Decimals and Percentages · Grade 6

How do you add and subtract decimal numbers?

Write one under the other with the decimal points lined up, not with the last digits lined up. Then tenths add to tenths and hundredths to hundredths, just as ones add to ones. If one number has fewer digits, add zeros at the end to fill the columns.

Learning objectives

Line up the point

Column addition only works when matching places sit in the same column. With whole numbers that happens automatically when you line up to the right, but with decimals the last digit can be a tenth in one number and a hundredth in the other.

So line up the decimal points. The point marks where the ones end, and once the points are aligned every other column sorts itself out.

You can say the same thing without a place value table: add pounds to pounds and pence to pence. Nobody would add a penny to a pound just because both were written last, and that is exactly the error that lining up by the final digit makes.

Zeros that fill the column

If one number has two digits after the point and the other only one, write a zero at the end of the shorter. The value does not change and the column is filled.

In subtraction this is almost essential. Borrowing across an empty column is awkward and easy to skip, and the zero turns it into an entirely ordinary exercise.

Estimate before you calculate

Before starting, say roughly what the answer will be: three and a half plus two and a quarter is almost six. That estimate takes a second.

It catches the most common error in this topic, a decimal point written in the wrong place. An answer ten times off the estimate announces itself at once, without redoing the calculation.

Check the point in the answer too. It comes straight down from the points above it; it is not placed afterwards by feel.

Worked examples

  1. Calculate 4.7 plus 2.35

    1. Line up by the point and pad with a zero: 4.70 plus 2.35
    2. Add hundredths: 0 plus 5 is 5
    3. Add tenths: 7 plus 3 is 10, write 0 and carry 1
    4. Add ones: 4 plus 2 plus 1 is 7

    Answer: 7.05

  2. Calculate 6 minus 2.4

    1. Write 6 as 6.0 to fill the tenths column
    2. In tenths you cannot do 0 minus 4, so borrow from the ones
    3. That gives 10 minus 4 in tenths, which is 6
    4. In the ones, 5 minus 2 remains

    Answer: 3.6

  3. Calculate 10.25 minus 3.8

    1. Line up and pad: 10.25 minus 3.80
    2. Estimate first: about ten minus four, so about six
    3. Subtract column by column, borrowing where needed

    Answer: 6.45 — close to the estimate, as expected

Common mistakes

Lining up by the last digit
The last digit can be a tenth in one number and a hundredth in the other. Lining up that way adds hundredths to tenths, and the answer is out by a factor of ten in one term.
Forgetting a padding zero before subtracting
An empty column makes borrowing awkward and easy to skip. Writing the zero turns the column into a subtraction you have done a hundred times.
Placing the point in the answer by feel at the end
The point in the result comes straight down from the points in the numbers. Placing it by feel is precisely what the estimate is there to catch.

What to remember

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