Calculations with Decimals (SQA National 5 Applications of Mathematics): Revision Note
Exam code: X844 75
Adding & subtracting with decimals
How do I add or subtract numbers given to two decimal places?
You can use the column method for addition and subtraction with decimals
Line the place value columns up carefully
Make sure the decimal points are all in the same column
Writing zeros (often called place value holders) can help keep everything in line
Addition
You can write 2.95 + 13.2 as
You might need to carry values to the next place value
e.g. 0.2 + 0.9 = 1.1 which means you need to carry a 1 over to the ones columns
Subtraction
You can write 5.73 - 3.64 as
You might to borrow values from the next place value
e.g. 0.03 - 0.04 can be done by borrowing a tenth to give 0.13 - 0.04
Worked Example
Johnny has £32.50 and spends £1.74.
Calculate how much money Johnny has left.
Answer:
This is a subtraction question as Johnny has spent money
Align the digits by place value
£32.50 is the top number
Align the decimal point
Use zeroes in empty spaces
The column furthest right is the hundredths column
0 is smaller than 4 so borrow 10 hundredths from the tenths column
It is now 0.10 - 0.04
Next is the tenths column
4 is smaller than 7 so borrow 10 tenths from the ones column
It is now 1.4 - 0.7
Continue
Johnny has £30.76 left
Multiplying & dividing with decimals
How do I multiply a number given to two decimal places by a whole number?
One method is to temporarily ignore the decimal point
Increase the place value of all digits to get rid of the decimal places
e.g. to calculate you can first calculate
Carry out that multiplication using any method such as a grid
e.g.
Decrease the place value of all digits by the same number of moves as previously
e.g.
An alternative method is to carry out the multiplication as normal
Consider the place value of each value
e.g. 4 lots of 5 ones is 20 ones = 20
e.g. 4 lots of 3 tenths is 12 tenths = 1.2
e.g. 4 lots of 2 hundredths is 8 hundredths = 0.08
Examiner Tips and Tricks
You can use any multiplication method you like, they all have their advantages.
Worked Example
Burgers costs £3.25 each. Ailsa buys 6 burgers for her and her friends.
Find the total amount that Ailsa pays.
Answer:
Method 1
Calculate
× | 300 | 20 | 5 |
|---|---|---|---|
6 | 1800 | 120 | 30 |
Readjust the place value by two places
Method 2
Multiply normally by thinking about the place value
× | 3 | 0.2 | 0.05 |
|---|---|---|---|
6 | 18 | 1.2 | 0.30 |
How do I divide a number given to two decimal places by a whole number?
One method is to temporarily ignore the decimal point
Increase the place value of all digits to get rid of the decimal places
e.g. to calculate you can first calculate
Carry out that division using any method such as a bus stop or chunking
e.g.
Decrease the place value of all digits by the same number of moves as previously
e.g.
An alternative method is to carry out the division as normal
Consider the place value of each value
e.g. 1 ten shared 7 ways is 0 tens remainder 1 (or 10 ones)
e.g. 11 ones shared 7 ways is 1 one remainder 4 (or 40 tenths)
e.g. 44 tenths shared 7 ways is 6 tenths remainder 2 (or 20 hundredths)
e.g. 28 hundredths shared 7 ways is 4 hundredths
Worked Example
Rory cuts 203.60 centimetres of ribbon into 8 strips of equal length.
Given that there is no ribbon left over, find the length of each strip of ribbon.
Answer:
Method 1
Calculate
Readjust the place value by two places
25.45 cm
Method 2
Divide normally by thinking about the place value
25.45 cm
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