Fractions & Rational Expressions — Quiz 3

Questions in this quiz (9)

1. Simplify the expression:$$\frac{\frac{2}{5} + \frac{1}{3}}{\frac{3}{4} - \frac{1}{2}} \div \frac{5}{6}$$

   • $$\frac{44}{15}$$
   • $$\frac{88}{35}$$
   • $$\frac{88}{25}$$
   • $$\frac{22}{9}$$

2. Simplify the expression:$$\frac{\left( \frac{1}{x} - \frac{1}{y} \right)}{\left( \frac{1}{x} + \frac{1}{y} \right)}$$

   • $$\frac{2y + x}{y + x}$$
   • $$\frac{y - x}{y + x}$$
   • $$\frac{y - x}{y}$$
   • $$\frac{- x}{y + x}$$

3. Simplify the expression:$$\frac{\frac{7}{4} - \frac{2}{3}}{\frac{7}{4} - \frac{2}{3} - \frac{1}{2}} \div \left( \frac{7}{4} - \frac{2}{3} - \frac{1}{2} \right)$$

   • $$\frac{56}{49}$$
   • $$\frac{156}{49}$$
   • $$\frac{21}{13}$$
   • $$\frac{49}{52}$$

4. A cake is divided into 10 portions. Each portion is then cut into half, creating two equal slices per portion. If Mia eats 5 of these slices, what fraction of the whole cake does she eat?

   • $$\frac{1}{8}$$
   • $$\frac{1}{2}$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{10}$$

5. Emily used a coupon to buy a jacket for $$C$$ dollars less than the retail price of $$P$$. The discounted price that Emily paid represents what fraction of the retail price of the jacket?

   • $$\frac{C}{P}$$
   • $$\frac{P}{C}$$
   • $$\frac{P-C}{C}$$
   • $$\frac{P-C}{P}$$

6. If a mixed fraction is denoted by $$X\frac{3}{4}=\frac{9}{4}$$, then what is the value of: $$\frac{1}{3X-4}$$?

   • $$\frac{3}{4}$$
   • $$2$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$

7. What is the value of $$(m - 3)^3$$ if $$m = \left(\frac{5}{3} + \frac{5}{6} + \frac{1}{2}\right)$$?

   • $$\frac{100}{7}$$
   • $$\frac{27}{6}$$
   • $$\frac{1000}{27}$$
   • $$0$$

8. If $$N = \frac{S}{\frac{p}{q} - 1}$$, then express $$q$$ in terms of $$N, S, p$$.

   • $$\frac{NS}{p + N}$$
   • $$\frac{Np}{S + N}$$
   • $$\frac{NS}{p + s}$$
   • $$\frac{pS}{2N}$$

9. If $$p = \frac{1 + \frac{x}{y}}{1 + \frac{xy}{z^2}}$$, $$x = \frac{z}{2}$$ and $$y = 3z$$, find the value of $$p$$.

   • $$\frac{3}{2}$$
   • $$\frac{3}{5}$$
   • $$\frac{7}{6}$$
   • $$\frac{7}{15}$$