Writing Algebraic Expressions

If you want to translate simple problems into algebra, you make use of algebraic expressions. Yes, these expressions can be used to combine variable, constants and even symbols. But remember, algebraic expressions won’t contain an equals sign in it.

Usually in algebra, you will be asked about changing words and phrases into a language that is understood in mathematics. So that is where algebraic expressions help you in translating words into a simple expression.

To make things simple, just imagine what comes into your mind first when you hear the word “sum”. Obviously, the symbol “+” is the one that comes into your mind as you need to add any given numbers. So, when we say that the “sum of 25 and x”, it means it refers to nothing but the addition of both numbers. But as we learnt that since they are not like terms, we cannot make it any simpler, but just represent it in an algebraic expression of 25 + x.

Let’s look at some phrases that involves addition:

  • Write 6 plus a as an algebraic expression

= 6 + a

  • Write an algebraic expression that means “add 5 and x”

= 5 + x

  • Write an algebraic expression for 15 increased by a number x

= 15 + x

Let’s look at some phrases that involve subtraction:

In expressions that involve additions, we can change the order in any way you want, but when it comes to expressions that involve subtraction, you cannot change the order. Say for example, 2+4 is always equal to 4+2, but remember 4-2 is not equal to 2-4 as both provide different results. Hence in expression involving subtraction, you need to have the order provided as is.

  • Write an algebraic expression for “10 less than a number y”

= y – 10

  • Write an algebraic expression to represent the phrase “7 minus X”

= 7 – X

  • How can you express the expression “two times the difference between b and seven?”

= 2 (b -7)

  • Fifteen less than twice a number

2x – 15

  • Three times a number, increased by seventeen

3x + 17

  • The product of nine and a number, decreased by six

9x – 6

Always remember that whenever you hear the terms less, decrease, minus, difference or diminished, then it is an expression that involves subtraction. Even though it is a little bit more difficult when compared with addition, with practice you can improve quite easily.

Example 1: A company is celebrating its ten years anniversary function and as a token of appreciation decides to reward its employees with a bonus amount. So how will you represent if the company decides to give a total of $1000 to its employees and how much each employee will get as a bonus amount?

In order to simplify this expression and write it as an algebraic expression, let’s first make use of a variable to represent the number of employees in the company. Since there is no detail about the actual number, we’ll just use the variable X and the amount every employee in the company as a bonus amount can be represented as:

= 1000 / X

Example 2: An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.

Let x represent the number of hours the electrician works in one day.

  • $45 per hour is the rate. So, if he works for 8 hours, it is 45 * 8. This can be expressed as 45x.
  • Is he spends 20 dollars on gasoline each day, he is taking away from his amount, so he is subtracting.

The electrician’s earnings can be represented by the following algebraic expression:

Solution: 45x – 20