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The World Explained In Plain English.
The World Explained In Plain English.
Algebra in Layman's Terms


Algebra in Layman's Terms

The Basics

Constants - Commonly displayed as letters a,b or c,. Represents a permanent value that never change.

Expression - Has two or more terms with no equal sign for example, 2x² + 4x

Equation - Has two or more terms with an equal sign for example,  2x² + 4x = 7

Term - Is a number, letter or both on either side of the operation sign. For example in the expression 2x² + 4x, 2x² is the first term and 4x is the second term.

Operation - Sometimes called "operand" are the signs between the terms that tells you whether to add, subtract, divide or multiply (+.-, /, x).

Variables - Commonly displayed as x, y or z represents an unknown value.

Exponents

An exponent is the superscript next to a number or letter. In 7⁵, 5 is the exponent. It can also include a letter like 7ˣ or a fraction like 7¹/³. In word problems it is often referred to as "power". If we look back at our previous example, 7⁵ would be worded as 7 to the 5th power. If a term has an exponent, it means you have to multiply the base value times itself indicated by the exponent. For example in 8³, you have multiply the number 8 three times, 8 x 8 x 8 = 512 . Do not multiply 8 x 3 = 24 because you will get an incorrect answer.

 

  • Multiplying Exponents - To multiply exponents the base numbers has to be the same. For example  2⁴ x 2⁶ = 2¹⁰.You cannot multiply exponents when the base numbers are different. For example 5³ x 3⁷.
  • Adding Exponents - To add exponents you have to first solve the exponential terms. For example in the expression 6³ + 9², you have to multiply 6 x 6 x 6 = 216, then multiply  9 x 9 = 81 then we add both sets of numbers together 216 + 81 = 297.
  • Subtracting Exponents - Works the same way as adding exponents except the plus sign is swapped for the minus sign. Here's the same example, 6³ - 9². First we solve the first term 6 x 6 x 6 = 216, then 9 x 9 = 81 and subtract the two sets of numbers 216 - 81 = 135.
Previous Exponents