# How to Evaluate Algebraic Expressions

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- Evaluating Algebraic Expressions

Evaluating Expressions

The term “evaluating expressions” refers to the process of replacing a variable by a numeral in an expression.

How do we evaluate an algebraic expression?

Here's the three-step method to evaluate an algebraic expression.

1. Replace each variable with the given numerical value.

2. Perform the order of operations.

3. Simplify the numerical expression.

1. Substitute the unknown variable with a numeral

a. Evaluate the expression 7 + y, when y = 5,

Plug-in the numeral for y and simplify the expression.

7 + y

= 7 + 5

= 12

2. Substitute the numerals in the variable and use the order of operations.

b. Evaluate the expression 4x + 2y, when x = 2, y = 5,

4x + 2y

Rewrite the expression by substituting the values of the variable in the expression.

4x + 2y = (4 × 2) + (2 × 5)

Use the order of operation and simplifying, we get

4x + 2y = 8 + 10

= 18

Application of evaluating an expression in the real world

Adam buys 2 pens for $m each and 3 pencils for $n each.

The above scenario gives rise to an expression, 2m + 3n which helps us to find the total cost.

Let's assume the cost of each pen and pencil is $5 and $2 respectively.

Substitute m = 5 and n = 2 in the expression to find the total cost of his purchase.

2m + 3n

= (2 × 5) + (3 × 2)

[ Substituting the value of m and n ]

= 10 + 6

[ Adding 10 and 6 ]

= 16

Adam has spent $16 to buy 2 pens and 3 pencils.

The lesson in a nutshell:

⮚ Rewrite the expression with numerical values in the place of variables.

⮚ Follow the order of operations.

⮚ Simplify to find the numerical value of the expression.

Reinforce your skills with our free printable Evaluating Algebraic Expression worksheets.

Solved Examples:

Example 1

1. Evaluate p + 7 at p = 10

p + 7

= 10 + 7

[ Substituting p = 10 ]

= 17

Example 2

2. Evaluate 2r – 3q at r = 3 and q = 9

2r – 3q

= 2(3) – 3(9)

[ Substituting the value of r and q ]

= 6 – 27

[ Multiplying the terms ]

= – 21

Example 3

3. Evaluate x + y – (2a + 5b), when x = 2, y = 3, a = 5, b = 7

x + y – (2a + 5b)

= 2 + 3 – ((2 × 5) + (5 × 7))

[ Substituting the value of variables ]

= 5 – (10 + 35)

[ Performing order of operations ]

= 5 – 45

= – 40