Math Homework. Do It Faster, Learn It Better.

Word Problems: Equivalent Expressions

Sometimes, we need to translate a statement of equivalence back and forth between words and symbols.

For example, "Cubing a number and then dividing the result by 8 is the same as dividing the number by 2 and then finding its cube."

Let’s translate this into math symbols. “Cubing a number” means multiplying it 3 times, or

x x x = x 3

Now divide this by 8 :

x 3 8

On the other side, start by dividing x by 2 , and then cube the result. (Use parentheses.)

( x 2 ) 3

So the translation of the full statement becomes:

x 3 8 = ( x 2 ) 3

(In this case, you can check that the equation is true using the Power of a Quotient Property .)