Decimals

NZ Level 5

Multiply numbers with decimals by whole numbers using the algorithm

Lesson

You can use all the strategies that you already know for multiplication when you have numbers with decimals (see Time for some Times if you need a refresher).

But here's a tip:

If you have a lot of decimal places just pretend that the decimal point isn't there and do the multiplication as a whole number. Why can we do this? We are simply expressing these numbers as values of their decimal values (for example, $1.32$1.32 can be expressed as $132$132 hundredths).

Then we just need to remember to place the decimal point in the answer so that it has the same number of decimal places as the number being multiplied.

**Evaluate: **$2.253\times9$2.253×9

**Think:** We can solve it as $2253\times9=20277$2253×9=20277, then we remember that we had thousandths, so we count back $3$3 decimal places

**Do:** $20.277$20.277

**Evaluate:**$0.005\times8$0.005×8

**Think:** $5\times8=40$5×8=40 and there are $3$3 decimal places in question (thousandths)

**Do:**

$0.005\times8$0.005×8 | $=$= | $0.040$0.040 |

$=$= | $0.04$0.04 |

We want to find $3\times0.4$3×0.4.

Will $3\times0.4$3×0.4 be greater than or less than one whole?

Greater than

ALess than

BGreater than

ALess than

BUse the vertical algorithm to find $3\times0.4$3×0.4.

$0$0 $.$. $4$4 $\times$× $3$3 $\editable{}$ $.$. $\editable{}$

We want to find $6.79\times9$6.79×9.

First, choose the most reasonable approximation for $6.79\times9$6.79×9.

$63$63

A$48$48

B$80$80

C$63$63

A$48$48

B$80$80

CUse the vertical algorithm to find $6.79\times9$6.79×9.

$\editable{}$ $\editable{}$ $6$6 $.$. $7$7 $9$9 $\times$× $9$9 $\editable{}$ $\editable{}$ $.$. $\editable{}$ $\editable{}$

We want to find $97\times1.04$97×1.04.

First, choose the most reasonable approximation for $97\times1.04$97×1.04.

$202$202

A$97$97

B$50$50

C$202$202

A$97$97

B$50$50

CWe are going to use the vertical algorithm to find $97\times1.04$97×1.04.

Let's do the first component and multiply $1.04$1.04 by $7$7.

$\editable{}$ $1$1 $.$. $0$0 $4$4 $\times$× $9$9 $7$7 $\editable{}$ $.$. $\editable{}$ $\editable{}$ $+$+ $.$. $.$. Now let's multiply $1.04$1.04 by $90$90 and then add the two results to find $97\times1.04$97×1.04.

$\editable{}$ $1$1 $.$. $0$0 $4$4 $\times$× $9$9 $7$7 $7$7 $.$. $2$2 $8$8 $+$+ $\editable{}$ $\editable{}$ $.$. $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $.$. $\editable{}$ $\editable{}$

Understand operations on fractions, decimals, percentages, and integers