Topics
7. Decimal operations
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AustraliaVIC
Level 6

7.04 Story problems with addition and subtraction

Lesson
Practice
Lesson

Are you ready?

Let's review how to  add and subtract decimals  .

Examples

Example 1

Find 4.095-2.609+2.27, writing your answer in decimal form.

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.

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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.

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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.

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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.

Key words for additionKey words for subtraction
moreless
longershorter
laterearlier
boughtsold
joinedleft

Outcomes

VCMNA214

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

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