## Are They Equivalent?

**Work Time**

# Are They Equivalent?

Two algebraic expressions are equivalent if they are equal for all variable values.

Decide whether each expression is equivalent to $\frac{a}{b}$. If it is, explain how you know. If it is not, give values of a and b for which the expression is *not equal* to $\frac{a}{b}$.

a) $a\cdot \frac{1}{b}$

b) $\left|\frac{a}{b}\right|$

c) $\frac{b}{a}$

d) $\frac{1}{ab}$

e) $\frac{10a}{10b}$

f) $\frac{-a}{-b}$

g) $\frac{a-1}{b-1}$

Consider the expressions in the previous problem that are

*not*equivalent to $\frac{a}{b}$. Tell whether each expression would have the same value as $\frac{a}{b}$ under certain conditions. Is so, specify those conditions.