 Lesson

## Ideas

The skills we have learned and used when  adding whole numbers  will be utilised once again when adding decimals. Let's review.

### Examples

#### Example 1

Find the value of 1832 + 6361.

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&1&8&3&2 \\ +& &6&3&6&1 \\ \hline \\ \hline \end{array}

Add the values down each column.\begin{array}{c} &&{}^11&8&3&2 \\ +& &6&3&6&1 \\ \hline &&8&1&9&3\\ \hline \end{array}

Idea summary

We can add large numbers using a vertical algorithm. We add the digits starting from the lowest place value and move left.

This video shows us how to add numbers with decimals.

### Examples

#### Example 2

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&0&.&1&7 \\ + &&0 &.&5&2\\ \hline \\ \hline \end{array}

Add the values down each column and copy the decimal point in the same position.\begin{array}{c} &&0&.&1&7 \\ + &&0 &.&5&2\\ \hline & &0&.&6&9 \\ \hline \end{array}

Idea summary

When adding decimals using a vertical algorithm, we must make sure to align the decimal points. If the decimals have a different number of decimal places, then we can use zeros as place holders.

What if our numbers get larger but still have decimals? The same strategies still apply, this video shows us.

### Examples

#### Example 3

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&1&3&.&7&4 \\ + &&3&7&.&2&6 \\ \hline \\ \hline \end{array}

First we add the hundredths to get 4+6 =10. So we write 0 in the hundredths column and carry the 1 to the tenths column.

\begin{array}{c} &&1&3&.&{}^17&4 \\ + &&3&7&.&2&6 \\ \hline &&&&&&0 \\ \hline \end{array}

Next we add the tenths to get 1+7+2 =10. So we write 0 in the tenths column and carry the 1 to the units column. We should also copy the decimal point down.

\begin{array}{c} &&1&{}^13&.&{}^17&4 \\ + &&3&7&.&2&6 \\ \hline &&&&.&0&0 \\ \hline \end{array}

Next we add the units to get 1+3+7 =11. So we write 1 in the units column and carry the 1 to the tens column.

\begin{array}{c} &&{}^11&{}^13&.&{}^17&4 \\ + &&3&7&.&2&6 \\ \hline &&&1&.&0&0 \\ \hline \end{array}

Lastly we add the tens to get 1+1+3 =5. So we write 5 in the tens column.

\begin{array}{c} &&{}^11&{}^13&.&{}^17&4 \\ + &&3&7&.&2&6 \\ \hline &&5&1&.&0&0 \\ \hline \end{array}

Idea summary

We can add larger decimals using the vertical algorithm. It will just require more steps.

When adding decimals we can use regrouping in the same way that we use it when adding whole numbers.

## Patterns with addition of decimals

This video shows us how to continue patterns with decimals.

### Examples

#### Example 4

Consider the following pattern.

0.03, \ 0.12, \ 0.21, \ ⬚, \ ⬚, \ ⬚

a

Complete the pattern.

Worked Solution
Create a strategy

Find how much the numbers are increasing by each time and add that to the last given value to complete the pattern.

Apply the idea

To work out how much the numbers are increasing by each time we can count up by hundredths.

The first two numbers are 0.03 or 3 hundredths, and 0.12 or 12 hundredths.

To get from 3 hundredths to 12 hundredths we need to count up by 9 hundredths or 0.09.

So we need to add 0.09 to the previous number to find the next number.

\begin{array}{c} & & &0 &. &\text{}^1 2 &1 \\ &+ & &0 &. &0 &9 \\ \hline & & &0 &. &3 &0 \\ \hline \end{array}

\begin{array}{c} & & &0 &. &3 &0 \\ &+ & &0 &. &0 &9 \\ \hline & & &0 &. &3 &9 \\ \hline \end{array}

\begin{array}{c} & & &0 &. &\text{}^1 3 &9 \\ &+ & &0 &. &0 &9 \\ \hline & & &0 &. &4 &8 \\ \hline \end{array}

The complete pattern is:

0.03, \ 0.12, \ 0.21, \ 0.30, \ 0.39, \ 0.48

b

What is the pattern?

A
The numbers are increasing by 0.09.
B
The numbers are increasing by 90.
C
The numbers are increasing by 9.
D
The numbers are increasing by 0.9.
Worked Solution
Create a strategy

Consider what operation we were doing in part (a).

Apply the idea

In part (a) we added 0.09 to the previous number. So the pattern is increasing by 0.09.

The correct answer is option A.

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