Chapter 11

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(2 x+\frac{x}{3}=28\)

Multiply and reduce. Do some by calculator. $$\frac{1}{3} \times \frac{2}{5}$$

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{3}{5}+\frac{2}{5}$$

Simplify. Leave your answers as improper fractions. $$\frac{\frac{2}{3}+\frac{3}{4}}{\frac{1}{5}}$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{12}{x}$$

Factor completely.$$4-x^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}-10 x+21$$

Multiply and reduce. Do some by calculator. $$\frac{3}{7} \times \frac{21}{24}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(4 x+\frac{x}{5}=42\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{1}{8}-\frac{3}{8}$$

Simplify. Leave your answers as improper fractions. $$\frac{\frac{3}{4}-\frac{1}{3}}{\frac{1}{2}+\frac{1}{6}}$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{x}{12}$$

Factor completely.$$x^{2}-9$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}-15 x+56$$

Multiply and reduce. Do some by calculator. $$\frac{2}{3} \times \frac{9}{7}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(x+\frac{x}{5}=24\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{2}{7}+\frac{5}{7}-\frac{6}{7}$$

Simplify. Leave your answers as improper fractions. $$\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{3-\frac{4}{5}}$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{18}{x-5}$$

Factor completely.$$9 a^{2}-x^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}-10 x+9$$

Multiply and reduce. Do some by calculator. $$\frac{11}{3} \times 7$$

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{5}{9}+\frac{7}{9}-\frac{1}{9}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{x}{6}+x=21\)

Simplify. Leave your answers as improper fractions. $$\frac{\frac{4}{5}}{\frac{1}{5}+\frac{2}{3}}$$

Factor completely.$$25-x^{2}$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{5 x}{x^{2}-49}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}+13 x+30$$

Multiply and reduce. Do some by calculator. $$\frac{2}{3} \times 3 \frac{1}{5}$$

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{1}{3}-\frac{7}{3}+\frac{11}{3}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(3 x-\frac{x}{7}=40\)

Simplify. Leave your answers as improper fractions. $$\frac{5-\frac{2}{5}}{6+\frac{1}{3}}$$

Factor completely.$$4 x^{2}-4 y^{2}$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{7}{x^{2}-3 x+2}$$

Factor completely, by hand or by calculator. Check your results. $$3 a+a^{2}-3 a^{3}$$

Multiply and reduce. Do some by calculator. $$3 \times 7 \frac{2}{5}$$

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{1}{5}-\frac{9}{5}+\frac{12}{5}-\frac{2}{5}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(x-\frac{x}{6}=25\)

Simplify. Leave your answers as improper fractions. $$\frac{1}{2}+\frac{3}{\frac{2}{5}+\frac{1}{3}}$$

Factor completely.$$9 x^{2}-y^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}+3 x+2$$

In each fraction, what values of \(x,\) if any, are not permitted? $$\frac{3 x}{8 x^{2}-14 x+3}$$

Multiply and reduce. Do some by calculator. $$3 \frac{3}{4} \times 2 \frac{1}{2}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{2 x}{3}-x=-24\)

Simplify. Leave your answers as improper fractions. $$\frac{x+\frac{y}{4}}{x-\frac{y}{3}}$$

Factor completely.$$x^{2}-9 y^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}+7 x+12$$

Simplify each fraction by manipulating the algebraic signs. $$\frac{a-b}{b-a}$$

Multiply and reduce. Do some by calculator. $$\frac{3}{5} \times \frac{2}{7} \times \frac{5}{9}$$

Solve for \(x .\) Try some by calculator. $$a^{2} x-c d=b-a x+d x$$