Year 7 Maths Decimals

Adding and Subtracting Decimals

Q: Can you add zeros to the end of a decimal?

Yes. Zeros at the end do not change the value: 6.9 = 6.90.

Q: How do you check a subtraction?

Add the answer to the number you took away. 26.43 + 13.57 = 40.

Q: How do you find a missing number in a decimal sum?

Undo the addition by subtracting. □ + 1.36 = 5.2 gives □ = 3.84.

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Theory

To add or subtract decimals, line up the decimal points and fill any gaps with zeros, then work column by column from the right, just like whole numbers. This Year 7 maths page shows how to estimate first, use the column method, borrow through zeros, find missing numbers and check answers.

Line up the decimal points so that tenths sit under tenths and hundredths under hundredths. The point in the answer lines up too.

Fill the gaps with zeros so every number has the same number of decimal places: \(12.6 = 12.60\). This does not change the value.

A whole number has a hidden decimal point at the end: \(8 = 8.00\) and \(51 = 51.000\).

Estimate first by rounding each number to a whole number: \(12.6 + 3.85 \approx 13 + 4 = 17\). Use the estimate to check your answer.

\(6 + 8 = 14\) tenths: write \(4\), carry \(1\). \(12.6 + 3.85 = 16.45\).

Borrow through the zeros: \(8.00\) is \(7\) ones, \(9\) tenths and \(10\) hundredths. \(8 - 2.35 = 5.65\).

The steps, every time:

Estimate.
Line up the decimal points and fill with zeros.
Work each column from the right, carrying or borrowing.
Check against the estimate (or add back).

\[ 5.65 + 2.35 = 8.00 \]

5.65 + 2.35 = 8.00

\[ -1.8 + 4.5 = -1.8 + 1.8 + 2.7 = 2.7 \]

- 1.8 + 4.5 = - 1.8 + 1.8 + 2.7 = 2.7

          Missing numbers. Undo adding by subtracting, and undo subtracting by adding: \(\square + 1.2 = 4\) gives \(\square = 4 - 1.2 = 2.8\).
        

          Across zero. With a negative decimal, go to \(0\) first, as for integers: \(-1.8 + 4.5 = 2.7\).
        

How to add or subtract decimals

Estimate by rounding to whole numbers.
Write the numbers in columns with the points lined up; fill with zeros.
Add or subtract from the right, carrying when a column reaches \(10\) and borrowing when the top digit is too small.
Put the point in the answer under the other points, then check.

Example 1 — Adding tenths

Work out
(i) \(0.6 + 0.8\)
(ii) \(1.5 - 0.7\)

Solution

(i) \(6\) tenths \(+\) \(8\) tenths \(=\) \(14\) tenths \(=\) \(1\) one and \(4\) tenths.
(ii) \(1.5\) is \(15\) tenths, and \(15 - 7 = 8\) tenths.

(i) \(1.4\)
(ii) \(0.8\) (check: \(0.8 + 0.7 = 1.5\))

Example 2 — Four numbers

Find the sum of \(12.34\), \(1.526\), \(51\) and \(0.32\).

Solution

Estimate \(12 + 2 + 51 + 0 = 65\). The sum is \(65.186\).

Example 3 — The column method

Add \(27.48 + 6.9\) without a calculator.

Solution

Estimate: \(27 + 7 = 34\). Fill: \(6.9 = 6.90\).

Tenths \(4 + 9 = 13\) (carry \(1\)); ones \(7 + 6 + 1 = 14\) (carry \(1\)). The answer is \(34.38\).

Example 4 — Taking from a decimal

Find the difference when \(12.821\) is taken from \(83.4\).

Solution

Check: \(70.579 + 12.821 = 83.400\). The difference is \(70.579\).

Example 5 — Subtracting from a whole number

Work out \(40 - 13.57\).

Solution

Estimate \(40 - 14 = 26\). Write \(40 = 40.00\) and borrow through the zeros.

\(40.00 - 13.57\)

\(=\)

\(26.43\)

40.00 - 13.57 = 26.43

Check: \(26.43 + 13.57 = 40.00\).

Example 6 — Missing number

Find the missing number: \(\square + 1.36 = 5.2\)

Solution

\(\square\)	\(=\)	\(5.2 - 1.36\)
\(\)	\(=\)	\(5.20 - 1.36\)
\(\)	\(=\)	\(3.84\)

= 5.20 - 1.36 = 3.84

\(3.84\)

Example 7 — Phone data

Noah’s plan gives \(20\) GB of data a month. He uses \(6.75\) GB, \(4.8\) GB and \(5.35\) GB in three weeks.
(i) How much has he used?
(ii) How much is left?

Solution

\(6.75 + 4.80\)	\(=\)	\(11.55\)
\(11.55 + 5.35\)	\(=\)	\(16.90\)
\(20.00 - 16.90\)	\(=\)	\(3.10\)

6.75 + 4.80 = 11.55, 11.55 + 5.35 = 16.90, 20.00 - 16.90 = 3.10

(i) \(16.9\) GB (estimate \(7 + 5 + 5 = 17\))
(ii) \(3.1\) GB

Common pitfalls

Lining up the last digits. \(5.2 + 1.34 = 5.20 + 1.34 = 6.54\), not \(1.86\).

Forgetting the hidden point. \(9 - 3.4 = 9.0 - 3.4 = 5.6\), not \(6.4\).

Ignoring the estimate. A sum must be larger than each number in it. If \(3.7 + 1.45\) gives \(1.82\), something is wrong.

Borrowing through zeros. In \(8.00 - 2.35\), \(8.00\) becomes \(7\) ones, \(9\) tenths and \(10\) hundredths.

Frequently asked questions

Why do you line up the decimal points?

So that digits with the same place value are added or subtracted together: tenths with tenths, hundredths with hundredths.

Can you add zeros to the end of a decimal?

Yes. Zeros at the end do not change the value: \(6.9 = 6.90\).

Where is the decimal point in a whole number?

At the end. \(40 = 40.00\).

How do you check a subtraction?

Add the answer to the number you took away. \(26.43 + 13.57 = 40\).

How do you find a missing number in a decimal sum?

Undo the addition by subtracting. \(\square + 1.36 = 5.2\) gives \(\square = 3.84\).

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Multiplying and Dividing by Powers of 10

Adding and Subtracting Decimals

📖 Theory

How to add or subtract decimals

Common pitfalls

Frequently asked questions

Theory