Sometimes you multiply three numbers: 2 × 3 × 5.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Group them however you like
(2 × 3) × 5 is 6 × 5 = 30. And 2 × (3 × 5) is 2 × 15 = 30. Same answer.
This has a name too.
Associative property lets you group factors in any way without changing the product.
Pick the easy pair
For 4 × 15, think 4 × 5 × 3: do 4 × 5 = 20 first, then 20 × 3 = 60.
Grouping three factors
To work out 2 × 3 × 5, you can do (2 × 3) × 5 = 6 × 5 = 30, or 2 × (3 × 5) = 2 × 15 = 30. The grouping does not change the answer. That is the associative property, and it is different from the commutative property, which is about order.
Grouping to make it easy
For 4 × 7 × 25, do the 4 × 25 = 100 first, then 100 × 7 = 700. Multiplying in the given order would mean 28 × 25, which is much harder. Scanning for a friendly pair before you start is worth the moment it takes.
Using both properties together
Commutativity lets you reorder and associativity lets you regroup. Together they mean a chain of multiplications can be rearranged completely freely. That freedom is what makes mental multiplication of several numbers possible at all.
Step 2: Try It Yourself
Tap and try it out.
2 × 3 = 6
2 rows of 3 makes 6.
Step 3: Watch an Example
One step at a time.
Watch Ana Regroup
Ana is asked for 4 × 15.
- Step 1
She rewrites 15 as 5 × 3.
Step 4: Your Turn
Practice makes it stick.
Three Factors
Problem 1 of 2
2 × 4 × 5 = ?
The Crates
Problem 2 of 2
3 crates each hold 2 boxes of 6 apples. How many apples?
apples
Group the Easy Pair
1 of 3
2 × 3 × 5 = ?
2 of 3
5 × 2 × 7 = ?
3 of 3
3 × 12 = ? Try 3 × 2 × 6.
Step 5: Quick Check
Show what you know.
Question 1 of 2
2 × 5 × 6 = ?
Question 2 of 2
Does regrouping change the product?
What You Learned
- Three factors can be grouped in any order.
- Do the easy pair first.
- The product never changes.