Читать книгу Algebra II For Dummies - Sterling Mary Jane - Страница 6

When mathematicians switched from words to symbols to describe mathematical processes, their goal was to make dealing with problems as simple as possible; however, at the same time, they wanted everyone to know what was meant by an expression and for everyone to get the same answer to the same problem. Along with the special notation came a special set of rules on how to handle more than one operation in an expression. For instance, if you do the problem , you have to decide when to add, subtract, multiply, divide, take the root, and deal with the exponent.

The order of operations dictates that you follow this sequence:

1. Raise to powers or find roots.

2. Multiply or divide.

3. Add or subtract.

If you have to perform more than one operation from the same level, work those operations moving from left to right. If any grouping symbols appear, perform the operation inside the grouping symbols first.

So, to simplify , follow the order of operations:

1. The radical acts like a grouping symbol, so you subtract what’s in the radical first: .

2. Raise the power and find the root: .

3. Multiply and divide, working from left to right: 4 + 9 – 30 + 4 + 7.

4. Add and subtract, moving from left to right: 4 + 9 – 30 + 4 + 7 = –6.