In Algebra, an expression is a combination of numbers and variables, having a form such as,
x \space {\text{--}} \space 4 \space \space , \space \space 2x.
Here we will see how to evaluate algebraic expressions when required.
How to Evaluate Algebraic Expressions:
Evaluating an algebraic expression is the process of assigning a value to the variable or variables in the expression.Then carrying out the order of operations in the expression.
Examples
(1.1)
Evaluate a + 3 for a = 5.
Solution
a + 3 = 5 + 3 = 8
(1.2)
Evaluate a + 2 + b for a = 1 and b = 4.
Solution
a + 2 + b = 1 + 2 + 4 = 7
(1.3)
Evaluate 3a + 4 − 5b for a = 7 and b = 2.
Solution
3(7) + 4 − 5(2) = 21 + 4 − 10 = 15
Evaluate Algebraic Expressions,
Further Examples
(2.1)
Evaluate {\frac{x}{3x + 2}} for x = 6.
Solution
{\frac{6}{3(6) + 2}} = {\frac{6}{18 + 2}} = {\frac{6}{20}} = {\frac{3}{10}}
(2.2)
Evaluate {\frac{1}{2}}\pi t^2 for t = 4.
Solution
{\frac{1}{2}}\pi 4^2 = {\frac{1}{2}}\pi(16) = {\frac{16}{2}}\pi = 8\pi
(2.3)
Evaluate r + rs ÷ 4r for r = 2 and s = 3.
Solution
2 + 2(3) ÷ 4(2) = 2 + 6 ÷ 8 = 8 ÷ 8 = 1