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Order of Operations in Algebra

Part of the Algebra I For Dummies Cheat Sheet

Solve algebra problems correctly by following the order of operations. When performing more than one operation on an algebraic expression, work out the operations and signs in the following order:

  1. First calculate powers and roots.

  2. Then perform all multiplication and division.

  3. Finish with addition and subtraction.

If you have more than two operations of the same level, do them in order from left to right, following the order of operations.

For example, to solve 24 ÷ 3 + 11 – 32 × 2, you would

  1. First calculate powers and roots.

    This problem doesn't have any roots, but it does have one power, 32. You know that 32 = 3 × 3 = 9. Substitute 9 into the problem, and you get 24 ÷ 3 + 11 – 9 × 2.

  2. Then perform all multiplication and division.

    Working left to right, 24 ÷ 3 = 8 and 9 × 2 = 18. Substitute those numbers into the problem, and you have 8 + 11 – 18.

  3. Finish with addition and subtraction.

    So, you end up with 8 + 11 – 18 = 19 – 18 = 1.

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