Order of operations
The order of operations is a collection of rules that gives the correct sequence of steps in a calculation.
BIDMAS is often used as a way to remember the order.
Brackets
Indices (power)
Division
Multiplication
Addition
Subtraction
Note:
When only addition and subtraction are left in the calculation, work them out in the order you find them - starting from the left of the calculation and working towards the right.
Bobby: Hi Berry, nice to meet you.
Berry: Hi, nice to meet you.
Bobby: So, you’re a musician, right?
Berry: Yeah, I’m a bassist in a band called Red Ivory.
Bobby: Exciting, so how long have you been with Red Ivory for?
Berry: We’ve been around for about a year but I’ve been playing bass and guitar for nearly two years.
Bobby: So, does your band go and perform in public?
Berry: Yeah, we gig around all of London.
Bobby: So, if people came to see your gigs, do you get paid for these?
Berry: Yeah, we get paid by how many people attend our shows and how much the tickets cost.
Bobby: So you've got money coming in but I presume you’ve also got expenses. So, how do you work out how much each member gets paid?
Berry: So, obviously, you have to subtract costs of damaged equipment, like a broken guitar string, and you also have to pay for the transportation of our equipment to and from the gigs. But after that, we can divide it equally between the four members.
Bobby: Ah! So to me, mathematically, that sounds like an ‘order of operations’. To get your pay per member, you need to multiply the ticket price by the number of tickets sold, and then subtract your expenses from that total. All before dividing by the number of band members. Since multiplication and division come before addition and subtraction in the order of operations, subtracting expenses would need to be inside the brackets.
Bobby: Does that play a part in other parts of your band or maybe even the future?
Berry: Well, we do want to release as much music that we can into the world and so, we have to save up for recording and then we have to save up for mastering those recordings, and then we can release it onto platforms.
Bobby: It sounds like you use maths quite regularly in your life as a musician.
Berry: Yeah, we do, definitely.
Examples

Image caption, Use the correct order of operations to do this calculation: 1. Brackets, 2. Indices, 3. Division and Multiplication, 4. Addition and Subtraction.

Image caption, Remember to perform the multiplication before the addition.

Image caption, Once the multiplication is done, then do the addition.

Image caption, The calculation is now complete. 2 + 3 × 6 = 20
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Image caption, Calculate 4 + 2 × 3² using the correct order of operations.

Image caption, There are no brackets, check to see if there are any indices. Calculate 3² first.

Image caption, Calculate 3². 3² = 9. Check to see if there are any multiplication or division calculations. Multiply 2 × 9

Image caption, 2 × 9 = 18. Check for any addition or subtraction calculations. Calculate 4 + 18. 4 + 18 = 22
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Image caption, Calculate 60 – (4² + 2 x 5) using the correct order of operations.

Image caption, Using the correct order of operations, the calculation inside the brackets is first. In order to do the calculation inside the brackets check for indices. Calculate 4². 4² = 16

Image caption, Now that 4² has been calculated, check for any multiplication or division calculations. There is a multiplication of 2 x 5

Image caption, 2 x 5 = 10. Do the addition, 16 + 10 = 26 and finally the subtraction, 60 – 26 = 34
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Question
Calculate
9 × 2 + 20 ÷ 2
Solution
9 × 2 + 20 ÷ 2 Multipication
= 18 + 10 Addition
Answer
= 28
Question
Find the value of
2³ + 6 ÷ 2
Solution
2³ + 6 ÷ 2 Indices
= 8 + 6 ÷ 2 Division
= 8 + 3 Addition
Answer
= 11
Question
Calculate the value of
8 + 3(5 − 1)
Solution
= 8 + 3(4) Brackets
= 8 + 12 Multiplication
= 20 Addition
Questions
Calculate the value of
5 × 3 + (5 + 2²)
Solution
5 × 3 + (5 + 4) Brackets
= 5 × 3 + 9 Multiplication
= 15 + 9 Addition
= 24
Test yourself
More on M1: Number
Find out more by working through a topic
- count6 of 7

- count7 of 7

- count1 of 7

- count2 of 7
