Chapter 2

Perform the operations as indicated, and express answers in lowest terms. $$\left(-\frac{4}{3}\right) \div\left(\frac{4}{5}\right)\left(\frac{3}{5}\right)$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(\frac{3}{5} y-\frac{2}{3} y-\frac{7}{15} y \quad\) for \(y=-\frac{5}{2} \quad \frac{4}{3}\)

Simplify each numerical expressio: and express your answers in reduced form. $$4-\frac{2}{3} \cdot \frac{3}{5}-6$$

. The length of a side of a square is \(s\) yards. What is the area of the square in square feet?

For Problems \(65-74\), reduce each fraction to simplest form. $$ \frac{-24 a b c^{2}}{32 b c} $$

Perform the operations as indicated, and express answers in lowest terms. $$\left(\frac{4}{9}\right)\left(-\frac{9}{8}\right) \div\left(-\frac{3}{4}\right)$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(\frac{1}{2} x+\frac{2}{3} x-\frac{3}{4} x \quad\) for \(x=\frac{7}{8}\)

Simplify each numerical expressio: and express your answers in reduced form. $$3+\frac{1}{2} \cdot \frac{1}{3}-2$$

The length of a side of a square is \(y\) centimeters. What is the area of the square in square millimeters?

For Problems \(65-74\), reduce each fraction to simplest form. $$ \frac{4 a^{2} c^{3}}{-22 b^{2} c^{4}} $$

Perform the operations as indicated, and express answers in lowest terms. $$\left(-\frac{7}{8}\right)\left(\frac{4}{7}\right) \div\left(-\frac{3}{2}\right)$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(-x-2 y+4 z\) for \(x=1.7, y=-2.3\), and \(z=3.6\)

Simplify each numerical expressio: and express your answers in reduced form. $$\frac{4}{5}-\frac{10}{12}-\frac{5}{6} \div \frac{14}{8}+\frac{10}{21}$$

What does the phrase "translating from English to algebra" mean to you?

For Problems \(65-74\), reduce each fraction to simplest form. $$ \frac{-5 x^{4} y^{3}}{-20 x^{2} y} $$

Perform the operations as indicated, and express answers in lowest terms. $$\left(\frac{5}{2}\right)\left(\frac{2}{3}\right) \div\left(-\frac{1}{4}\right) \div(-3)$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(-2 x+y-5 z\) for \(x=-2.9, y=7.4\), and \(z=-6.7\)

Simplify each numerical expressio: and express your answers in reduced form. $$\frac{3}{4} \div \frac{6}{5}+\frac{8}{12} \cdot \frac{6}{9}-\frac{5}{12}$$

For Problems \(65-74\), reduce each fraction to simplest form. $$ \frac{-32 x y^{2} z^{4}}{-48 x^{3} y^{3} z} $$

Perform the operations as indicated, and express answers in lowest terms. $$\frac{1}{3} \div\left(\frac{3}{4}\right)\left(\frac{1}{2}\right) \div 2$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(5 x-7 y\) for \(x=-7.8\) and \(y=8.4\)

Simplify each numerical expressio: and express your answers in reduced form. $$24\left(\frac{3}{4}-\frac{1}{6}\right)$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \left(\frac{7 x^{2}}{9 y}\right)\left(\frac{12 y}{21 x}\right) $$

Solve the word problems. Maria's department has \(\frac{3}{4}\) of all of the accounts within the \(\mathrm{ABC}\) Advertising Agency. Maria is personally responsible for \(\frac{1}{3}\) of all accounts in her department. For what portion of all of the accounts at \(\mathrm{ABC}\) is Maria personally responsible?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(8 x-9 y\) for \(x=-4.3\) and \(y=5.2\)

Simplify each numerical expressio: and express your answers in reduced form. $$18\left(\frac{2}{3}+\frac{1}{9}\right)$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \left(\frac{3 x}{8 y^{2}}\right)\left(\frac{14 x y}{9 y}\right) $$

Solve the word problems. Pablo has a board that is \(4 \frac{1}{2}\) feet long, and he wants to cut it into three pieces of the same length (see Figure 2.1). Find the length of each of the three pieces.

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(0.7 x+0.6 y \quad\) for \(x=-2\) and \(y=6\)

Simplify each numerical expressio: and express your answers in reduced form. $$64\left(\frac{3}{16}+\frac{5}{8}-\frac{1}{4}+\frac{1}{2}\right)$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \left(\frac{5 c}{a^{2} b^{2}}\right) \div\left(\frac{12 c}{a b}\right) $$

Solve the word problems. A recipe for a birthday cake calls for \(\frac{3}{4}\) cup of sugar. How much sugar is needed to make 3 cakes?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(0.8 x+2.1 y\) for \(x=5\) and \(y=-9\)

Simplify each numerical expressio: and express your answers in reduced form. $$48\left(\frac{5}{12}-\frac{1}{6}+\frac{3}{8}\right)$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \left(\frac{13 a b^{2}}{12 c}\right) \div\left(\frac{26 b}{14 c}\right) $$

Solve the word problems. Jonas left an estate valued at \(\$ 750,000\). His will states that three- fourths of the estate is to be divided equally among his three children. How much should each receive?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(1.2 x+2.3 x-1.4 x-7.6 x\) for \(x=-2.5\)

Simplify each numerical expressio: and express your answers in reduced form. $$\frac{7}{13}\left(\frac{2}{3}-\frac{1}{6}\right)$$

Solve the word problems. One of Arlene's recipes calls for \(3 \frac{1}{2}\) cups of milk. If she wants to make one-half of the recipe, how much milk should she use?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(3.4 x-1.9 x+5.2 x\) for \(x=0.3\)

Simplify each numerical expressio: and express your answers in reduced form. $$\frac{5}{9}\left(\frac{1}{2}+\frac{1}{4}\right)$$

Solve the word problems. The total length of the four sides of a square is \(8 \frac{2}{3}\) yards. How long is each side of the square?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(-3 a-1+7 a-2\) for \(a=0.9\)

Simplify each algebraic expression by combinang similar terms. $$\frac{1}{3} x+\frac{2}{5} x$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \frac{5}{x^{4}}-\frac{7}{x^{2}} $$

Solve the word problems. If it takes \(3 \frac{1}{4}\) yards of material to make one dress, how much material is needed for 20 dresses?

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(5 x-2+6 x+4\) for \(x=-1.1\)

Simplify each algebraic expression by combinang similar terms. $$\frac{1}{4} x+\frac{2}{3} x$$

For Problems \(75-92\), perform the indicated operations and express your answers in reduced form. $$ \frac{9}{x}-\frac{11}{x^{3}} $$

Tanya bought 400 shares of one stock at \(\$ 14.78\) per share, and 250 shares of another stock at \(\$ 16.36\) per share. How much did she pay for the 650 shares?