# data[].attributes.body
1:

8.0

× 0.9

2:

6.0

× 0.2

3:

2.0

× 0.6

4:

7.0

× 0.5

5:

2.0

× 0.5

6:

0.5

× 3.0

7:

7.0

× 0.4

8:

0.2

× 8.0

9:

7.0

× 0.7

10:

0.8

× 9.0

11:

0.9

× 6.0

12:

6.0

× 0.8

13:

0.4

× 9.0

14:

9.0

× 0.6

15:

0.4

× 5.0

16:

2.0

× 0.9

17:

4.0

× 0.8

18:

9.0

× 0.8

19:

0.2

× 6.0

20:

7.0

× 0.3

# data[].attributes.body
1:

0.9

− 0.9

2:

0.5

− 0.3

3:

0.7

− 0.2

4:

9.0

− 4.0

5:

0.8

− 0.6

6:

0.4

− 0.2

7:

0.7

− 0.3

8:

9.0

− 8.0

9:

4.0

− 3.0

10:

5.0

− 5.0

11:

5.0

− 3.0

12:

2.0

− 2.0

13:

8.0

− 6.0

14:

6.0

− 2.0

15:

0.9

− 0.3

16:

9.0

− 2.0

17:

0.6

− 0.2

18:

8.0

− 2.0

19:

9.0

− 5.0

20:

0.3

− 0.3

# data[].attributes.body
1:

8.0

+ 9.0

2:

0.2

+ 8.0

3:

0.8

+ 7.0

4:

2.0

+ 0.5

5:

3.0

+ 0.2

6:

6.0

+ 0.2

7:

7.0

+ 7.0

8:

9.0

+ 4.0

9:

3.0

+ 6.0

10:

0.4

+ 9.0

11:

0.6

+ 0.8

12:

2.0

+ 2.0

13:

4.0

+ 8.0

14:

0.8

+ 6.0

15:

0.2

+ 7.0

16:

0.6

+ 0.6

17:

7.0

+ 0.6

18:

5.0

+ 6.0

19:

9.0

+ 9.0

20:

0.8

+ 0.9

# data[].attributes.body
Because when you multiply without the decimal point, you are really shifting the decimal point to the right to get it out of the way:

Original: |  | 1 Move: |  | 2 Moves: |  | 3 Moves:
0,03 × 1,1 |      | 0,3 × 1,1 |      | 3. × 1,1 |      | 3. × 11.

Then we do the (now easy) multiplication:

3. × 11. = 33.

But remember, we did 3 Moves of the decimal point, so we need to undo that:

3 Moves: |  | 2 Moves: |  | 1 Move: |  | Correct
33. | | 3,3 | | 0,33 | | 0,033

Here are some more examples:

Example: Multiply 0,25 by 0,2

start with: |  0,25 × 0,2
multiply without decimal points: |  25 × 2 = 50
0,25 has 2 decimal places,
and 0,2 has 1 decimal place,
so the answer has 3 decimal places: |  0,050

Example: Multiply 102 by 0,22

start with: |  102 × 0,22
multiply without decimal points: |  102 × 22 = 2.244
102 has 0 decimal places,
and 0,22 has 2 decimal place,
so the answer has 2 decimal places: |  22,44

Common Sense

As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor get only one-tenth of what you need!

And that's all.

Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.

# data[].attributes.body
Multiplying Decimals

Multiply without the decimal point, then re-insert it in the correct spot!

How to Multiply Decimals

Just follow these steps:

Multiply normally, ignoring the decimal points.

Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

Example: Multiply 0,03 by 1,1

start with: |  0,03 × 1,1
multiply without decimal points: |  3 × 11 = 33
0,03 has 2 decimal places,
and 1,1 has 1 decimal place,
so the answer has 3 decimal places: |  0,033

# data[].attributes.body
Subtracting decimals is easy when you keep your work neat

To subtract decimals, follow these steps:

Write down the two numbers, one under the other, with the decimal points lined up.

Add zeros so the numbers have the same length

Then subtract normally, remembering to put the decimal point in the answer

Example: Subtract 0,03 from 1,1

Line the decimals up: |   |   | 1.1
|   | − | 0.03
|   |   |
"Pad" with zeros: |   |   | 1,10
|   | − | 0,03
|   |   |
Subtract: |   |   | 1,10
|   | − | 0,03
|   |   | 1,07

Answer: 1,07

So, that was just like 110 − 3 = 107, but with the decimal point in a different position

Example: Calculate 7,005-0,55

Line the decimals up: |   |   | 7.005
|   | − | 0.55
|   |   |
"Pad" with zeros: |   |   | 7,005
|   | − | 0,550
|   |   |
Subtract: |   |   | 7,005
|   | − | 0,550
|   |   | 6,455

Answer: 6,455

And that was just like 7.005 − 550 = 6.455

# data[].attributes.body
Adding decimals is easy when you keep your work neat

To add decimals, follow these steps:

Write down the numbers, one under the other, with the decimal points lined up

Put in zeros so the numbers have the same length (see below for why that is OK)

Then add using column addition, remembering to put the decimal point in the answer

Example: Add 1,452 to 1,3

Line the decimals up: |   |   | 1.452
|   | + | 1.3
|   |   |
"Pad" with zeros: |   |   | 1,452
|   | + | 1,300
|   |   |
Add: |   |   | 1,452
|   | + | 1,300
|   |   | 2,752

Example: Add 3,25, 0,075 and 5

Line the decimals up: |   |   | 3.25
|   |   | 0.075
|   | + | 5.
|   |   |
"Pad" with zeros: |   |   | 3,250
|   |   | 0,075
|   | + | 5.000
|   |   |
Add: |   |   | 3,250
|   |   | 0,075
|   | + | 5,000
|   |   | 8,325

That's all there is to it - just remember to line up the decimals, then add normally.

Subtracting

To subtract, follow the same method: line up the decimals, then subtract.

Example: What is 7,368 − 1,15 ?

Line the decimals up: |   |   | 7.368
|   | − | 1.15
|   |   |
"Pad" with zeros: |   |   | 7,368
|   | − | 1,150
|   |   |
Subtract: |   |   | 7,368
|   | − | 1,150
|   |   | 6,218

To check we can add the answer to the number subtracted:

Example (continued): Check by adding 6,218 to 1,15

Line the decimals up: |   |   | 6.218
|   | + | 1.15
|   |   |
"Pad" with zeros: |   |   | 6,218
|   | + | 1,150
|   |   |
Add: |   |   | 6,218
|   | + | 1,150
|   |   | 7,368

It matches the number we started with, so it checks out.

Putting In Zeros

Why can we put in extra zeros?

A zero is really saying "there is no value at this decimal place".

In a number like 10, the zero is saying "no ones"

In a number like 2,50 the zero is saying "no hundredths"

So it is safe to take a number like 2,5 and make it 2,50 or 2,500 etc

But DON'T take 2,5 and make it 20,5, that is plain wrong.