2
Does the order of factors matter?
Discover Mathematics P3: Term 1, Lessons 11–20
GoalSee that changing the order of the factors does not change the product.
New words
order · which factor is written firstturn an array · to turn it so that rows become columnscommutative property · changing the order of the factors does not change the product
Explanation
The array of stars has 3 rows with 5 stars in each row. There are 15 stars: 3 × 5 = 15. Now turn the array a quarter turn. It has 5 rows with 3 stars in each row. We did not add or take away any star, so there are still 15: 5 × 3 = 15. This works for every multiplication: 3 × 5 = 5 × 3. We can swap the factors and the product stays the same. This helps us remember facts: if you know 4 × 7 = 28, you also know 7 × 4 = 28. Be careful: swapping does not work for taking away. 8 − 3 is not 3 − 8.
Worked examples
Turn the array of 3 rows of 5. Now there are 5 rows with 3 stars in each row. 5 × 3 = 15, the same product as 3 × 5.
Karim knows 4 × 8 = 32, the array of 4 rows of 8. If he turns it, he gets 8 rows of 4, so he also knows 8 × 4 = 32.
Do 6 × 2 and 2 × 6 give the same product? Two baskets with 6 apples each make 12 apples. Six baskets with 2 apples each also make 12 apples. So 2 × 6 = 6 × 2 = 12.
Class activity
Turn it around. Take 12 buttons or beans. Make an array of 2 rows of 6 and write the equation. Turn the paper a quarter turn and write the new equation. Then do the same with 3 rows of 4, and with 1 row of 12. What do you notice about the products?
Practice
1
The array has 3 rows of 6. Write two multiplication equations for it.
3 × 6 = 18 and 6 × 3 = 18.
2
If 7 × 4 = 28, what is 4 × 7?
28, because we can swap the factors.
3
Fill in the blank: 9 × 5 = 5 × ___. What is the product?
9. The product is 45.
4
Hana says 6 × 3 = 18 but 3 × 6 = 15. Is she right?
No. We can swap the factors, so 3 × 6 = 18 too.
5
Write two multiplication equations for 12 stars in 4 rows of 3.
4 × 3 = 12 and 3 × 4 = 12.