 # 7.04 Story problems with addition and subtraction

Lesson

Let's review how to  add and subtract decimals  .

### Examples

#### Example 1

Worked Solution
Create a strategy

Start by performing the subtraction first then the addition using vertical algorithms.

Apply the idea

To subtract 2.609 from 4.095 we write it in a vertical algorithm.

\begin{array}{c} &&4&.&0&9&5 \\ - &&2&.&6&0&9 \\ \hline \\ \hline \end{array}

Subtract the values down each column, regrouping where necessary.

\begin{array}{c} &&3&.&{}^10&8&{}^15 \\ - &&2&.&6&0&9 \\ \hline &&1&.&4&8&6 \\ \hline \end{array}

Now that we have found 4.095-2.609, we can add 2.27 to our answer.

Write it in a vertical algorithm. Use 0 as placeholder.

\begin{array}{c} &&1&.&4&8&6 \\ + &&2&.&2&7&0 \\ \hline \\ \hline \end{array}

Add the values down each column, regrouping where necessary.

\begin{array}{c} &&1&.&{}^14&8&6 \\ + &&2&.&2&7&0 \\ \hline &&3&.&7&5&6\\ \hline \end{array}

Idea summary

We can use order of operations with decimals, by performing each operation one at a time in a vertical algorithm.

## Problems with addition of decimals in tenths

This video looks at story problems involving mass measured to tenths and addition.

### Examples

#### Example 2

Ned trains 3 days a week. On Wednesday he ran 3.4 km, on Friday he ran 7.9 km and on Saturday he ran 2.5 km. How far had he run in total before Saturday?

Worked Solution
Create a strategy

Add the distances Ned ran on Wednesday and Friday using a vertical algorithm.

Apply the idea

Write it in a vertical algorithm.

\begin{array}{c} &&3&.&4 \\ + &&7&.&9 \\ \hline \\ \hline \end{array}

Add the values down each column, regrouping where necessary.

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

The total distance Ned ran before Saturday is 11.3 km.

Idea summary

To solve addition problems with decimals, we can use a vertical algorithm to add the decimals.

## Problems with addition of decimals in hundredths

This video uses a story problem that involves units of kilometres measured to hundredths and addition.

### Examples

#### Example 3

During a small earthquake event, two large rocks fell from a cliff. A geologist measured the mass of the two rocks. One rock had a mass of 69.22 kg, and the second rock had a mass of 72.74 kg.

What was the total mass of the two rocks that fell from the cliff?

Worked Solution
Create a strategy

Add the mass of the two rocks using a vertical algortihm.

Apply the idea

Write it in a vertical algorithm.

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

Add the values down each column, regrouping where necessary.

\begin{array}{c} &&{}^16&9&.&2&2 \\ + &&7&2&.&7&4 \\ \hline &1&4&1&.&9&6\\ \hline \end{array}

The total mass of the two rocks is 141.96 kg.

Idea summary

To solve addition problems with decimals to hundredths, we can use a vertical algorithm to add the decimals.

## Problems with subtraction of decimals

This video uses a story problem as the basis for a subtraction question. We also work out which order to subtract in.

### Examples

#### Example 4

Susana pays for a mandarin at the kiosk. The mandarin cost \$1.50 and Susana paid with a \$5 note.

How much change should Susana receive?

Worked Solution
Create a strategy

Subtract the cost of the mandarin from the amount Susana paid.

Apply the idea

Write the subtraction in a vertical algorithm. Use 0 for placeholders.

\begin{array}{c} &&5&.&0&0 \\ - &&1&.&5&0 \\ \hline \\ \hline \end{array}

In the tenths column, 0 is less than 5, so we will trade 1 from the units column which leaves us with 4 and carry it over to the tenths column which gives us 10. Now we can subtract down each column.

\begin{array}{c} &&4&.&{}^10&0 \\ - &&1&.&5&0 \\ \hline &&3&.&5&0\\ \hline \end{array}

The change that Susana will receive is \\$3.50.

Idea summary

Story problems have key words that help us know if we need to use addition or subtraction. This is not a complete list, so we need to understand the context of the question, to work out whether to add or subtract.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages