Order of Operations

Mathematics involves the use of various operations such as addition (+), subtraction (-), multiplication (x) and division (÷).

When equations contain more than one of these operations, it’s important to know the correct sequence in which to execute them. This specific sequence is known as the order of operations and it’s essential for obtaining accurate results.

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The BODMAS Rule

The acronym BODMAS provides a convenient way to remember the correct sequence of operations. BODMAS stands for:

  • Brackets
  • Orders (also known as Indices or Exponents)
  • Division
  • Multiplication
  • Addition
  • Subtraction

How to Use BODMAS in Equations

To apply BODMAS, start by examining the equation to identify which operations it contains. Then use the BODMAS rule to figure out which operations to perform first and in what order.

Step-by-Step Example

Consider the equation 4 + 3 \times 2.

1. Identify Operations: The equation has both addition and multiplication operations.

2. Use BODMAS: According to BODMAS, comes before addition.

3. Perform Calculations:

  • First, deal with the multiplication: 3 \times 2 equals 6
  • Next, execute the addition: 4 + 6 equals 10

The final result of the equation 4 + 3 \times 2 is 10.

Practice Questions

Question 1:

What is 2 + 3?

Solution

2 + 3 = 5.

As there’s only one operation, addition, you directly add the numbers.


Question 2:

What is 5 \times 2 + 3?

Solution

Using BODMAS, multiplication should be done first.

First, 5 \times 2 = 10.

Next, 10 + 3 = 13.


Question 3:

What is 6 - 2 \times (1 + 2)?

Solution

With BODMAS, you start with the brackets: 1 + 2 = 3.

Then comes multiplication: 2 \times 3 = 6.

Finally, subtraction: 6 - 6 = 0.


Question 4:

What is 8 \div 2(2 + 2)?

Solution

According to BODMAS, deal with the brackets first: 2 + 2 = 4.

Next, perform multiplication and division from left to right: 8 \div 2 = 4.

Then, 4 \times 4 = 16.

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