Close this window

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

Now divide this by 8:

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

So the translation of the full statement becomes:

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