Solving for a Variable
Another application of algebra is to solve an equation for a given variable.
Example: Using the formula given in Figure 1-12, find the total capacitance (CT) of the series circuit containing three capacitors with
Therefore, CT = 1/96.66 = .01034 microfarad. The microfarad (10-6 farad) is a unit of measurement of capacitance. This will be discussed in greater length beginning on page 10-51 in chapter 10, Electricity.
Use of Parentheses
In algebraic equations, parentheses are used to group numbers or symbols together. The use of parentheses helps us to identify the order in which we should apply mathematical operations. The operations inside the parentheses are always performed first in algebraic equations.
Example: Solve the algebraic equation N = (4 + 3)2. First, perform the operation inside the parentheses. That is, 4 + 3 = 7. Then complete the exponent calculation N = (7)2 = 7 x 7 = 49.
When using more complex equations, which may combine several terms and use multiple operations, grouping the terms together helps organize the equation. Parentheses, ( ), are most commonly used in grouping, but you may also see brackets, [ ]. When a term or expression is inside one of these grouping symbols, it means that any operation indicated to be done on the group is done to the entire term or expression.
Order of Operation
In algebra, rules have been set for the order in which operations are evaluated. These same universally accepted rules are also used when programming algebraic equations in calculators. When solving the following equation, the order of operation is given below:
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