Cross Products

I am learning to multiply multi-digit whole numbers.

37 X 28 = ?

Before starting this lesson make sure you are confident with the lesson Paper Power (for multiplication).

There are 17 rows with 32 counters in each row. How many counters are there in total? 17 X 32= ?

32

17

Imagine this displayed as a rectangle.Now split the 32 and 17 into a tidy number and an amount left over.

30 2

10

7

You can see there are 4 rectangles. By finding the area of each of these we can work out the area of the whole rectangle and the answer to our question.

30 X 10 = 300 2 X 10 = 20 2 X 7 = 14 30 X 7 = 210

Add all the areas together.

300 + 20 + 14 + 210 = 544

So 17 X 32 = 544

There are 27 rows with 47 counters in each row. How many counters are there in total? 27 X 47= ?

47

27

Imagine this displayed as a rectangle.Now split the 27 and 47 into a tidy number and an amount left over.

40 7

20

7

You can see there are 4 rectangles. By finding the area of each of these we can work out the area of the whole rectangle and the answer to our question.

40 X 20 = 800 7 X 20 = 140 7 X 7 = 49 40 X 7 = 280

Add all the areas together.

800 + 140 + 49 + 280 = 1,269

So 27 X 47 = 1,269

Now let’s try an example without the diagram.

18 X 43 = ? Firstly split the numbers into a tidy number and an amount left over.

(10 + 8) X (40 + 3) = ? You saw from our earlier diagrams that every number on the left hand side of the multiplication sign must be multiplied by every number on the right hand side of this sign.

10 X 40 = 400 10 X 3 = 30 8 X 40 = 320 8 X 3 = 24

Now add the amounts together. 400 + 30 + 320 + 24 = 774

18 X 43 = 774

Below is an example of how I like to set out my working for these types of question. 32 X 52 = ?

(30 + 2) X (50 + 2) = ? Step 1: I expand the number

Step 2: I draw in lines showing all the numbers I must multiply together. I always do 2 above and 2 below so I don’t mix any of my lines up.

As I draw in the lines I record each part of the multiplication.

(30 X 50) + (30 X 2) + (2 X 50) + (2 X 2)

Step 3: Below this I record the answers.

1500 + 60 + 100 + 4 = 1,664

So 32 X 52 = 1,664

Use this strategy (cross products) to work out answers to the questions below.

1) 25 X 33 = ?

2) 17 X 42 = ?

3) 32 X 45 = ?

4) 18 X 23 = ?

5) 26 X 23 = ?Need some more practise? Try Pg45 & 46 of Teacher Tools Multiplication and Division Book Numeracy resources

Click again when you have worked out all your answers. 825

714

1,440

414

598