Chapter 1

Without using a number line, describe how to add two numbers with the same sign. Give an example.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{17}{18}-\frac{4}{9}$$

Find the value of each expression. $$-|-9-(-6)|-(-12)$$

Insert either \(<,>,\) or \(=\) in the shaded area to make a true statement. $$\frac{8}{13} \div \frac{8}{13}\square|-1|$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$7-4[3-(4 y-5)]$$

Simplify each algebraic expression. $$6 b-7 b$$

Explain how to add like terms. Give an example.

Without using a number line, describe how to add two numbers with different signs. Give an example.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{4}{3}-\frac{3}{4}$$

Find the value of each expression. $$-|-8-(-2)|-(-6)$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$6-5[8-(2 y-4)]$$

Simplify each algebraic expression. $$12 b-13 b$$

What does it mean to simplify an algebraic expression?

Write a problem that can be solved by finding the sum of at least three numbers, some positive and some negative. Then explain how to solve the problem.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{2}-\frac{2}{3}$$

Find the value of each expression. $$\frac{5}{8}-\left(\frac{1}{2}-\frac{3}{4}\right)$$

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Shoe sizes of students on campus

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$2\left(3 x^{2}-5\right)-\left[4\left(2 x^{2}-1\right)+3\right]$$

Simplify each algebraic expression. $$-y+4 y$$

An algebra student incorrectly used the distributive property and wrote \(3(5 x+7)=15 x+7 .\) If you were that student's teacher, what would you say to help the student avoid this kind of error?

Without a calculator, you can add numbers using a number line, using absolute value, or using gains and losses. Which method do you find most helpful? Why is this so?

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{10}-\frac{3}{16}$$

Find the value of each expression. $$\frac{9}{10}-\left(\frac{1}{4}-\frac{7}{10}\right)$$

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Recorded heights of students on campus

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$4\left(6 x^{2}-3\right)-\left[2\left(5 x^{2}-1\right)+1\right]$$

Simplify each algebraic expression. $$-y+9 y$$

You can transpose the letters in the word "conversation" to form the phrase "voices rant on." From "total abstainers" we can form "sit not at ale bars." What two algebraic properties do each of these transpositions (called anagrams) remind you of? Explain your answer.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. It takes me too much time to add real numbers with a number line.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{30}-\frac{5}{24}$$

Find the value of each expression. $$|-9-(-3+7)|-|-17-(-2)|$$

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Temperatures in weather reports

In Exercises \(89-92,\) express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Cube \(-2 .\) Subtract this exponential expression from \(-10\)

Simplify each algebraic expression. $$-4(2 x-3)$$

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is a variable?

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{3}{4}-2 \frac{1}{3}$$

Find the value of each expression. $$|24-(-16)|-|-51-(-31+2)|$$

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Class sizes of algebra courses

In Exercises \(89-92,\) express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Cube \(-5 .\) Subtract this exponential expression from \(-100 .\)

Simplify each algebraic expression. $$-3(4 x-5)$$

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is an algebraic expression?

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{2}{3}-2 \frac{1}{2}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 6 times a number and \(-5\) times the number.

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Values of \(d\) given by the formula \(d=\sqrt{1.5 h},\) where \(d\) is the distance, in miles, that you can see to the horizon from a height of \(h\) feet

In Exercises \(89-92,\) express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Subtract 10 from \(7 .\) Multiply this difference by \(2 .\) Square this product.

Simplify each algebraic expression. $$-3(-2 x+4)$$

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. Explain how to evaluate \(2+5 x\) for \(x=3\)

Determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. I did not use the distributive property to simplify \(3(2 x+5 x)\)

Determine whether the given number is a solution of the equation. $$\frac{7}{2} x=28 ; 8$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 9 times a number and \(-4\) times the number.

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Values of \(C\) given by the formula \(C=2 \pi r,\) where \(C\) is the circumference of a circle with radius \(r\)