☰ Year plan · Mathematics

Commutative property and multiplying by tens

Week 9 · Commutative property and multiplying by tens · 3 lessons
1

Swap the factors, keep the product

Discover Mathematics P4: Term 1, Unit 5, Lessons 4–8
GoalUse arrays to see that changing the order of the factors does not change the product.
New words
array · objects in equal rows and equal columnscommutative property of multiplication · a × b = b × aproduct · the answer of a multiplication
Explanation

An array shows multiplication as rows and columns. An array with 3 rows of 8 has 3 × 8 = 24 dots. Turn the array on its side and we see 8 rows of 3, which is 8 × 3 = 24. The picture is the same, so the product is the same. This is the commutative property of multiplication: the order of the factors does not change the product. We can use it to pick the order that is easier for us. If you know 7 × 8 = 56, then you also know 8 × 7 = 56. It works for big numbers too: 25 × 4 = 4 × 25 = 100. Remember that this works for multiplication and addition but not for subtraction: 9 − 4 is not 4 − 9.

Worked examples
ArrayEquation
3 rows of 83 × 8 = 24
8 rows of 38 × 3 = 24
3 rows of 8 dots make 3 × 8 = 24 dots. Turn the array and there are 8 rows of 3, so 8 × 3 = 24 too.
A tray holds 9 rows of 4 eggs. 9 × 4 = 36 eggs. Another tray holds 4 rows of 9 eggs, 4 × 9 = 36 eggs. The two trays hold the same number of eggs.
Is 8 × 6 equal to 6 × 8? 8 × 6 = 48 and 6 × 8 = 48. Yes. Use it to solve 12 × 5 from 5 × 12 = 60, and 25 × 8 from 8 × 25 = 200.
Class activity

Array hunt. Look for arrays at home: a box of tea bags, a tray of eggs, a muffin tin, floor tiles. Count the rows and the columns and write two multiplications for each array. Is the product the same for both?

Practice
1
Write two multiplications for an array of 5 rows and 7 columns.
2
You know 6 × 9 = 54. What is 9 × 6?
3
Write the missing number: 7 × __ = 8 × 7.
4
A classroom has 6 rows of 5 desks. A hall has 5 rows of 6 chairs. Which has more seats?
5
Karim says 12 − 5 = 5 − 12 because of the commutative property. What is wrong?