# How to Evaluate Algebraic Expressions

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

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