Chapter 1

Perform the following operations with real numbers. $$(-56) \div(-4)$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The rational numbers

Simplify the algebraic expressions in Problems \(1-14\) by combining similar terms. $$8 x y^{2}-5 x^{2} y+2 x y^{2}+7 x^{2} y$$

State the property that justifies each of the statements. For example, \(3+(-4)=(-4)+3\) because of the commutative property of addition. $$\left(\frac{3}{4}\right)\left(\frac{4}{3}\right)=1$$

Perform the following operations with real numbers. $$(-81) \div(-3)$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The integers

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(x+2)+5(x+3)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$36+(-14)+(-12)+21+(-9)-4$$

Perform the following operations with real numbers. $$\frac{-112}{16}$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The nonnegative integers

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$5(x-1)+7(x+4)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$-37+42+18+37+(-42)-6$$

Perform the following operations with real numbers. $$\frac{-75}{5}$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The irrational numbers

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-2(a-4)-3(a+2)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$[83+(-99)]+18$$

Perform the following operations with real numbers. $$-2 \frac{3}{8}+5 \frac{7}{8}$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The real numbers

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-7(a+1)-9(a+4)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$[63+(-87)]+(-64)$$

Perform the following operations with real numbers. $$-1 \frac{1}{5}+3 \frac{4}{5}$$

From the list \(0,14, \frac{2}{3}, \pi, \sqrt{7},-\frac{11}{14}\), \(2.34,3.2 \overline{1}, \frac{55}{8},-\sqrt{17},-19\), and \(-2.6\), identify each of the following. The nonpositive integers

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3\left(n^{2}+1\right)-8\left(n^{2}-1\right)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$(25)(-13)(4)$$

Perform the following operations with real numbers. $$4 \frac{1}{3}-\left(-1 \frac{1}{6}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(R\)_____ \(N\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$4\left(n^{2}+3\right)+\left(n^{2}-7\right)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$(14)(25)(-13)(4)$$

Perform the following operations with real numbers. $$1 \frac{1}{12}-\left(-5 \frac{3}{4}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(N\)_____ \(R\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-6\left(x^{2}-5\right)-\left(x^{2}-2\right)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$17(97)+17(3)$$

Perform the following operations with real numbers. $$\left(-\frac{1}{3}\right)\left(\frac{2}{5}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(I\)_____ \(Q\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(x+y)-2(x-y)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$-86[49+(-48)]$$

Perform the following operations with real numbers. $$(-8)\left(\frac{1}{3}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(N\)_____ \(I\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$5(2 x+1)+4(3 x-2)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$14-12-21-14+17-18+19-32$$

Perform the following operations with real numbers. $$\frac{1}{2} \div\left(-\frac{1}{8}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(Q\)_____ \(H\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$5(3 x-1)+6(2 x+3)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$16-14-13-18+19+14-17+21$$

Perform the following operations with real numbers. $$\frac{2}{3} \div\left(-\frac{1}{6}\right)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(H\)_____ \(Q\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(2 x-5)-4(5 x-2)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$(-50)(15)(-2)-(-4)(17)(25)$$

Perform the following operations with real numbers. $$0 \div(-14)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(N\)_____ \(W\)