An array of 3 rows of 4 turned sideways is 4 rows of 3. Nothing was added or taken away.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
So the order does not matter.
Commutative property means you can multiply in either order and get the same product.
Why this is worth knowing
It halves how many facts you have to learn. Knowing 8 × 3 gives you 3 × 8 free.
Same product, different story
3 plates of 4 buns and 4 plates of 3 buns both give 12, but they are not the same picture.
Why turning the array proves it
An array with 3 rows of 6 has 18 counters. Turn the page a quarter turn and the same array now reads as 6 rows of 3 — still 18 counters, because rotating a picture does not remove anything. That single observation proves 3 × 6 = 6 × 3 without calculating either one.
It halves how much you must learn
The times tables up to 10 contain 100 facts, but because order does not matter, nearly half are repeats. Learn 7 × 3 and you have 3 × 7 for free. The 100 facts are really about 55 distinct ones, which is a much less daunting number.
Division does not work this way
12 ÷ 3 = 4, but 3 ÷ 12 is not 4. Multiplication can be flipped and division cannot, in exactly the way addition can be flipped and subtraction cannot. When a property holds it is worth naming, and it is just as worth knowing where it stops.
Step 2: Try It Yourself
Tap and try it out.
4 + 4 + 4 = 12
3 × 4 = 12
3 rows of 4 makes 12.
Step 3: Watch an Example
One step at a time.
Watch Leo Halve His Work
Leo is learning his facts and is asked for 2 × 9.
- Step 1
He does not know 2 × 9 by heart yet.
Step 4: Your Turn
Practice makes it stick.
The Garden
Problem 1 of 2
A garden has 5 rows of 7 plants. How many plants? What is 7 × 5?
plants
Two Ways
Problem 2 of 2
You know 6 × 4 = 24. What is 4 × 6?
Either Order
1 of 4
You know 8 × 2 = 16. What is 2 × 8?
2 of 4
5 × 3 = ?
3 of 4
10 × 4 = ?
4 of 4
Does 7 × 6 give the same product as 6 × 7?
Step 5: Quick Check
Show what you know.
Question 1 of 2
You know 9 × 2 = 18. What is 2 × 9?
Question 2 of 2
Why is the commutative property useful?
What You Learned
- Multiplication can be done in either order.
- 3 × 4 and 4 × 3 both give 12.
- That halves how many facts you have to learn.