Before solving word problems, which are equations, we should get comfortable with algebraic expressions. The difference between the two, remember, is that an equation has an equals sign, while an expression does not.

Equation: 3x + 4y = 13

Expression: 3x + 4y

So you might think of an expression as a piece of an equation.

To convert phrases to expressions, you'll need to understand a few simple rules. Certain phrases or words indicate specific operations. The operations are listed below, with common phrases used to represent them.

Addition: Sum, total, more than, in all, altogether, combined, plus

Subtraction: Decreased by, minus, takeaway, less than*, fewer than*

Multiplication: Times, product, increased by (often used with percents), of (often used with fractions, as in "half of"), twice, tripled, quadrupled, etc.

Division: Per, ratio, quotient, divided by

This is not a comprehensive list, but it's enough to get started with simple expressions!

* Watch out for "less than" and "fewer than" - if you see the phrase "5 less than x", a common mistake is to write "5 - x", but it's actually "x - 5"! If you forget this rule, try remembering what happens if there's no x in the problem. If I said, "What's 5 less than 7," you wouldn't say 5 - 7 = -2!

Sample #1

Write the following as an algebraic expression: four more than x

Solution #1

4 + x

Sample #2

Write the following as an alegebraic expression: three less than twice a number

Solution #2

2x - 3

Sample #3

If the price of a book was x dollars, and it increased by 7%, what is the new price?

Solution #3

x + 0.07x (or 1.07x)

Write each of the following as algebraic expressions. Remember that, since they are expression instead of equations, you don't need an equals sign

.

1.

The sum of x and y

2.

The product of 5 and x

3.

Ten decreased by x

4.

If Joan has x dollars, Dave has y dollars, and Sue has z dollars, how much money do they have altogether?

5.

The ratio of x to y

6.

If the temperature was 72 degrees, and it decreases by x degrees, what is the new temperature?

7.

If the population of a city was z, and it increased by 25% last year, what is the new population?

8.

A number tripled

9.

Five pens cost x dollars. What is the price per pen?

10.

Two thirds of x

11.

What is the quotient of x and z?

12.

Four times a number is decreased by 7

13.

5 less than the ratio of 4 to x

14.

Seven more than y

15.

x times y, decreased by z