Multiply numbers with decimals by double digit numbers
Multiplication strategies
When we perform multiplication problems with whole numbers, we can use some strategies to help us. These strategies, including doubling, partitioning and multiplying by powers of 10, can help us when solving decimal multiplication problems also.
In the first video, we look at approximating our answer, and then solving using some of the strategies above. You might want to pause the video and check your understanding, before you move on to the final example.
The area method
Using area to solve multiplication, as we did with whole numbers, can also be used for decimal problems involving multiplication. By using rectangle, we can break it into a series of smaller rectangles, allowing us to work out our problem in smaller steps. Then, we can add our answers together at the end.
We can solve something like $3.4\times34$3.4×34 by thinking of it as a rectangle whose length and width measure $3.4$3.4 and $34$34. Then, we can break it into smaller rectangles, and solve it in four parts. We then add the individual solutions together to find our overall answer to our original problem.
| x | 3 | 0.4 | |
|---|---|---|---|
| 30 | |||
| 4 | |||
| Total |
Video 2 shows you how to do this.
When using the area model, think of breaking your number up by its place value parts.
Worked examples
Question 1
Use the area model to find $14\times0.08$14×0.08.
Fill in the area of the rectangle.
$0.08$0.08 $10$10 $\editable{}$ $4$4 $\editable{}$ What is the total area of the two rectangles, and therefore the answer to $14\times0.08$14×0.08?
Question 2
Use the area model to find $1.93\times20$1.93×20.
Fill in the areas of each rectangle.
$1$1 $0.9$0.9 $0.03$0.03 $20$20 $\editable{}$ $\editable{}$ $\editable{}$ What is the total area of all three rectangles, and therefore the answer to $1.93\times20$1.93×20?
Question 3
Use the area model to find $47\times5.4$47×5.4.
Fill in the areas of each rectangle.
$5$5 $0.4$0.4 $40$40 $\editable{}$ $\editable{}$ $7$7 $\editable{}$ $\editable{}$ What is the total area of the four rectangles, and therefore the answer to $47\times5.4$47×5.4?