Multi-step addition & subtraction problems
Theory
A multi-step problem needs two or more calculations, done in a sensible order. This Year 5 maths page shows how to plan the steps, keep track of what each answer means, work with large numbers, money and decimals (lining up the decimal points), and check the final answer.
A multi-step problem needs more than one operation. Each step answers a smaller question, and the last step answers the question asked.
Work from the start of the story: things added (bought, arrived, joined) are added; things removed (sold, used, left, given away) are subtracted. \(4280 + 1650 - 2390\) means start with \(4280\), add \(1650\), then take away \(2390\).
To add or subtract decimals, line up the decimal points so tenths are under tenths and hundredths under hundredths. Fill gaps with zeros: \(9.6\) is \(9.60\). It works like dollars and cents: \(\$9.60\) is \(9\) dollars and \(60\) cents.
Change is the money given back: amount paid minus the total cost.
Useful facts for multi-step problems:
How to solve a multi-step problem
- Read the whole problem and find the final question.
- Plan the steps in order: what do you need to know first?
- Calculate each step, lining up places (and decimal points).
- Check with an estimate and make sure the answer makes sense.
| \(4280 + 1650\) | \(=\) | \(5930\) |
| \(5930 - 2390\) | \(=\) | \(3540\) |
The library has \(3540\) books.
| \(20\,000 - 7450\) | \(=\) | \(12\,550\) |
| \(12\,550 - 5680\) | \(=\) | \(6870\) |
\(6870\) L is left.
(i) What is the total cost?
(ii) How much change does she get?
| \(32.40 + 15.85\) | \(=\) | \(48.25\) |
| \(60.00 - 48.25\) | \(=\) | \(11.75\) |
(i) \(\$48.25\).
(ii) \(\$11.75\).
| \(9.60 + 4.75\) | \(=\) | \(14.35\) |
| \(14.35 - 3.80\) | \(=\) | \(10.55\) |
\(10.55\). Writing \(9.6\) as \(9.60\) and \(3.8\) as \(3.80\) keeps the places lined up.
(i) How much did they raise?
(ii) How much more do they need?
| \(1380 + 945 + 1260\) | \(=\) | \(3585\) |
| \(5000 - 3585\) | \(=\) | \(1415\) |
(i) \(\$3585\).
(ii) \(\$1415\).
(i) How many people are there now?
(ii) How many seats are empty?
| \(9200 - 3150\) | \(=\) | \(6050\) |
| \(6050 + 2475\) | \(=\) | \(8525\) |
| \(9200 - 8525\) | \(=\) | \(675\) |
(i) \(8525\) people.
(ii) \(675\) empty seats.
| \(4.50 + 2.35 + 1.70\) | \(=\) | \(8.55\) |
| \(15.00 - 8.55\) | \(=\) | \(6.45\) |
It can take \(6.45\) kg more.
Common pitfalls
Frequently asked questions
How do you solve a multi-step problem?
Find the final question, plan the steps in order, calculate each step carefully and check the answer makes sense.
How do you add and subtract decimals?
Line up the decimal points, fill any gaps with zeros, then add or subtract as with whole numbers. \(9.6 + 4.75 = 14.35\).
How do you work out change?
Add up the cost, then subtract it from the amount paid. \(\$60 - \$48.25 = \$11.75\).
Can you subtract two amounts at once?
Yes. Subtracting \(7450\) and then \(5680\) is the same as subtracting their total, \(13\,130\).
How do I check my answer?
Estimate by rounding, and check the answer fits the story, for example an amount left over is less than the starting amount.