X Tables
Times Table Methods

Odd and even products

Explore what happens when odd and even numbers are multiplied.

Quick answer

When you multiply two numbers, the product (the answer) is even if at least one of the numbers is even. The product is odd only if both numbers are odd.

Learning outcome

By the end of this page, you will understand how odd and even numbers behave when multiplied together. Success signs:
  • You can tell if a product will be odd or even just by looking at the two numbers you are multiplying.
  • You can explain why multiplying an odd number by an even number always gives an even product.
  • You can find patterns in multiplication tables with odd and even numbers.
  • You can use your knowledge to solve problems quickly.

Why this matters

Knowing about odd and even products helps you understand multiplication better. It’s useful in games, puzzles, and everyday life. For example, if you're sharing items equally, it helps to know if the total number is odd or even. In sports, you might need to know if a team score is even or odd to decide how to divide players or equipment. This skill also helps you check your work quickly when doing multiplication.

How it works

To understand what happens when you multiply odd and even numbers, let’s think about what makes a number odd or even:
  • An even number can be split into two equal groups with nothing left over.
  • An odd number cannot be split into two equal groups without something left over.
When we multiply numbers, we make groups of equal size. If we have an even number of groups, or at least one group with an even number of items, the total will be even. If we have only odd groups with odd numbers of items, the total will be odd. Let’s look at this step by step:
  1. Odd × Odd = Odd
  2. Even × Odd = Even
  3. Odd × Even = Even
  4. Even × Even = Even
We can test these rules with small numbers and see how they work.

Examples you can see

Let’s explore with some examples: Example 1: Odd × Odd If we have 3 groups of 5 items each, we have 3 × 5 = 15 items. We can’t split 15 into two equal groups without having one left over, so 15 is odd. So, Odd × Odd = Odd Example 2: Even × Odd If we have 4 groups of 3 items each, we have 4 × 3 = 12 items. We can split 12 into two equal groups of 6, so 12 is even. So, Even × Odd = Even Example 3: Odd × Even If we have 5 groups of 4 items each, we have 5 × 4 = 20 items. We can split 20 into two equal groups of 10, so 20 is even. So, Odd × Even = Even Example 4: Even × Even If we have 2 groups of 6 items each, we have 2 × 6 = 12 items. We can split 12 into two equal groups of 6, so 12 is even. So, Even × Even = Even Let’s try some more with real-world examples. Real-world example: Sharing cookies Imagine you have 6 cookies and want to share them equally between 2 friends. You have 6 cookies and 2 friends, so 6 ÷ 2 = 3 cookies each. This is even × even = even. Now, imagine you have 7 cookies and 3 friends. 7 ÷ 3 = 2 cookies each with 1 left over. This is odd × odd = odd.

Try it as a mini adventure

Adventure: The Number Kingdom You are a brave explorer in the Kingdom of Numbers. You find a magical chest that opens only if you can solve the mystery of odd and even products. The chest has four locks, each with a multiplication problem:
  1. Lock 1: 5 × 7 = ?
  2. Lock 2: 6 × 4 = ?
  3. Lock 3: 3 × 8 = ?
  4. Lock 4: 9 × 11 = ?
Your mission is to figure out if each answer is odd or even without calculating the full product.
  1. 5 × 7 = ?
  2. 6 × 4 = ?
  3. 3 × 8 = ?
  4. 9 × 11 = ?
Can you open all the locks?
  1. 5 is odd, 7 is odd → Odd × Odd = Odd
  2. 6 is even, 4 is even → Even × Even = Even
  3. 3 is odd, 8 is even → Odd × Even = Even
  4. 9 is odd, 11 is odd → Odd × Odd = Odd
Great job! You’ve opened the chest and found a treasure map. The next clue says: “Look for the pattern in the times tables!”

Common mistakes

  • Mistake: Thinking that Odd × Odd = Even.
    Why it happens: Confusing the rules or not understanding that two odd numbers together always make an odd product.
    Fix: Remember that when you add two odd numbers, you get an even number. When you multiply two odd numbers, you get an odd number.
  • Mistake: Thinking that any multiplication with an even number gives an even product.
    Why it happens: Remembering that even × odd = even, but forgetting that odd × odd = odd.
    Fix: Always check both numbers. If both are odd, the product is odd. If at least one is even, the product is even.
  • Mistake: Trying to calculate the full product to decide if it's odd or even.
    Why it happens: Not knowing the shortcut rules.
    Fix: Use the shortcut: look at the numbers, decide if they’re odd or even, and apply the rules.

Parent and carer guide

Parents and carers can help children learn about odd and even products in a few simple ways:
  • Use everyday examples like sharing snacks or counting toys to show odd and even numbers.
  • Play games where you say a multiplication and ask if the product is odd or even.
  • Draw arrays to show how multiplication works, and then count to see if the total is odd or even.
  • Use physical objects like blocks or counters to demonstrate the concept.
  • Encourage children to explain their thinking. Ask: “How did you know that?”
Try this activity: Set up a small multiplication challenge using a dice or a spinner. Each player picks a number and multiplies it by a random number. Then, they decide if the product is odd or even. This helps children practice quickly and build confidence.

Practice questions

  1. What is 7 × 9? Is it odd or even?
  2. What is 4 × 6? Is it odd or even?
  3. What is 3 × 5? Is it odd or even?
  4. What is 8 × 11? Is it odd or even?
  5. What is 2 × 13? Is it odd or even?
Answers:
  1. 7 × 9 = 63 → Odd
  2. 4 × 6 = 24 → Even
  3. 3 × 5 = 15 → Odd
  4. 8 × 11 = 88 → Even
  5. 2 × 13 = 26 → Even

FAQ

Q: Why is odd × odd = odd?

A: When you multiply two odd numbers, you are making groups where each group has an odd number of items. When you add these odd groups together, you get an odd total.

Q: Does this rule work for all numbers?

A: Yes, this rule works for all whole numbers, no matter how big they are.

Q: Can I use this to check my multiplication?

A: Yes! If you know the rule, you can quickly check if your answer makes sense. For example, if you multiply an even number by an odd number, your answer must be even.

Q: What if I have three numbers to multiply?

A: You can still use the same rule. If any one of the numbers is even, the final product will be even. Only if all three numbers are odd will the product be odd.

Q: Are there any patterns in the times tables?

A: Yes! In the times tables, if you look at the columns for even numbers, the products are always even. For odd numbers, the products are odd only when you multiply two odd numbers.