Chapter 1

Why is division by zero undefined?

Order the expressions \(|x-y|,|x|-|y|,\) and \(|x+y|\) from least to greatest for \(x=-6\) and \(y=-8\)

Explain how to simplify an algebraic expression in which a negative sign precedes parentheses.

Determine whether 2 is a solution of \(13 x+3=3(5 x-1)\)

Explain how to convert a mixed number to an improper fraction and give an example.

Determine whether 2 is a solution of \(13 x+3=3(5 x-1)\) Simplify: \(5(3 x+2 y)+6(5 y)\). (Section 1.4, Example 11)

Explain how to convert an improper fraction to a mixed number and give an example.

Give an example of an integer that is not a natural number.

Describe the difference between a prime number and a composite number.

Find this sum, indicated by a question mark. \(4(-3)=(-3)+(-3)+(-3)+(-3)=?\)

What is meant by the prime factorization of a composite number?

In Exercises \(135-138\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Both the addition and the multiplication of two negative numbers result in a positive number.

Find this sum, indicated by a question mark. \(3(-3)=(-3)+(-3)+(-3)=?\)

What is the Fundamental Principle of Fractions?

In Exercises \(135-138\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Multiplying a negative number by a non negative number will always give a negative number.

Find this sum, indicated by a question mark. $$3(-3)=(-3)+(-3)+(-3)=?$$ \(\begin{aligned} 2(-3) &=-6 \\ 1(-3) &=-3 \\ 0(-3) &=0 \\\\-1(-3) &=3 \\\\-2(-3) &=6 \\\\-3(-3) &=9 \\\\-4(-3) &=? \end{aligned}\)

Explain how to reduce a fraction to its lowest terms. Give an example with your explanation.

Explain how to multiply fractions and give an example.

Explain how to divide fractions and give an example.

In Exercises \(139-142\), write an algebraic expression for the given English phrase. The value, in cents, of \(x\) nickels

Describe how to add or subtract fractions with identical denominators. Provide an example with your description.

In Exercises \(139-142\), write an algebraic expression for the given English phrase. The distance covered by a car traveling at 50 miles per hour for \(x\) hours

Explain how to add fractions with different denominators. Use \(\frac{5}{6}+\frac{1}{2}\) as an example.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I find it easier to multiply \(\frac{1}{5}\) and \(\frac{3}{4}\) than to add them.

In Exercises \(139-142\), write an algebraic expression for the given English phrase. The fraction of people in a room who are women if there are 40 women and \(x\) men in the room

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Fractions frustrated me in arithmetic, so I'm glad I won't have to use them in algebra.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I need to be able to perform operations with fractions to determine whether \(\frac{3}{2}\) is a solution of \(8 x=12\left(x-\frac{1}{2}\right)\).

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I saved money by buying a computer for \(\frac{3}{2}\) of its original price.

Simplify using a calculator: $$ 0.3(4.7 x-5.9)-0.07(3.8 x-61) $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{1}{2}+\frac{1}{5}=\frac{2}{7}$$

Use your calculator to attempt to find the quotient of \(-3\) and \(0 .\) Describe what happens. Does the same thing occur when finding the quotient of 0 and \(-3 ?\) Explain the difference. Finally, what happens when you enter the quotient of \(\overline{0 \text { and itself? }}\)

In Exercises \(147-149,\) perform the indicated operation. $$(-6)^{2}=(-6)(-6)=?$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every fraction has infinitely many equivalent fractions.

In Exercises \(147-149,\) perform the indicated operation. \(-6-(-3)\) (Section \(1.6,\) Example 1 )

In Exercises \(147-149,\) perform the indicated operation. \(-6+(-3)\) (Section \(1.7,\) Example 4 )

Exercises \(150-152\) will help you prepare for the material covered in the next section. In each exercise, an expression with an exponent is written as a repeated multiplication. Find this product, indicated by a question mark. $$(-6)^{2}=(-6)(-6)=?$$

Exercises \(150-152\) will help you prepare for the material covered in the next section. In each exercise, an expression with an exponent is written as a repeated multiplication. Find this product, indicated by a question mark. $$(-5)^{3}=(-5)(-5)(-5)=?$$

Exercises \(150-152\) will help you prepare for the material covered in the next section. In each exercise, an expression with an exponent is written as a repeated multiplication. Find this product, indicated by a question mark. $$(-2)^{4}=(-2)(-2)(-2)(-2)=?$$