Q&A for How to Apply the Order of Operations

BODMAS stands for Brackets, Order, Division, Multiplication, Addition, and Subtraction. Like PEMDAS, it is an abbreviation for the order of operations. In this case, Brackets stand for Parentheses; Order stands for Exponents (as in Order of Powers).

Twenty-five came from 5 squared, or 5x5. The 5 came from 8-3, and the 8 came from 6+2.

It's customary when only adding and subtracting (or only multiplying and dividing) to work from left to right. It's not mandatory, however: in this case, you would have arrived at 85 no matter in what order you added or subtracted.

When adding and subtracting, work from left to right.

When doing addition and subtraction, work from left to right.

There’s no difference, but Americans like to use PEMDAS most frequently.

First do what's inside the parentheses: add 7 plus 3. That's 10. Next, do what's inside the brackets: multiply by 4. That's 40. Now do what's inside the braces: square 4. That's 16. Then add 16 plus 40. That's 56. Finally, divide everything inside the braces by 7: 56/7 = 8, which is the answer.

When working within a certain priority (such as parentheses, exponents, multiplication/division or addition/subtraction), you typically move left to right, although it actually doesn't matter which direction you move as long as you remain within that priority until it's finished. (For example, don't do any adding or subtracting until all the multiplying and dividing have been done.)

Do what's inside the parentheses first: 10 - 3 = 7. Next, do what's inside the brackets, multiplication first: 2(7) = 14. 3 + 14 = 17. Finally, do the remaining multiplication: 2(17) = 34.

You don't have to. When adding and subtracting (or when multiplying and dividing), it's merely customary to work from left to right.

Because (8) - 3 means to subtract, not multiply. If it had been (8)3, that would have indicated multiplication.

Don't make this common mistake. Addition and subtraction have the same priority, so you should work from left to right when they appear together.

You always multiply and/or divide before adding and/or subtracting. So, 25 x 3 = 75.

PEMDAS and BODMAS are similar; however, P (parentheses) is replaced with B (brackets), and E (exponents) is replaced with O (orders). When performing multiplication and division, work from left to right. For example, 12 / 3 x 4 is not 12 / 12 or 1; instead, you divide 12 by 3 to get 4 and then multiply by 4 to get 16.