Chapter Contents

• Numbers
• 1. Integers
• 2. Number Properties
• 3. Order of Operations
• 4. Powers, Roots and Radicals
• 5. Approximate Numbers
• 6. Scientific Notation
• 7. Ratio and Proportion
• Math of Beauty
• Pi
• Numbers Problem Solver

• Comments, Questions?

Feelings about Math

Recommendation

Easy to understand algebra lessons on DVD. Try before you commit. More info:
MathTutorDVD.com

Online Algebra Solver

Solve your algebra problem step by step!

Online Algebra Solver »

Share

Share this page.

From the math blog...

3. Order of Operations

Problem: There are 2 ways to answer this question:

2 + 3 × 7

We can either

• Add the 2 and 3 first and then multiply the result by 7 (we would get 35), OR
• We could multiply the 3 and 7 then add the 2 (giving us 23).

Which is correct?

To reduce confusion and so that we all get the same answer, the following convention is used.

BODMAS

BODMAS is the agreed convention for answering problems that are a mixture of adding, subtracting, multiplying and dividing. It stands for:

B:	Do what is inside brackets first
O:	Order is important in mathematics!
DM:	Do multiplications and divisions as you come to them, from left to right
AS:	Finally, do additions and subtractions as you come to them, from left to right.

So for our problem above, the correct answer would be:

2 + 3 × 7

= 2 + 21

= 23

Example 1

Evaluate 10 − 2 × 3

Answer

Example 2

Evaluate (10 − 2) × 3

Answer

Example 3

Simplify -3 + 5 × (7² + 5)

Answer

Example 4

Simplify 12(5 + 6 × 3) ÷ (4 + 2)

Answer

Example 5

Simplify -2(x + 5 × 7 + 3)

[Note the difference between the letter "x" and the multiplication operator "×".]

Answer