12 ÷ 4 = 3

This means: "If you have 12 cookies and put them into groups of 4, you can make 3 groups."

Group 1: 🍪 🍪 🍪 🍪
Group 2: 🍪 🍪 🍪 🍪
Group 3: 🍪 🍪 🍪 🍪

Same 12 cookies, different way to divide!

Division Symbols

There are different ways to write division:

• 12 ÷ 3 = 4
• 12 / 3 = 4
• Or like this: 12 over 3 (as a fraction)

They all mean the same thing: 12 divided by 3 equals 4.

Division Vocabulary (Words to Know)

In 12 ÷ 3 = 4:

• 12 is what you're dividing up (the whole amount)
• 3 is how many groups (or how many in each group)
• 4 is the answer (how many in each group, or how many groups)

Don't worry about fancy words yet! Just understand what you're doing.

Division is the Opposite of Multiplication

If you know your times tables, division is easy!

Think: 3 × 4 = 12

So:

• 12 ÷ 3 = 4 (because 3 times 4 equals 12)
• 12 ÷ 4 = 3 (because 4 times 3 equals 12)

Division asks: "What number times this equals that?"

Example with Pictures

Problem: 10 ÷ 2 = ?

Think: 10 stars shared between 2 groups

Group 1: ⭐ ⭐ ⭐ ⭐ ⭐
Group 2: ⭐ ⭐ ⭐ ⭐ ⭐

Each group gets 5 stars, so 10 ÷ 2 = 5.

Easy Division Facts

Just like addition and multiplication, some divisions are easy to remember:

• Any number ÷ 1 = that same number (7 ÷ 1 = 7)
• Any number ÷ itself = 1 (8 ÷ 8 = 1)
• 0 ÷ any number = 0 (0 ÷ 5 = 0)

For Junior High Students

Division Terminology

Now let's learn the proper vocabulary:

In 12 ÷ 3 = 4:

• Dividend — the number being divided (12)
• Divisor — the number you divide by (3)
• Quotient — the result (4)

Formula: Dividend ÷ Divisor = Quotient

The Relationship Between Multiplication and Division

Division and multiplication are inverse operations (opposites).

Fact family: If a × b = c, then c ÷ a = b and c ÷ b = a

Example:

• 5 × 4 = 20
• 20 ÷ 5 = 4
• 20 ÷ 4 = 5

Check your division: Multiply the quotient by the divisor. You should get the dividend!

20 ÷ 5 = 4 → Check: 4 × 5 = 20 ✓

Division Rules to Remember

Rule 1: Dividing by 1

Any number divided by 1 equals itself.

• 9 ÷ 1 = 9
• 100 ÷ 1 = 100

Why? If you have 9 items and put them all in 1 group, that group has 9 items!

Rule 2: Dividing a Number by Itself

Any non-zero number divided by itself equals 1.

• 7 ÷ 7 = 1
• 50 ÷ 50 = 1

Why? If you have 7 items and make groups of 7, you can make 1 group!

Rule 3: Dividing Zero

Zero divided by any non-zero number is 0.

• 0 ÷ 5 = 0
• 0 ÷ 100 = 0

Why? If you have nothing (0) to share, everyone gets nothing!

Rule 4: You CANNOT Divide by Zero

Division by zero is undefined — it doesn't make sense mathematically.

• 5 ÷ 0 = ? has no answer!

Why? You can't split 5 things into zero groups. It's impossible!

Remainders

Sometimes numbers don't divide evenly. The amount left over is called the remainder.

Example: 14 ÷ 3 = ?

Step 1: How many groups of 3 can you make from 14?

• 3 × 4 = 12 (closest without going over)

Step 2: How many are left?

• 14 - 12 = 2

Answer: 14 ÷ 3 = 4 remainder 2 (written as 4 R2)

Check: (4 × 3) + 2 = 12 + 2 = 14 ✓

Remainder Examples

Example 1: 17 ÷ 5

• 5 × 3 = 15 (closest)
• 17 - 15 = 2
• Answer: 3 R2

Example 2: 23 ÷ 4

• 4 × 5 = 20
• 23 - 20 = 3
• Answer: 5 R3

Real-World Uses of Division

Sharing: "We have 20 candies and 4 kids. How many does each kid get?"

• 20 ÷ 4 = 5 candies each

Making groups: "We have 30 students. If we make teams of 6, how many teams?"

• 30 ÷ 6 = 5 teams

Finding how many fit: "A box holds 8 books. How many boxes for 50 books?"

• 50 ÷ 8 = 6 R2 → Need 7 boxes (6 full boxes + 1 for the remaining 2)

Mental Math Strategies

Use known facts: 24 ÷ 6 = ?

• Think: "What times 6 equals 24?" → 4 × 6 = 24 → Answer is 4

Break it apart: 36 ÷ 3 = ?

• Break 36 into easier parts: 30 ÷ 3 = 10 and 6 ÷ 3 = 2
• Add: 10 + 2 = 12

Use patterns: Dividing by 10 moves the decimal left

• 80 ÷ 10 = 8
• 350 ÷ 10 = 35

Practice