Chapter 8

Solve the following proportions. \(\frac{12}{7}=\frac{60}{x}\)

Explain, in your own words, two ways to simplify \(\frac{\frac{2}{9}}{\frac{5}{18}}\) Then, simplify it both ways. Which method do you prefer and why?

Add or subtract, as indicated. $$\frac{8}{11}-\frac{3}{11}$$

Find the LCD of each group of rational expressions. \(\frac{5}{8}, \frac{9}{20}\)

When does a fraction or a rational expression equal \(0 ?\)

Multiply. $$\frac{7}{8} \cdot \frac{1}{3}$$

When adding or subtracting two rational expressions, do you keep the LCD throughout the problem or do you eliminate the denominators?

Solve the following proportions. \(\frac{30}{18}=\frac{45}{y}\)

Explain, in your own words, two ways to simplify \(\frac{\frac{3}{2}-\frac{1}{5}}{\frac{1}{10}+\frac{3}{5}} .\) Then, simplify it both ways. Which method do you prefer and why?

Add or subtract, as indicated. $$\frac{4}{15}+\frac{7}{15}$$

Find the LCD of each group of rational expressions. \(\frac{11}{12}, \frac{5}{16}\)

When is a fraction or a rational expression undefined?

Multiply. $$\frac{2}{5} \cdot \frac{3}{11}$$

Solve the following proportions. \(\frac{6}{13}=\frac{x}{x+56}\)

Simplify completely. $$\frac{\frac{7}{10}}{\frac{5}{4}}$$

Find the LCD of each group of rational expressions. \(\frac{17}{28}, \frac{1}{12}, \frac{8}{21}\)

Add or subtract, as indicated. $$\frac{7}{20}+\frac{9}{20}$$

Multiply. $$\frac{9}{14} \cdot \frac{7}{6}$$

How do you determine the value of the variable for which a rational expression is undefined?

Solve the following proportions. \(\frac{15}{8}=\frac{x}{x-63}\)

Simplify completely. $$\frac{\frac{3}{8}}{\frac{4}{3}}$$

Find the LCD of each group of rational expressions. \(\frac{23}{56}, \frac{9}{16}, \frac{13}{14}\)

Add or subtract, as indicated. $$\frac{11}{12}-\frac{5}{12}$$

Multiply. $$\frac{4}{15} \cdot \frac{25}{36}$$

If \(x^{2}+5\) is the numerator of a rational expression, can that expression equal zero? Give a reason.

Determine whether each is an equation or is a sum or difference of expressions. Then, solve the equation or find the sum or difference. $$\frac{2 f-19}{20}=\frac{f}{4}+\frac{2}{5}$$

Simplify completely. $$\frac{\frac{a^{2}}{b}}{\frac{a}{b^{3}}}$$

Find the LCD of each group of rational expressions. \(\frac{6}{c^{4}}, \frac{7}{c^{3}}\)

Add or subtract, as indicated. $$\frac{8}{a}+\frac{2}{a}$$

Multiply. $$\frac{22}{15 r^{2}} \cdot \frac{5 r^{4}}{2}$$

Evaluate (if possible) for a) \(x=2\) and b) \(x=-1\). $$\frac{7 x+1}{3 x-1}$$

Determine whether each is an equation or is a sum or difference of expressions. Then, solve the equation or find the sum or difference. $$\frac{2 h}{5}+\frac{2}{3}=\frac{h+3}{5}$$

Write an equation for cach and solve. The ratio of students in a history lecture who took notes in pen to those who took notes in pencil was 8 to \(3 .\) If 72 students took notes in pen, bow many took notes in pencil?

Simplify completely. $$\frac{\frac{u^{5}}{v^{2}}}{\frac{u^{2}}{v}}$$

Find the LCD of each group of rational expressions. \(\frac{4}{n^{5}}, \frac{1}{n^{9}}\)

Add or subtract, as indicated. $$\frac{3}{p}-\frac{9}{p}$$

Multiply. $$\frac{27 b^{4}}{4} \cdot \frac{3}{81 b}$$

Write an equation for cach and solve. In a gluten-free flour mixture, the ratio of potatostarch flour to tapioca flour is 2 to \(1 .\) If a mixture contains 3 more cups of potato-starch flour than tapioca flour how much of each type of flour is in the mixture?

Simplify completely. $$\frac{\frac{s^{3}}{r^{3}}}{\frac{s^{4}}{t}}$$

Find the LCD of each group of rational expressions. \(\frac{8}{9 p^{3}}, \frac{5}{12 p^{8}}\)

Add or subtract, as indicated. $$\frac{10}{3 k^{2}}-\frac{2}{3 k^{2}}$$

Multiply. $$\frac{14 u^{5}}{15 v^{2}} \cdot \frac{20 v^{6}}{7 u^{8}}$$

Evaluate (if possible) for a) \(z=-3\) and b) \(z=4\). $$\frac{(2 z)^{2}}{z^{2}+5 z+6}$$

Write an equation for cach and solve. Rosa Cruz won an electron over her opponent by a ratio of 6 to \(5 .\) If her opponent received 372 fewer votes than she did, how many votes did cach candidate receive?

Simplify completely. $$\frac{\frac{x^{4}}{y}}{\frac{x^{2}}{y^{3}}}$$

Find the LCD of each group of rational expressions. \(\frac{4}{15 r^{6}}, \frac{7}{6 r^{2}}\)

Add or subtract, as indicated. $$\frac{6}{5 c}+\frac{14}{5 c}$$

Multiply. $$\frac{15 s^{3}}{21 r^{2}} \cdot \frac{42 t^{4}}{5 s^{12}}$$

Determine whether each is an equation or is a sum or difference of expressions. Then, solve the equation or find the sum or difference. $$1+\frac{4}{c+2}=\frac{9}{c+2}$$

Write an equation for cach and solve. The ancient Greeks belicved that the rectangle most pleasing to the eye, the golden rectangle, had sides in which the ratio of its length to its width was approximately 8 to 5 . They erected many buildings using this golden ratio, including the Parthcnon. The marble Tloot of a museum foyer is to be designed as a golden rectangle. If its width is to be 18 ft less than its length, find the length and wadth of the foyer.