To find the value of a numeric expression, determine the order of actions in a given example. For convenience, label it with a pencil over the appropriate signs. Will follow all of these steps in a certain order: the actions in parentheses, exponentiation, multiplication, division, addition, subtraction. The resulting number will be the value of a numeric expression.
Example. Find the value of the expression (34∙10+(489-296)∙8):4-410. Determine the order of action. The first action is run in the inner brackets 489-296=193. Then, multiply 193∙8=1544 34∙10=340. Next activity: 340+1544=1884. Then follow the division 1884:4=461, and then subtract 461-410=60. You have found the value of this expression.
To find the value of trigonometric expressions at a known angle α, the pre - simplify the expression. To do this, apply the appropriate trigonometric formula. Calculate the values of trigonometric functions, substitute them in the example. Follow the steps.
Example. Find the value of the expression 2sin 30 ° ∙cos 30º∙tg 30º∙ctg 30º. Simplify this expression. To do this, use the formula tg α∙ctg α=1. Get: 2sin 30 ° ∙cos 30º∙1=2sin 30 ° ∙cos 30º. It is known that sin 30º=1/2 cos 30º=√3/2. Therefore, 2sin 30 ° ∙cos 30º=2∙1/2∙√3/2=√3/2. You have found the value of this expression.
The value of an algebraic expression depends on the value of the variable. To find the value of algebraic expressions with given variables, simplify the expression. Substitute variable values. Take the appropriate action. In the end, you will receive a number, and that is the value of algebraic expressions with given variables.
Example. Find the value of expression 7(a+y)-3(2a+3y) when a=21 and y=10. Simplify this expression, we get: a–2y. Substitute appropriate values for the variables and calculate: a–2y=21-2∙10=1. This is the value of the expression 7(a+y)-3(2a+3y) when a=21 and y=10.
There are algebraic expressions that have no meaning for some values of the variables. For example, the expression x/(7–a) does not make sense if a=7, since the denominator becomes zero.