7. Decimal operations

Lesson

We have looked at visual models for multiplying whole numbers in previous lessons. Let's look to an area model as a review.

Let's use the area model to find 38\times7.

a

Fill in the areas of each rectangle.

Worked Solution

b

Find the sums of each column.

Worked Solution

c

What is the total area of the rectangles?

Worked Solution

Idea summary

We can use area models to multiply two-digit numbers.

This video looks at using visual models for multiplying decimals.

Use the area model to find 4\times1.209.

a

Fill in the areas of each rectangle.

Worked Solution

b

What is the total area of all three rectangles, and the answer to 4 \times1.209?

Worked Solution

Idea summary

We can use area models to multiply a decimal by a whole number.

This video uses the vertical algorithm and a couple of simple methods to check our answers for reasonableness. While this doesn't always tell us our answer is correct, it can definitely help us check our decimal place is in the correct spot.

We want to find 6\times 7.003.

a

First, choose the most reasonable approximation for 6\times 7.003.

A

80

B

42

C

4

Worked Solution

b

Find 6\times 7.003, giving your answer as a decimal.

Worked Solution

Idea summary

Whichever method we use to multiply decimals, the most important thing is to remember that we don't need to learn any new processes at all. The value of the digits change, but the way we solve the problem doesn't.