Chapter 1

Answer the question with an algebraic expression. The sum of two numbers is 65 , and one of the numbers is \(x\). What is the other number?

Simplify each numerical expression. $$-9.3-(10.4+12.8)$$

Answer the question with an algebraic expression. The difference of two numbers is 47 , and the smaller number is \(n\). What is the other number?

Simplify each numerical expression. $$3(2.1)-4(3.2)-2(-1.6)$$

Answer the question with an algebraic expression. The product of two numbers is 98 , and one of the numbers is \(n\). What is the other number?

Simplify each numerical expression. $$5(-1.6)-3(2.7)+5(6.6)$$

Answer the question with an algebraic expression. The quotient of two numbers is 8 , and the smaller number is \(y\). What is the other number?

Simplify each numerical expression. $$7(6.2-7.1)-6(-1.4-2.9)$$

Answer the question with an algebraic expression. The perimeter of a square is \(c\) centimeters. How long is each side of the square?

Simplify each numerical expression. $$-3(2.2-4.5)-2(1.9+4.5)$$

Answer the question with an algebraic expression. The perimeter of a square is \(m\) meters. How long, in centimeters, is each side of the square?

Simplify each numerical expression. $$\frac{2}{3}-\left(\frac{3}{4}-\frac{5}{6}\right)$$

Answer the question with an algebraic expression. Jesse has \(n\) nickels, \(d\) dimes, and \(q\) quarters in his bank. How much money, in cents, does he have in his bank?

Simplify each numerical expression. $$-\frac{1}{2}-\left(\frac{3}{8}+\frac{1}{4}\right)$$

Answer the question with an algebraic expression. Tina has \(c\) cents, which is all in quarters. How many quarters does she have?

Simplify each numerical expression. $$3\left(\frac{1}{2}\right)+4\left(\frac{2}{3}\right)-2\left(\frac{5}{6}\right)$$

Answer the question with an algebraic expression. If \(n\) represents a whole number, what represents the next larger whole number?

Simplify each numerical expression. $$2\left(\frac{3}{8}\right)-5\left(\frac{1}{2}\right)+6\left(\frac{3}{4}\right)$$

Answer the question with an algebraic expression. If \(n\) represents an odd integer, what represents the next larger odd integer?

Answer the question with an algebraic expression. If \(n\) represents an even integer, what represents the next larger even integer?

A scuba diver was 32 feet below sea level when he noticed that his partner had his extra knife. He ascended 13 feet to meet his partner and then continued to dive down for another 50 feet. How far below sea level is the diver?

Answer the question with an algebraic expression. The cost of a 5-pound box of candy is \(c\) cents. What is the price per pound?

Jeff played 18 holes of golf on Saturday. On each of 6 holes he was 1 under par, on each of 4 holes he was 2 over par, on 1 hole he was 3 over par, on each of 2 holes he shot par, and on each of 5 holes he was 1 over par. How did he finish relative to par?

Answer the question with an algebraic expression. Larry's annual salary is \(d\) dollars. What is his monthly salary?

After dieting for 30 days, Ignacio has lost 18 pounds. What number describes his average weight change per day?

Answer the question with an algebraic expression. Mila's monthly salary is \(d\) dollars. What is her annual salary?

Michael bet \(\$ 5\) on each of the 9 races at the racetrack. His only winnings were \(\$ 28.50\) on one race. How much did he win (or lose) for the day?

Answer the question with an algebraic expression. The perimeter of a square is \(i\) inches. What is the perimeter expressed in feet?

Max bought a piece of trim molding that measured \(11 \frac{3}{8}\) feet in length. Because of defects in the wood, he had to trim \(1 \frac{5}{8}\) feet off one end, and he also had to remove \(\frac{3}{4}\) of a foot off the other end. How long was the piece of molding after he trimmed the ends?

Answer the question with an algebraic expression. The perimeter of a rectangle is \(y\) yards and \(f\) feet. What is the perimeter expressed in feet?

Natasha recorded the daily gains or losses for her company stock for a week. On Monday it gained \(1.25\) dollars; on Tuesday it gained \(0.88\) dollars; on Wednesday it lost \(0.50\) dollars; on Thursday it lost \(1.13\) dollars; on Friday it gained \(0.38\) dollars. What was the net gain (or loss) for the week?

Answer the question with an algebraic expression. The length of a line segment is \(d\) decimeters. How long is the line segment expressed in meters?

On a summer day in Florida, the afternoon temperature was \(96^{\circ} \mathrm{F}\). After a thunderstorm, the temperature dropped \(8^{\circ} \mathrm{F}\). What would be the temperature if the sun came back out and the temperature rose \(5^{\circ} \mathrm{F}\) ?

Answer the question with an algebraic expression. The distance between two cities is \(m\) miles. How far is this, expressed in feet?

In an attempt to lighten a dragster, the racing team exchanged two rear wheels for wheels that each weighed \(15.6\) pounds less. They also exchanged the crankshaft for one that weighed \(4.8\) pounds less. They changed the rear axle for one that weighed \(23.7\) pounds less but had to add an additional roll bar that weighed \(10.6\) pounds. If they wanted to lighten the dragster by 50 pounds, did they meet their goal?

A large corporation has five divisions. Two of the divisions had earnings of \(\$ 2,300,000\) each. The other three divisions had a loss of \(\$ 1,450,000\), a loss of \(\$ 640,000\), and a gain of \(\$ 1,850,000\), respectively. What was the net gain (or loss) of the corporation for the year?

Explain the difference between simplifying a numerical expression and evaluating an algebraic expression.

Explain why \(\frac{0}{8}=0\), but \(\frac{8}{0}\) is undefined.

How would you help someone who is having difficulty expressing \(n\) nickels and \(d\) dimes in terms of cents?

The following simplification problem is incorrect. The answer should be \(-11\). Find and correct the error. $$ \begin{aligned} 8 \div(-4)(2)-3(4) \div 2+(-1) &=(-2)(2)-12 \div 1 \\ &=-4-12 \\ &=-16 \end{aligned} $$

When asked to write an algebraic expression for "8 more than a number," you wrote \(x+8\) and another student wrote \(8+x\). Are both expressions correct? Explain your answer.

When asked to write an algebraic expression for "6 less than a number," you wrote \(x-6\) and another student wrote \(6-x\). Are both expressions correct? Explain your answer.