Year 6 Maths Decimals

Add & subtract decimals - Same decimal places

Q: How do I carry with decimals?

10 hundredths make 1 tenth; 10 tenths make 1 one.

Q: How do I find change?

Subtract the total from the money paid: $30.00 - $23.55 = $6.45.

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Theory

To add or subtract decimals, write them in columns with the decimal points lined up, then work from the right just as with whole numbers, carrying or trading when needed. This Year 6 maths page shows column methods for tenths, hundredths and thousandths, with money and measurement problems.

Lining up the decimal points makes each column one place value: ones under ones, tenths under tenths, hundredths under hundredths.

Carrying: $10$ hundredths make $1$ tenth, and $10$ tenths make $1$ one.

Trading for subtraction: $1$ one becomes $10$ tenths; $1$ tenth becomes $10$ hundredths.

The decimal point in the answer goes directly under the other points. Check with an estimate: $6.47 + 2.86$ is about $6 + 3 = 9$.

$7 + 6 = 13$ hundredths: write $3$, carry $1$. Then $4 + 8 + 1 = 13$ tenths: write $3$, carry $1$. Total $9.33$.

Trade to get $12$ hundredths and $10$ tenths: $8.12 - 3.57 = 4.55$.

Exchanges between places:

\[ 10 \text{ hundredths} = 1 \text{ tenth} \]

10 hundredths = 1 tenth

\[ 10 \text{ tenths} = 1 \text{ one} \]

10 tenths = 1 one

\[ 6.47 + 2.86 = 9.33 \]

6.47 + 2.86 = 9.33

Points in a line. Line up the decimal points, not the last digits.

          Estimate first. \(8.12 - 3.57\) is about \(8 - 4 = 4\), so \(4.55\) is sensible.
        

Column addition or subtraction

Write the numbers with the decimal points lined up.
Start at the right-hand column.
Carry (adding) or trade (subtracting) as with whole numbers.
Put the decimal point in the answer under the others, then check with an estimate.

Example 1 — Tenths

Calculate $5.6 + 2.7$.

Solution

$5.6 + 2.7$

$=$

$8.3$

5.6 + 2.7 = 8.3

$6 + 7 = 13$ tenths: $8.3$.

Example 2 — Trading tenths

Calculate $9.3 - 4.8$.

Solution

$9.3 - 4.8$

$=$

$4.5$

9.3 - 4.8 = 4.5

Trade $1$ one for $10$ tenths: $13 - 8 = 5$ tenths. $4.5$.

Example 3 — Hundredths

Use the first diagram. Calculate $6.47 + 2.86$.

Solution

$6.47 + 2.86$

$=$

$9.33$

6.47 + 2.86 = 9.33

$9.33$.

Example 4 — Subtract hundredths

Use the second diagram. Calculate $8.12 - 3.57$.

Solution

$8.12 - 3.57$

$=$

$4.55$

8.12 - 3.57 = 4.55

$4.55$.

Example 5 — Thousandths

Calculate $1.234 + 2.598$.

Solution

$1.234 + 2.598$

$=$

$3.832$

1.234 + 2.598 = 3.832

$3.832$.

Example 6 — Change

Ruby buys a book for $\$14.60$ and a pen set for $\$8.95$.
(i) What is the total?
(ii) What change does she get from $\$30$?

Solution

$14.60 + 8.95$	$=$	$23.55$
$30.00 - 23.55$	$=$	$6.45$

14.60 + 8.95 = 23.55, 30.00 - 23.55 = 6.45

(i) $\$23.55$
(ii) $\$6.45$

Example 7 — Distances

A cyclist rides $5.8$ km, $4.6$ km and $3.7$ km.
(i) What is the total distance?
(ii) How much further was the first ride than the second?

Solution

$5.8 + 4.6 + 3.7$	$=$	$14.1$
$5.8 - 4.6$	$=$	$1.2$

5.8 + 4.6 + 3.7 = 14.1, 5.8 - 4.6 = 1.2

(i) $14.1$ km
(ii) $1.2$ km

Example 8 — Find the mistake

Ana wrote $6.47 + 2.86 = 93.3$. What went wrong?

Solution

The decimal point is in the wrong place. An estimate ($6 + 3 = 9$) shows the answer is $9.33$.

Common pitfalls

Misplacing the point. Keep the point in line in the answer.

Forgetting to carry. $13$ hundredths is $1$ tenth and $3$ hundredths.

Subtracting the smaller digit from the larger. In $8.12 - 3.57$, you cannot do $7 - 2$; trade instead.

Skipping the estimate. An estimate catches a misplaced point.

Frequently asked questions

What must line up when adding decimals?

The decimal points, so each column is one place value.

How do I carry with decimals?

$10$ hundredths make $1$ tenth; $10$ tenths make $1$ one.

How do I check my answer?

Estimate by rounding to whole numbers.

What is 9.3 − 4.8?

$4.5$.

How do I find change?

Subtract the total from the money paid: $\$30.00 - \$23.55 = \$6.45$.

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Multiply & divide decimals by 10, 100, 1000 - Divide by 10,100,1000

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Add & subtract decimals - Different decimal places

\(14.60 + 8.95\)	\(=\)	\(23.55\)
\(30.00 - 23.55\)	\(=\)	\(6.45\)

\(5.8 + 4.6 + 3.7\)	\(=\)	\(14.1\)
\(5.8 - 4.6\)	\(=\)	\(1.2\)

Add & subtract decimals - Same decimal places

📖 Theory

Column addition or subtraction

Common pitfalls

Frequently asked questions

Theory