Decoding Word Problems

I’m facing a word problem, and it is not telling me which operations to use.  What is the equation I should use in this situation?

Word problems sometimes rely on you to use certain equations without explicitly giving them to you or stating their names.  Most of the time, these equations involve finding the Perimeter or Area of a shape, but there are a few others as well.

Perimeter of a Rectangle

P = 2l + 2w      or         P = 2(l + w)

Perimeter equals two times the length, plus two times the width


Perimeter equals two times the sum of the length and the width

·         P: the total perimeter; the distance around the edges of the shape

·         l: the length of the rectangle; the left-to-right measurement of the shape

·         w: the width of the rectangle; the top-to-bottom measurement of the shape

Circumference of a Circle

C = 2πr            or         C = Dπ

Circumference equals two times pi times the radius


Circumference equals the diameter times pi

·         C: circumference; the distance around the outside of the circle

·         D: the diameter of the circle; the distance from one side of the circle to the other, passing through the center

·         r: the radius of the circle; the distance from the center of the circle to the edge

·         π: “pi” – a constant value, approximately 3.14159

Area of a Rectangle

A = lw

Area equals length times width

Area of a Triangle

A =           or        

Area equals one half of the base times the height

·         b: the base of the triangle; the measurement of the horizontal side of the triangle.

·         h: the height of the triangle; the measurement of the distance from the base to the opposite corner

Area of a Circle

A = πr2

The Area equals pi times the square of the radius

Distance Traveled

d = rt

Distance equals Rate times Time

·         d: the total distance traveled

·         r: the rate of travel; the average speed

·         t: the time; how long the object has been traveling

How can I convert one set of units to another?

Temperature Conversion: Fahrenheit to Celsius

·         C: the temperature in Celsius

·         F: the temperature in Fahrenheit

Length/Distance Conversions

12 inches = 1 foot                                           10 millimeters = 1 centimeter

3 feet = 1 yard                                                1 meter = 100 centimeters = 1000 millimeters

1 mile = 5280 feet = 1760 yards                     1 kilometer = 1000 meters

Time Conversions

60 seconds = 1 minute                                    7 days = 1 week

60 minutes = 1 hour                                        about 52 weeks = 1 year

24 hours = 1 day                                             365 days = 1 year

Common Key Phrases in Word Problems

These are some of the most common uses of English to describe Mathematical operations.

English                                                                        Mathematical Meaning

what                                                                            variables; x, y, etc.

is                                                                                  equals; =

sum, more than                                                            addition; +

difference, less than                                                    subtraction; –

product, times, of                                                        multiplication

quotient, divided by                                                   division

ratio of (this) to (that)                                     

(this) is directly proportional to (that)             y = kx              or        

(this) is inversely proportional to (that)                                     or         k = xy