Calculations with Decimals (SQA National 5 Applications of Mathematics): Revision Note

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

  • 

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

    • 

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

    •