# 7.03 Add and subtract to thousandths

Lesson

## Are you ready?

In previous lessons, we have looked at  how to add  and  subtract decimals  with up to 2 decimal places. We'll apply the same strategies when adding bigger decimals, so let's start with a bit of review

### Examples

#### Example 1

Find 13.74+37.26 giving your answer as a decimal.

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}

Add the values down each column and regroup where necessary.\begin{array}{c} &{}^11&{}^13&.&{}^17&4 \\ + &3&7&.&2&6 \\ \hline &5&1&.&0&0 \\ \hline \end{array}

#### Example 2

Find 53.29-42.29, giving your answer as a decimal.

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.

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

Idea summary

When we add and subtract numbers with decimals, the process is exactly the same as when we work with whole numbers. We always start from the far right place value position, and move left, regrouping if we need to.

## Add numbers with three decimal places

In this video, we work through an example of adding two numbers with 3 decimal places.

In this video, we use an example of adding two numbers with 3 decimal places where we need to rename some decimals, after regrouping.

### Examples

#### Example 3

Find 563.362 + 331.495, writing your answer in decimal form.

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &5&6&3&.&3&6&2 \\ + &3&3&1&.&4&9&5 \\ \hline \\ \hline \end{array}

Add the values in the thousandths column.

\begin{array}{c} &5&6&3&.&3&6&2 \\ + &3&3&1&.&4&9&5 \\ \hline &&&&&&&7 \\ \hline \end{array}

Add the values in the hundredths column to get 6+9=15 and carry the 1 to the tenths column.

\begin{array}{c} &5&6&3&.&{}^13&6&2 \\ + &3&3&1&.&4&9&5 \\ \hline &&&&&&5&7 \\ \hline \end{array}

Add the values in the remaining columns and copy down the decimal point.

\begin{array}{c} &5&6&3&.&{}^13&6&2 \\ + &3&3&1&.&4&9&5 \\ \hline &8&9&4&.&8&5&7 \\ \hline \end{array}

Idea summary

We can use a vertical algorithm to add decimals up to thousandths.

## Subtract decimals to thousandths

This video works through subtracting large numbers with decimals in the thousandths.

### Examples

#### Example 4

Find 96.689 - 83.413, writing your answer in decimal form.

Worked Solution
Create a strategy

Use a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&9&6&.&6&8&9 \\ - &&8&3&.&4&1&3 \\ \hline \\ \hline \end{array}

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

\begin{array}{c} &&9&6&.&6&8&9 \\ - &&8&3&.&4&1&3 \\ \hline &&1&3&.&2&7&6& \\ \hline \end{array}

Idea summary

We can use a vertical algorithm to subtract decimals up to thousandths.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages