3.11 Distributive property of multiplication

Fill in the areas of each rectangle.

For each rectangle, use the formula \text{Area} = \text{length} \times \text{width}.

Area of top left rectangle: 70 \times 2= 140

Area of top right rectangle: 7 \times 2= 14

Area of bottom left rectangle: 70 \times 1= 70

Area of bottom right rectangle: 7 \times 1= 7

What is the total area of all four rectangles?

Add the areas from part (a) together using a place value table.

Put the numbers in a place value table:

Now we can add the numbers down each column and regroup where needed:

So the total area is 231.

Find 77 \times 3.

Use the answer from part (b).

The rectangle from part (a) has a length of 77 and a width of 3. So we can find its area using 77\times 3. But since we already found its area in part (b) to be 231, we get: 77\times 3 = 231

This diagram shows how 2 groups of 19 objects can be split up.

Use the diagram to complete the blank to make the statement true.2\times19=2\times(10+⬚)

We can use the diagram to split up the number.

The diagram shown below that one group of 19, objects can be split up into 10 and 9.

This means: 19=10+9

For 2 groups of 19, we need to double this sum.

So 2 groups of 19 objects is the same as 2 \times 19 = 2 \times (10 + 9)

Complete the blanks to show how 2 groups of (10+9) can be split up into smaller multiplications.

2\times(10+9)=2\times10 + 2 \times ⬚

Count the groups of 10 and 9 in the diagram.

The above images shows 2 groups of 19 squares.

We can think of it as 2 groups of 10 squares on the left, and 2 groups of 9 squares on the right.

So 2 \times 19 is also equal to 2 \times 10 + 2 \times 9.But we already showed that 2 \times 19 = 2\times(10+9).So now we have:

2\times \left(10+9\right)=2\times 10+2\times 9