Decimals

Lesson

When we add one number to another, we make a bigger number. Likewise, if we subtract one number from another, we make a smaller number. If we have $\$22$$22, but need $\$30$$30, we can work out that we need to add another $\$8$$8 to make $\$30$$30.

With decimals, we are working with tenths and hundredths, rather than tens, hundreds etc., but otherwise the process is very similar. Our numbers can be made up of wholes and parts, or decimals. Let's look through examples of those:

- Suppose we have $\$1.20$$1.20, but need $\$2.00$$2.00. We can make $\$2.00$$2.00 by adding $\$1.20$$1.20 and $\$0.80$$0.80.

In our first video, we make a decimal by adding on tenths, and then move to an example where we add by hundredths. You can see the process is the same, we just need to think about the space, or difference, between the numbers we are adding. A number line can help you see how to add to a decimal number, moving to the right. So now, if you have $\$3.35$$3.35, and need to calculate how much you need to add to make $\$4.00$$4.00, you can use this method to work out that $\$3.35$$3.35$+$+$\$0.65$$0.65$=$=$\$4.00$$4.00.

Imagine that a book you want is on sale for $\$2.20$$2.20, but it was $\$3.00$$3.00 before the sale. How much will you save if you buy it at the sale price? Well, making a number by subtracting decimals can help you work this out. The amount you would save is the same as the amount you need to subtract from $\$3.00$$3.00 to get to $\$2.20$$2.20.

In our second video, we look at how making a decimal by subtracting can help solve problems such as this. We can use a number line to show that counting back by tenths, or increments of $0.1$0.1, until we reach $\$2.20$$2.20, means we saved $\$0.80$$0.80.

We also look at hundredths, allowing us to calculate how much we need to subtract from $\$5.00$$5.00 to get $\$3.75$$3.75. If you are paying $\$3.75$$3.75 for a snack, and have $\$5.00$$5.00, you can work out how much change you should receive, by starting at $\$5.00$$5.00 and subtracting until you reach $\$3.75$$3.75. Can you work out how much change you should expect?

Which of the options below make $6.8$6.8? There may be more than one correct answer.

$6+0.8$6+0.8

A$2.3+4.5$2.3+4.5

B$8.5-1.7$8.5−1.7

C$10.1-3.9$10.1−3.9

D$6+0.8$6+0.8

A$2.3+4.5$2.3+4.5

B$8.5-1.7$8.5−1.7

C$10.1-3.9$10.1−3.9

D

Which of the options below make $57.88$57.88? There may be more than one correct answer.

$28.64+29.04$28.64+29.04

A$46.52+11.36$46.52+11.36

B$72.97-15.09$72.97−15.09

C$65.83-6.93$65.83−6.93

D$28.64+29.04$28.64+29.04

A$46.52+11.36$46.52+11.36

B$72.97-15.09$72.97−15.09

C$65.83-6.93$65.83−6.93

D

Let’s play a game called target number. Here’s how it works. I give you a target number and starting number and you tell me what I need to subtract to get there.

For example, our target number is $0.05$0.05, and if I tell you the number $0.07$0.07 you would say $0.02$0.02, because $0.07-0.02=0.05$0.07−0.02=0.05.

Find the missing numbers below for our target number $0.05$0.05.

$0.06-\editable{}=0.05$0.06−=0.05

$0.08-\editable{}=0.05$0.08−=0.05

$0.09-\editable{}=0.05$0.09−=0.05

Let’s play a game called target number. Here’s how it works. I give you a target number and starting number and you tell me what I need to subtract to get there.

For example, our target number is $4.57$4.57, and if I tell you the number $6.99$6.99 you would say $2.42$2.42, because $6.99-2.42=4.57$6.99−2.42=4.57.

Find the missing numbers below for our target number $4.57$4.57.

$6.69-\editable{}=4.57$6.69−=4.57

$5.93-\editable{}=4.57$5.93−=4.57

$7.35-\editable{}=4.57$7.35−=4.57

Understand operations on fractions, decimals, percentages, and integers