Times Table Methods
Why multiplying by zero gives zero
Use empty groups and arrays with no dots to make the zero property sensible.
Quick answer
Multiplying any number by zero gives zero because you have zero groups of that number, which means nothing at all.Learning outcome
By the end of this page, you will understand why multiplying any number by zero always gives zero, using empty groups, arrays, and real-life examples. Success signs:- You can explain that multiplying by zero means having zero groups of something
- You can draw or show zero groups of 3, 5, or any number
- You can solve 7 × 0 or 0 × 9 without counting
- You can use zero in real-life situations like sharing nothing or having no items
Why this matters
Understanding why multiplying by zero gives zero helps you in maths and in everyday life. It's a special rule that makes maths work properly. When you're sharing things, or counting items, or even playing games, you'll meet zero often. Knowing that zero times anything is zero helps you solve problems faster and avoid silly mistakes. It's also a key part of learning bigger maths like algebra and equations later on.How it works
Multiplying by zero is like making empty groups. If you have 5 groups with 0 items in each group, how many items do you have in total? Zero. It doesn't matter how many groups you have, if each group has zero items, the total is zero. Let’s think of it this way:- 5 × 0 means 5 groups with 0 items in each group
- 0 × 5 means 0 groups with 5 items in each group
- Both give the same answer: zero
- 0 × 3 = 0 + 0 + 0 = 0
- 0 × 7 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
Examples you can see
Let’s look at some simple examples to help you understand. Example 1: Empty plates Imagine you have 4 plates, and each plate has 0 cookies on it. How many cookies are there in total?- 4 plates with 0 cookies each
- 4 × 0 = 0 cookies
- 6 sweets × 0 friends = 0 sweets
- 0 jumps × 3 steps = 0 steps
- 0 rows × 5 columns = 0 squares
Try it as a mini adventure
The Zero Treasure Hunt You are going on a treasure hunt, but there’s a twist! The treasure map says: “Find the treasure where there are 0 coins in each of 8 boxes.” Let’s go on this adventure together: 1st time: You find 8 boxes, but each box has 0 coins. 2nd time: You check each box carefully, and there are 0 coins in each one. 3rd time: You count all the coins. How many coins are there in total? 4th time: You write down the maths: 8 × 0 = ? 5th time: You find that there are 0 coins in total. Challenge: Try this with 3 boxes and 0 coins each. What is 3 × 0?Common mistakes
- Mistake: Thinking 0 × 5 = 5 or 0 × 3 = 3 Why it happens: Children might confuse multiplication with addition. Fix: Remember, 0 × 5 means 0 groups of 5, so it’s 0.
- Mistake: Thinking 0 × 0 = 0 because one of the numbers is zero Why it happens: It’s easy to get confused when both numbers are zero. Fix: 0 × 0 = 0 because you have 0 groups of 0 items, which is still 0.
- Mistake: Thinking that multiplying by zero makes the other number disappear Why it happens: Some children think the zero makes the number go away. Fix: The zero doesn’t make the number disappear. It means there are zero groups of that number.
Parent and carer guide
As a parent or carer, here’s how you can help your child understand why multiplying by zero gives zero:- Use real-life examples: Talk about empty plates, no friends to share with, or no toys in a box.
- Draw arrays: Draw 0 rows with 5 dots in each row. Show that there are 0 dots in total.
- Count together: Practice counting in 0s, like 0, 0, 0, 0…
- Play the zero game: Ask questions like, “If you have 0 apples and 5 friends, how many apples do you have?”
- Be patient: It can take time for this idea to click. Encourage questions and keep it fun!
Practice questions
- What is 5 × 0?
- What is 0 × 7?
- What is 0 × 12?
- What is 9 × 0?
- What is 0 × 0?
- 5 × 0 = 0
- 0 × 7 = 0
- 0 × 12 = 0
- 9 × 0 = 0
- 0 × 0 = 0
FAQ
Why does any number multiplied by zero equal zero?
Because multiplying by zero means you have zero groups of that number. No matter how big the number is, if you have zero groups, you have nothing.
Can you multiply zero by zero?
Yes! Zero times zero equals zero. It means zero groups of zero items, which is still zero.
Is multiplying by zero the same as adding zero?
No. Adding zero to a number doesn’t change it, but multiplying by zero means you have zero groups of that number, which gives zero.
Why is this rule important in maths?
This rule helps us solve equations and understand patterns. It makes maths work consistently, so we know that 0 × anything = 0 every time.
Can I use this in real life?
Yes! Think of sharing nothing, having no items, or not having any groups. It helps you solve problems where things are not there.
Times Table Facts: 0 × n to 12 × n
| 0 × n | 1 × n | 2 × n | 3 × n | 4 × n | 5 × n | 6 × n | 7 × n | 8 × n | 9 × n | 10 × n | 11 × n | 12 × n |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 × 0 = 0 | 1 × 0 = 0 | 2 × 0 = 0 | 3 × 0 = 0 | 4 × 0 = 0 | 5 × 0 = 0 | 6 × 0 = 0 | 7 × 0 = 0 | 8 × 0 = 0 | 9 × 0 = 0 | 10 × 0 = 0 | 11 × 0 = 0 | 12 × 0 = 0 |