Use known facts to add and subtract decimals below 1

Key Rules:

• 1. Use whole-number facts and pick the method to match the numbers: 0.3 + 0.4 = 0.7 straight away because 3 + 4 = 7, and columns are only needed when the digits get awkward.

Remember:

• •Line up the decimal points, fill gaps with zeros, and swap ten of one column for one of the next.

Don’t Forget...

• •Lining up the last digits instead of the decimal points when adding 3.4 and 1.26. That puts the 4 tenths under the 6 hundredths, adding digits worth different amounts; lined up by the point, 3.4 + 1.26 = 4.66.
• •Writing 0.35 + 0.75 = 0.110 because 35 + 75 = 110. 110 hundredths is more than a whole: 100 of them make 1, so the answer crosses into the ones and 0.35 + 0.75 = 1.1.
• •Moving the decimal point and tacking on a zero, so 3.65 x 10 becomes 3.650. Multiplying by 10 makes every digit worth ten times more, so each digit moves one place to the left: 3.65 x 10 = 36.5, while 3.650 is just 3.65 written with an extra zero.

Worked Example:

Work out 4.2 - 1.76.

Write 4.2 as 4.20 so both numbers have two decimal places, then line up the decimal points.

Subtract the hundredths: 0 take away 6 will not go, so exchange a tenth for 10 hundredths, leaving 1 tenth, and work out 10 - 6 = 4.

Subtract the tenths: 1 take away 7 will not go, so exchange a one for 10 tenths, leaving 3 ones, and work out 11 - 7 = 4.

Subtract the ones: 3 - 1 = 2.

Answer: 2.44

Why It Works:

Lining up the decimal points keeps every digit in the column that matches its value, so tenths are only ever added to tenths and hundredths to hundredths. Because ten hundredths make a tenth and ten tenths make a whole, exchanging works between decimal columns exactly as it does between whole-number columns.

Another Example:

Work out 3.65 x 100 and 3.65 ÷ 10.

To multiply by 100, move every digit two places to the left: the 3 ones become 3 hundreds, the 6 tenths become 6 tens and the 5 hundredths become 5 ones, giving 365.

To divide by 10, move every digit one place to the right: the 3 ones become 3 tenths, the 6 tenths become 6 hundredths and the 5 hundredths become 5 thousandths, giving 0.365.

Answer: 3.65 x 100 = 365 and 3.65 ÷ 10 = 0.365