How to Calculate Algebraic Expressions: 5 Steps (with Pictures)

2024 Author: Jason Gerald | [email protected]. Last modified: 2024-01-15 08:07

Struggling with algebra? Not even sure about the true meaning of the expression? This may be the first time you've come across random letters of the alphabet found in your math problems. Don't know what to do? Alright, here's a guide for you.

Step

Step 1. Understand the meaning of variable

The random letters you see in your math problems are called variables. Each variable represents a number you don't know.

Example: In 2x + 6, x is a variable.

Step 2. Understand the meaning of algebraic expressions

An algebraic expression is a collection of numbers and variables combined with any mathematical operation (addition, multiplication, exponents, etc.). Here are some examples:

• 2x + 3y is an expression. This expression is generated by adding the product of

  Step 2. and x with multiplication result

  Step 3. and y.

• 2x itself is also an expression. This expression is a number

  Step 2. and one variable x combined with the mathematical operation of multiplication.

Step 3. Understand the meaning of calculating algebraic expressions

Calculating an algebraic expression means entering a given number for a variable or replacing a certain variable with a given number.

For example, if you are asked to calculate 2x + 6 with x = 3, all you have to do is – rewrite the expression by replacing all x with 3. 2(3) + 6.

• Solve the final result you get:

  2(3) + 6

  = 2×3 + 6

  = 6 + 6

  = 12

  So, 2x + 6 = 12 when x = 3

Step 4. Try calculating an expression that has more than one variable

This is calculated in the exact same way as calculating an algebraic expression that has only one variable; You only do the same process more than once.

Suppose you are asked to calculate 4x + 3y with x = 2, y = 6

• Replace x with 2: 4(2) + 3y
• Replace y with 6: 4(2) + 3(6)

• Finish:

  4×2 + 3×6

  = 8 + 18

  = 26

  So, 4x + 3y = 26 where x = 2 and y = 6

Step 5. Try calculating an expression with a power of

Count 7x² - 12x + 13 where x = 4

• Insert 4 into: 7(4)² - 12(4) + 13

• Follow the order of your operations: K3BJK (Square Brackets Divide by Less). Since solving powers comes before multiplication, square 4 before doing your multiplication or division, and then adding or subtracting.

  So, solving the exponent gives, (4)² = 16.

  This step will return the expression 7(16) - 12(4) + 13

• Multiply or Divide:

  7×16 - 12×4 + 13

  = 112 - 48 + 13

• Add or Subtract:

  112 - 48 + 13

  = 77

  So, 7x² - 12x + 13 = 77 where x = 4