Order of Operations and Multi-Step Problems
Order of Operations and Multi-Step Problems covers the convention that decides which calculation to do first in an expression with more than one operation: brackets first, then multiplication and division, and finally addition and subtraction, each worked left to right.
Before you start
Make sure you're comfortable with these topics first:
Method
- Look for brackets in the expression first; always calculate what is inside a bracket before doing anything else.
- After brackets, scan the expression for any multiplication or division signs and carry these out next, working from left to right.
- Only once every multiplication and division has been done should you carry out any addition or subtraction, again working from left to right.
- For a word problem, read it through fully before calculating anything, and note each piece of information with its correct operation rather than guessing an order.
- Break a multi-step problem into smaller single-operation steps, writing down the result of each step so it can be used in the next one.
- A bar model can help show how the quantities in a word problem relate to each other, especially when an amount needs to be split, compared or combined in more than one way.
- Check the final answer by re-reading the question and confirming each step matches what was actually being asked, not just that the arithmetic is correct.
Worked example
Work out 6 + (15 - 3) x 4 divided by 2.
- Work out the brackets first: 15 - 3 = 12.
- Rewrite the expression using this result: 6 + 12 x 4 divided by 2.
- Carry out the multiplication and division next, working left to right: 12 x 4 = 48, then 48 divided by 2 = 24.
- Rewrite the expression again: 6 + 24.
- Finally carry out the addition: 6 + 24 = 30.
Practice questions
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Q1Work out 20 - 8 divided by 2.Show answer
Answer: 16
Q2Work out (9 + 3) x 5 - 14.Show answer
Answer: 46
Q3Work out 9 x 7 - 4 x 8.Show answer
Answer: 31
Q4Freddie buys 3 packets of stickers costing 45p each and a poster costing 2 pounds 10p. Work out the total amount he spends, in pounds.Show answer
Answer: 3.45 pounds
Q5A school hall has 8 rows of chairs with 14 chairs in each row, plus 3 extra rows of 6 chairs for latecomers. Work out the total number of chairs in the hall.Show answer
Answer: 130 chairs
Q6Work out 100 - (6 + 9) x 4.Show answer
Answer: 40
Q7Nadia has 84 pounds. She spends a third of it on a game, then splits the amount that is left equally between 4 charity boxes. Work out how much money goes into each charity box.Show answer
Answer: 14 pounds each
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Work out 5 x (12 - 7) + 18 divided by 3.
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A coach company has 6 coaches. Each coach can carry 52 passengers. For a school trip, 4 coaches are completely full and the other 2 coaches each carry 38 passengers. Work out the total number of passengers travelling on the trip.
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A stationery shop prices pens at 65p each. Zara buys 12 pens. The shop then takes off a bulk discount of 90p from the total because she bought more than 10. She pays with a 10 pound note. Using the correct order of operations, work out how much change Zara receives.
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Free printable worksheet
Want more practice on paper? Download the order of operations and multi-step problems worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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