What Is BODMAS And BIDMAS? Explained For Teachers, Parents And Kids
BODMAS and BIDMAS pop up throughout elementary school math, so here we cover what BODMAS and BIDMAS mean, and provide you with some BODMAS questions and exercises you can use to help your child accurately practice carrying out BODMAS calculations.
What is BODMAS?
BODMAS is an acronym to help children remember the order of mathematical operations – the correct order in which to solve math problems.
BODMAS stands for B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction.
What is the BODMAS rule
The BODMAS rule follows the order of the BODMAS acronym, i.e. B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. The BODMAS rule states that mathematical expressions with multiple operations need to be solved from left to right in the order of BODMAS. Division and Multiplication are considered as interchangeable and depend on which comes first in the expression, as are Addition and Subtraction.
Some children use the Bodmas rule as a mnemonic (like Roy G. Biv is used to remember the colors Red, Orange, Yellow, Green, Blue, Indigo, Violet).
What is BIDMAS?
The BIDMAS rule is an alternative acronym to BODMAS to help remember the order of operations. The only difference is that there’s an I instead of an O. The meaning is the same.
Bidmas stands for Brackets, Indices (another term for exponents), Division/Multiplication, Addition/Subtraction.
“Mathematical operations” are what you do to the numbers given. The four main operations are:
- addition (+);
- subtraction (-);
- multiplication (x);
- and division (÷).
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When presented with a number sentence containing more than one operation (such as 3 + 4 x 2), the operations cannot be completed from left to right, but instead in their order of “importance,” which is what BODMAS stands for.
BODMAS stands for:
“Orders” means square roots and indices (which you may know as square numbers, powers, or exponents).
Here “Indices” (square numbers, powers, or exponents) is used instead of “Orders.”
What does Order of Operations mean?
This is the order in which certain operations must be completed, from brackets first to addition and subtraction last.
It is important that division and multiplication are represented alongside each other as they are of equal importance (so must be completed from left to right, whichever appears first) – this is the same for addition and subtraction.
Below are some examples of BODMAS questions and answers children might see in schools. We’ve given you the right answer and at least one different answer to show you where children might go wrong.
BODMAS (BIDMAS) Questions and Answers
Question 1: 6 + 2 x 7
The correct answer is 20.
The multiplication must be completed first (2 x 7 = 14) and then the addition (6 + 14 = 20).
This may be commonly miscalculated as 56 by working from left to right (6 + 2 = 8, 8 x 7 = 56).
Question 2: 3 x (2 + 4) + 52
The correct answer is 43.
The BODMAS rule states we should calculate the Brackets first (2 + 4 = 6), then the Orders (52 = 25), then any Division or Multiplication (3 x 6 (the answer to the brackets) = 18), and finally any Addition or Subtraction (18 + 25 = 43).
Children can get the wrong answer of 35 by working from left to right.
Question 3: 5 – 2 + 6 ÷ 3
The correct answer is 5.
The division must be completed first (6 ÷ 3 = 2), which then leaves addition and subtraction; as both are of the same importance, we can then work from left to right. 5 – 2 + 2 (the answer to 6 ÷ 3) = 5.
This may be commonly miscalculated as either 3 by working from left to right, or as 1 by wrongly assuming that addition should be completed before subtraction.
Other parent and child math explainers
- Math dictionary for kids and parents – all the terms you’ll need to know
- Fractions for kids – step by step instructions for parents and carers teaching their children at home
- Division explained for children and their parents – step by step for every grade
As a parent trying to support your child with order of operations questions, you’ll find that most calculators and computers nowadays are sophisticated enough to complete calculations according to BODMAS. However, it’s worth testing any calculator out just to be sure. There are also plenty of BODMAS calculators available online.
Practice BODMAS questions
1) 29 – 4 x 6 + 5 =
2) Write what the two missing numbers could be.
(4 + ?) x ? = 100
Answer: 6 and 10 (4 + 6) x 10 = 100
3) Write the missing numbers to make these calculations correct.
a) 200 x ? – 200 = 200
b) (100 – ?) x 100 = 100
Answers: a) 2 b) 99
4) Write the correct sign >, < or = in each of the following
a) (10 + 5) – 9 [ ] (10 + 9) – 5
b) 3 x (4 + 5) [ ] (3 x 4) + 5
c) (10 x 4) ÷ 2 [ ] 10 x (4 ÷ 2)
a) (10 + 5) – 9 < (10 + 9) – 5
b) 3 x (4 + 5) > (3 x 4) + 5
c) (10 x 4) ÷ 2 = 10 x (4 ÷ 2)
Practice 5th Grade BODMAS questions
Other tricky elementary math curriculum topics you may need help on
- What is a unit fraction?
- What is a number sentence?
- What is place value?
- What are number bonds?
- Properties of shapes
- What are 2D shapes?
- What are 3D shapes?
- What is long multiplication?
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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.