Chapter 1

To _____ the expression \(5(6 x)\) means to write it in simpler form: \(5(6 x)=30 x\)

Fill in the blanks. Variables and/or numbers can be combined with the operations of arithmetic to create algebraic _____.

In the exponential expression \(7^{5}, 7\) is the_____ \(\quad,\) and 5 is the____ \(.7^{5}\) is the fifth_____ \(\quad\) of seven.

Fill in the blanks. The answer to a multiplication problem is called a_____. The answer to a division problem is called a _____.

Fill in the blanks. The set of ___ numbers is \(\\{0,1,2,3,4,5, \ldots\\}.\)

Fill in the blanks. A _____ is the result of an addition. A _____ of a subtraction. A _____ is the result of a multiplication. A ____ is the result of a division.

\(5(6 x)\) and \(30 x\) are ______ expressions because for each value of \(x,\) they represent the same number.

Fill in the blanks. A _____ is a product or quotient of numbers and/or variables. Examples are: \(8 x, \frac{t}{2},\) and \(-c d^{3}\)

\(10^{2}\) can be read as ten_______ \(\quad,\) and \(10^{3}\) can be read as ten______.

Fill in the blanks. The ______ property of multiplication states that changing the order when multiplying does not affect the answer.

Two numbers that are the same distance from 0 on a number line, but on opposite sides of it, are called __________ or additive _________.

Fill in the blanks. The set of ___ numbers is \(\\{1,2,3,4,5, \ldots\\}.\)

Fill in the blanks. _____ are letters (or symbols) that stand for numbers.

Fill in the blanks. Numbers that have only 1 and themselves as factors, such as \(23,37,\) and \(41,\) are called __numbers.

Fill in the blanks. Addition coefficient symbols separate algebraic expressions into parts called _____.

An__________ is used to represent repeated multiplication.

Fill in the blanks. The _____ property of multiplication states that changing the grouping when multiplying does not affect the answer.

The _________ property of addition states that changing the order when adding does not affect the answer. The __________ property of addition states that changing the grouping when adding does not affect the answer.

The difference between the maximum and the minimum value of a collection of measurements is called the _____ of the values.

Fill in the blanks. A number, such as \(8,\) is called a ______ because it does not change.

Fill in the blanks. When we write 60 as \(2 \cdot 2 \cdot 3 \cdot 5,\) we say that we have written 60 in ___ form.

Fill in the blanks. A term, such as \(27,\) that consists of a single number is called a _____ term.

To____________the expression \(2\left(-1+4^{2}\right)\) means to find its value.

Fill in the blanks. Division of a nonzero number by 0 is _____.

since any number added to 0 remains the same (is identical), the number 0 is called the __________ element for addition.

Fill in the blanks. The set of _____ numbers is \(\\{\ldots,-2,-1,0,1,2, \ldots\\}.\)

To find the _____ in a quantity, subtract the earlier value from the later value.

Fill in the blanks. Variables and numbers can be combined with the operations of addition, subtraction, multiplication, and division to create algebraic ______

Terms such as \(7 x^{2}\) and \(5 x^{2},\) which have the same variables raised to exactly the same power, are called ______ terms.

Fill in the blanks. The _____ of the term \(10 x\) is \(10 .\)

Fill in the blanks. a. The product or quotient of two numbers with like signs is _____. b. The product or quotient of two numbers with unlike signs is _____.

For each pair of numbers, which one has the larger absolute value? a. 6 or 5 b. 8.9 or \(-9.2\)

Fill in the blanks. Positive and negative numbers are called _____ numbers.

Fill in the blanks. An ______ is a mathematical sentence that contains an \(=\) symbol. An algebraic ______ does not.

Find the opposite (additive inverse) of each number. a. 12 b. \(-\frac{1}{5}\) c. 2.71 d. 0

Fill in the blanks. Two fractions that represent the same number, such as \(\frac{1}{2}\) and \(\frac{2}{4}\), are called ___fractions.

When we write \(9 x+x\) as \(10 x,\) we say we have ______ like terms.

Fill in the blanks. a. The product of an even number of negative numbers is _____. b. The product of an odd number of negative numbers is _____.

Determine whether each statement is true or false. a. The sum of a number and its opposite is always \(0 .\) b. The sum of two negative numbers is always negative. c. The sum of two numbers with different signs is always negative.

Complete each statement. a. \(a-b=a+\) ____ To subtract two numbers, add the first number to the _____ of the number to be subtracted. b. \(-(-a)=\) ____ The opposite of the opposite of a number is that _____.

Fill in the blanks. \(\frac{2}{3}\) is the ___of \(\frac{3}{2},\) because their product is 1

a. Fill in the blanks to simplify the expression. \(4(9 t)=\) \((\quad \cdot \quad) t=\quad t\) b. What property did you use in part a?

Fill in the blanks. a. \(\frac{-9}{3}=-3\) because _____ \(\cdot\) _____ = _____ b. \(\frac{0}{8}=0\) because _____ \(\cdot\) _____ = _____

To evaluate each expression, what operation should be performed first? a. \(24-4+2\) b. \(32 \div 8 \cdot 4\) c. \(8-(3+5)^{2}\) d. \(65 \cdot 3^{3}\)

For each addition, just determine the sign of the answer. a. \(39.6+(-64.9)\) b. \(-18.9+19.8\)

Fill in the blanks. The _____ axis of a graph extends left and right and the vertical axis extends up and down.

Fill in the blanks. The symbols \(<\) and \(>\) are ____ symbols.

Fill in the blanks. The ___ common denominator for a set of fractions is the smallest number each denominator will divide exactly.

a. Fill in the blanks to simplify the expression. \(-6 y \cdot 2=\) \(\cdot \quad \cdot y=\quad y\) b. What property did you use in part a?

Complete the table below on the right to determine the number of minutes in \(s\) seconds. $$ \begin{array}{|c|c|} \hline \text { Number } & {\text { Number }} \\ {\text { of weeks }} & {\text { of days }} \\ \hline 1 \\ \hline 2 & {} \\ \hline 3 & {} \\ \hline w & {} \\ \hline \end{array} $$ $$ \begin{array}{|c|c|} \hline \text { Number } & {\text { Number }} \\ \hline \text { of seconds } & {\text { of minutes }} \\ \hline 60 & {} \\ \hline 120 & {} \\ \hline 180 & {} \\ \hline s & {} \\ \hline \end{array} $$