The Order of Operations: Examples

(Links are provided for additional review of working with negatives, grouping symbols, and powers.)

• Simplify 4 − 3[4 −2(6 − 3)] ÷ 2

Remember that, in leiu of grouping symbols telling you otherwise, the division comes before the addition, which is why this expression simplified, in the end, down to "4 + 3", and not "10 ÷ 2".

(If you're not feeling comfortable with all of those "minus" signs, review Negatives.)

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• Simplify 16 − 3(8 − 3)² ÷ 5

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If you have learned about variables and combining "like" terms, you may also see exercises such as this:

• Simplify 14x + 5[6 − (2x + 3)].

It isn't required that you rearrange the terms to group "like" terms together, but it's generally a good idea to do so, certainly when you're just starting out. But, by grouping appropriately, it's a lot harder to lose terms when you're adding things up.

• Simplify −{2x − [3 − (4 − 3x)] + 6x}

(For more examples of this sort, review Simplifying with Parentheses.)

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Expressions containing fractional forms can cause confusion, too. But, as long as you work the numerator (that is, the top) and the denominator (that is, the bottom) separately, until they're completely simplified first, and only then combine (or reduce), if possible, then you should be fine.

If a fractional form is added to, or subtracted from, another term, fractional or otherwise, make sure you've completely simplified and reduced the fractional form before you try to do the addition or subtraction.

• Simplify

As it happens, each of the fractions above simplified to whole numbers, so I didn't have to muck about with common denominators. You will not usually be so lucky.

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• Simplify

(For examples with loads of exponents, review Simplifying with Exponents.)

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