Chapter 1

In the following exercises, simplify each expression. $$ 8-|2-4(4-1)+3| $$

In the following exercises, simplify each expression. $$ 7-|5-3(4-1)-6| $$

In the following exercises, simplify each expression. $$ 9-3|2(2-6)-(3-7)| $$

In the following exercises, simplify each expression. $$ 5-2|2(1-4)-(2-5)| $$

In the following exercises, simplify each expression. $$ (-3)^{2}-24 \div(8-2) $$

In the following exercises, simplify each expression. $$ (-4)^{2}-32 \div(12-4) $$

In the following exercises, evaluate each expression. \(y+(-14)\) when (a) \(y=-33\) (b) \(y=30\)

In the following exercises, evaluate each expression. \(x+(-21)\) when (a) \(x=-27\) (b) \(x=44\)

In the following exercises, evaluate each expression. \((x+y)^{2}\) when \(x=-3, y=14\)

In the following exercises, evaluate each expression. \((y+z)^{2}\) when \(y=-3, z=15\)

In the following exercises, evaluate each expression. \(9 a-2 b-8\) when \(a=-6\) and \(b=-3\)

In the following exercises, evaluate each expression. \(7 m-4 n-2\) when \(m=-4\) and \(n=-9\)

In the following exercises, evaluate each expression. \(3 x^{2}-4 x y+2 y^{2}\) when \(x=-2, y=-3\)

In the following exercises, evaluate each expression. \(4 x^{2}-x y+3 y^{2}\) when \(x=-3, y=-2\)

In the following exercises, translate to an algebraic expression and simplify if possible. the sum of 3 and -15 , increased by 7

In the following exercises, translate to an algebraic expression and simplify if possible. the sum of -8 and -9 , increased by 23

In the following exercises, translate to an algebraic expression and simplify if possible. (a) the difference of 10 and -18 (b) subtract 11 from -25

In the following exercises, translate to an algebraic expression and simplify if possible. (a) the difference of -5 and -30 (b) subtract -6 from -13

In the following exercises, translate to an algebraic expression and simplify if possible. the quotient of -6 and the sum of \(a\) and \(b\)

In the following exercises, translate to an algebraic expression and simplify if possible. the product of -13 and the difference of \(c\) and \(d\)

In the following exercises, solve. Temperature On January 15 , the high temperature in Anaheim, California, was \(84^{\circ} .\) That same day, the high temperature in Embarrass, Minnesota, was \(-12^{\circ} .\) What was the difference between the temperature in Anaheim and the temperature in Embarrass?

In the following exercises, solve. Temperature On January 21, the high temperature in Palm Springs, California, was \(89^{\circ}\), and the high temperature in Whitefield, New Hampshire, was \(-31^{\circ}\). What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

In the following exercises, solve. Football On the first down, the Chargers had the ball on their 25 -yard line. They lost 6 yards on the firstdown play, gained 10 yards on the second-down play, and lost 8 yards on the third-down play. What was the yard line at the end of the third-down play?

In the following exercises, solve. Football On first down, the Steelers had the ball on their 30 -yard line. They gained 9 yards on the firstdown play, lost 14 yards on the second-down play, and lost 2 yards on the third-down play. What was the yard line at the end of the third-down play?

In the following exercises, solve. Checking Account Mayra has \(\$ 124\) in her checking account. She writes a check for \(\$ 152 .\) What is the new balance in her checking account?

In the following exercises, solve. Checking Account Reymonte has a balance of -\$49 in his checking account. He deposits \(\$ 281\) to the account. What is the new balance?

Explain why the sum of -8 and 2 is negative, but the sum of 8 and -2 is positive.

In your own words, state the rules for multiplying and dividing integers.

In the following exercises, simplify. $$ -\frac{108}{63} $$

In the following exercises, simplify. $$ -\frac{104}{48} $$

In the following exercises, simplify. $$ \frac{182}{294} $$

In the following exercises, simplify. $$ \frac{14 x^{2}}{21 y} $$

In the following exercises, simplify. $$ \frac{24 a}{32 b^{2}} $$

In the following exercises, simplify. $$ -\frac{210 a^{2}}{110 b^{2}} $$

In the following exercises, simplify. $$ -\frac{30 x^{2}}{105 y^{2}} $$

In the following exercises, perform the indicated operation. $$ -\frac{3}{4}\left(-\frac{4}{9}\right) $$

In the following exercises, perform the indicated operation. $$ -\frac{3}{8} \cdot \frac{4}{15} $$

In the following exercises, perform the indicated operation. $$ \left(-\frac{14}{15}\right)\left(\frac{9}{20}\right) $$

In the following exercises, perform the indicated operation. $$ \left(-\frac{9}{10}\right)\left(\frac{25}{33}\right) $$

In the following exercises, perform the indicated operation. $$ \left(-\frac{63}{84}\right)\left(-\frac{44}{90}\right) $$

In the following exercises, perform the indicated operation. $$ \left(-\frac{33}{60}\right)\left(-\frac{40}{88}\right) $$

In the following exercises, perform the indicated operation. $$ \frac{3}{7} \cdot 21 n $$

In the following exercises, perform the indicated operation. $$ \frac{5}{6} \cdot 30 m $$

In the following exercises, perform the indicated operation. $$ \frac{3}{4} \div \frac{x}{11} $$

In the following exercises, perform the indicated operation. $$ \frac{2}{5} \div \frac{y}{9} $$

In the following exercises, perform the indicated operation. $$ \frac{5}{18} \div\left(-\frac{15}{24}\right) $$

In the following exercises, perform the indicated operation. $$ \frac{7}{18} \div\left(-\frac{14}{27}\right) $$

In the following exercises, perform the indicated operation. $$ \frac{8 u}{15} \div \frac{12 y}{25} $$

In the following exercises, perform the indicated operation. $$ \frac{12 r}{25} \div \frac{18 s}{35} $$

In the following exercises, perform the indicated operation. $$ \frac{3}{4} \div(-12) $$