Algebra, The Beginnings

So let’s leave statistics for a while and return to algebra. This post will be a bit more basic but it illustrates a skill needed when converting word problems to equations. First, a couple of definitions:

An Expression in algebra is basically anything you can write down in algebra without the “equal” symbol. You can think of an expression as either side of an equation. Examples are


They can be complex with more than one unknown or as simple as a number.

An Equation in algebra is two expressions with an “equal” symbol between them. Examples are


So let’s look at creating expressions. In what follows, I am going to write an english phrase and follow that with the equivalent algebraic expression.

Double a number: 2x

One more than a number: x + 1

Half of a number: x/2

Seven less than triple a number: 3x -7

Take 5 more than a number then double it: 2(x + 5)

Other letters can be used to show an unknown number, but x is mostly used. Sometimes more that one unknown is needed:

Cost of 3 pears that cost each: 3p

Cost of 7 apples that cost a each: 7a

Total cost of the above fruit: 3p + 7a

The individual price 3 people pay at a restaurant if they split the bill: C/3

The total number of pencils in a classroom if each girl has 3 pencils and each boy has 2: 3g + 2b

It is usually a good practice to break down a word problem and write down the expressions first before generating an equation.

Let’s look at creating equations in my next post.