Chapter 1Section 1.4

Order of Operations

ExponentsAn exponent appears as a small number just above and to the right of another number. This means to multiply the number by itself the exponent number of times.

RootsA root is a number in front of the sign . This the number you need to multiply by itself that number of times to get the number under the root sign.

On a calculator use either the or keys.

On a calculator use the key for square roots.

For other roots use the , , , and keys by changing the root to a fraction exponent.

Order of operationsThere is a standard way decide when you look at numbers being combined with different operations which you do first.1) ()[]{}|| Grouping2) ^, Exponents and roots3) ·, ÷, negative Multiplication,

division and negative signs4) +,- Addition and Subtraction

Using grouping symbols, either (), [],{}, or || change the order you do the operations.

Example,

No grouping do the multiplication before the addition.

Example,

No grouping do the exponent before the multiplication.

Example,

No grouping do negative sign last.

Find, Find, Find,

FormulasTo "plug in" or evaluate a formula for given values of the variables you replace each variable in the formula with its corresponding value. For negative values you should also put the value in () parenthesis to make sure the order of operations.Find,

Replace each by ,

Find the value for,

For the values, , , and

Evaluating Formulas with CalculatorIt is useful to be able to use a calculator to find the value for very complicated expressions. When doing this the sequence of calculations that you do on the calculator needs to follow the order of operations which is not always what your intuition might suggest.Find the future value using the formula,

Where , , and ,

We want to find,

Start inside the parenthesis,

Now clear the calculator to do what is in the exponent,

Now clear the calculator to do the exponent,

Keep the display (do not clear!),

Changing words into formulas,This can be as many people think not very easy. There are several key words that can be used to indicate certain operations.+ (increased, also, and, more, sum)- (decreased, fewer, less, difference)(product, multiplied, by)÷(quotient, divided, into)^(raise to, square, cube, to the power)(root, square root, radical)

There are other words to indicated the order of operations such as: this,then, first, the result, now, finally

Write an expression for the following:Four is subtracted from x. This difference is divided by 10y. The quotient is then cubed. Finally, 19 is added to the expression.1. Four is subtracted from x: 2. Difference divided by 10y: 3. Quotient is cubed: 4. 19 added to expression: Find the value when and ,