📚 Learn about Arrays

An array is a set of objects arranged in equal rows and columns. We can use multiplication to find the total number of objects.

For example, 3 rows of 4 can be written as 3 × 4 = 12. Turning the array around gives 4 rows of 3, so 4 × 3 = 12.

This is the commutative property of multiplication: changing the order of the factors does not change the product.

✏️ Practise and Apply

a) 3 × 9 = 27, so 9 × 3 = ______

b) 6 × 8 = 48, so 8 × 6 = ______

c) 4 × 12 = 48, so 12 × 4 = ______

d) 7 × 5 = 35, so 5 × 7 = ______

e) 11 × 2 = 22, so 2 × 11 = ______

f) 9 × 7 = 63, so 7 × 9 = ______

g) 10 × 6 = 60, so 6 × 10 = ______

h) 8 × 8 = 64, so 8 × 8 = ______

a) 4 × ______ = 36

b) ______ × 7 = 56

c) 12 × ______ = 84

d) ______ × 9 = 108

a) A garden has 6 rows of kūmara plants with 8 plants in each row. How many plants are there altogether?

b) A hall has 9 columns of chairs with 7 chairs in each column. How many chairs are there?

c) A baker packs 4 rows of 12 muffins. How many muffins are packed? Write a related equation using the commutative property.

✅ Answer Key

1. 3 × 6 = 18 counters.

2. 4 × 8 = 32 and 8 × 4 = 32.

3. An array with 5 rows of 7; 5 × 7 = 35.

4. An array with 7 rows of 5; 7 × 5 = 35.

5. a) 27   b) 48   c) 48   d) 35   e) 22   f) 63   g) 60   h) 64.

6. a) 9   b) 8   c) 7   d) 12.

7. a) 6 × 8 = 48 plants.   b) 9 × 7 = 63 chairs.   c) 4 × 12 = 48 muffins; related equation: 12 × 4 = 48.

8. 12 ÷ 3 = 4, but 3 ÷ 12 = 1/4. Division describes sharing or grouping, so changing the order changes the meaning and answer.