 # 7.02 Subtract decimals

Lesson

We have learned and used tools to help us  subtract whole numbers  . Now we will utilise these same tools when we subtract decimals. Let's review.

### Examples

#### Example 1

Find the value of 6353 - 129.

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} & &6&3&5&3 \\ &- &&1&2&9 \\ \hline \\ \hline \end{array}

Subtract the values down each column.

In the units column since 3 is less than 9, we need to trade 1 from the tens column which leaves us with 4 and carry it over to the units column which gives us 13. So 13-9=4. We can then subtract the remaining numbers in each place value column to get:\begin{array}{c} &&6&3&4&{}^13 \\ &- &&1&2&9 \\ \hline &&6&2&2&4\\ \hline \end{array}

Idea summary

We can use a vertical algorithm to subtract whole numbers. We can use regrouping when necessary.

## Subtract decimals

There are a few strategies that can be used to subtract a whole number from a number with a decimal. This video looks at renaming numbers.

### Examples

#### Example 2

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&&5&3&.&2&9 \\ &- &&4&2&.&2&9 \\ \hline \\ \hline \end{array}

Subtract the values down each column and copy the decimal point down.

\begin{array}{c} &&&5&3&.&2&9 \\ &- &&4&2&.&2&9 \\ \hline && &1&1&.&0&0 \\ \hline \end{array}

Idea summary

When using the vertical algorithm to subtract decimals, it works in the same way as with whole numbers but we must remember to copy the decimal point to the same position.

## Subtract decimals with regrouping

Sometimes there is a need to regroup, or rename, some values before we can subtract. We use the same process as we use with whole numbers, so using place value columns can really help.

### Examples

#### Example 3

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&3&.&1&2 \\ - &&0&.&0&4 \\ \hline \\ \hline \end{array}

In the hundredths column since 2 is less than 4, we need to trade 1 from the tenths column which leaves us with 0 and carry it over to the hundredths column which gives us 12. So 12-4=8.\begin{array}{c} &&&3&.&0&{}^12 \\ &- &&0&.&0&4 \\ \hline &&&&&&8 \\ \hline \end{array}

Now we can subtract the zeros in the tenths column to get 0, and in the units column: 3-0=3. We must also remember to copy the decimal point down. \begin{array}{c} &&&3&.&0&{}^12 \\ &- &&0&.&0&4 \\ \hline &&&3&.&0&8 \\ \hline \end{array}

Idea summary

All of the things we've been learning with decimals follow the same processes as we use with whole numbers. The only difference is the value of the digits. Saying decimals out loud can help to work out what the value of our decimals is.

## Patterns with subtraction of decimals

This video explores how to complete a pattern that involves decimals.

### Examples

#### Example 4

Consider the following pattern.

0.63,\,0.56,\,0.49,\, ⬚,\, ⬚,\, ⬚

a

What is the pattern?

A
The numbers are decreasing by 0.7.
B
The numbers are decreasing by 7.
C
The numbers are decreasing by 0.07.
D
The numbers are decreasing by 70.
Worked Solution
Create a strategy

Subtract the second number from the first number.

Apply the idea

Write it in a vertical algorithm. \begin{array}{c} & & &0 &. &6 &3\\ &- & &0 &. &5 &6 \\ \hline \\ \hline \end{array}

In the hundredths column since 3 is less than 6, we need to trade 1 from the tenths column which leaves us with 5 and carry it over to the hundredths column which gives us 13. So 13-6=7. We can then subtract the remaining numbers in each place value column to get:\begin{array}{c} & & &0 &. &5 &{}^13\\ &- & &0 &. &5 &6 \\ \hline & & &0 &. &0 &7\\ \hline \end{array}

We can see that the numbers are decreasing by 0.07. So the correct answer is option C.

b

Complete the pattern: 0.63,\,0.56,\,0.49,\, ⬚,\, ⬚,\, ⬚

Worked Solution
Create a strategy

Subtract the value from part (a) from the last number.

Apply the idea

The numbers are decreasing so we need to subtract 0.07 from the previous number to find the next number.

Subtract 0.07 from 0.49.

\begin{array}{c} & & &0 &. &4 &9\\ &- & &0 &. &0 &7 \\ \hline & & &0 &. &4 &2 \\ \hline \end{array}

Subtract 0.07 from 0.42.

\begin{array}{c} & & &0 &. &4 &2\\ &- & &0 &. &0 &7 \\ \hline & & & & & & \\ \hline \end{array}

In the hundredths column since 2 is less than 7, need to trade 1 from the tenths column which leaves us with 3 and carry it over to the hundredths column which gives us 12. So 12-7=5. We can then subtract the remaining numbers in each place value column to get:

\begin{array}{c} & & &0 &. &3 &{}^12 \\ &- & &0 &. &0 &7 \\ \hline & & &0 &. &3 &5 \\ \hline \end{array}

Subtract 0.07 from 0.35.

\begin{array}{c} & & &0 &. &3 &5\\ &- & &0 &. &0 &7 \\ \hline & & & & & & \\ \hline \end{array}

In the hundredths column since 5 is less than 7, we need to trade 1 from the tenths column which leaves us with 2 and carry it over to the hundredths column which gives us 15. So 15-7=8. We can then subtract the remaining numbers in each place value column to get:

\begin{array}{c} & & &0 &. &2 &{}^15 \\ &- & &0 &. &0 &7 \\ \hline & & &0 &. &2 &8 \\ \hline \end{array}

The complete pattern is:0.63,\,0.56,\,0.49,\, 0.42,\, 0.35,\, 0.28

Idea summary

To complete a pattern of decimals, it may help to write the numbers as tenths, hundredths or thousandths or as fractions to see how the pattern changes each time.

### Outcomes

#### VCMNA214

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers