Chapter 3

Circle the correct words to complete each sentence. In the addition problem \(-5+(-11),\) the signs of the addends are the same/different. Because both addends are negative, the sign of the sum will be positive/negative.

Determine which of the numbers are a. integers, b. rational numbers, c. irrational numbers, and d. real numbers. List all that apply. $$-\frac{15}{2}, 0,-3, \pi, 2 . \overline{33}, 4.232232223 \ldots, \frac{\sqrt{5}}{4}, \sqrt{7}$$

Fill in the blank with left or right. a. On a number line, the number \(-8\) is to the \(_______\) \(-3\) b. On a number line, the number 0 is to the \(________\) \(-4\)

To simplify the expression \(6-4 \div(-2),\) the first operation that must be performed is ________.

Circle the correct words to complete each sentence. In the addition problem \(-7+16\), the signs of the addends are the same/different. Because the positive addend has the larger absolute value, the sign of the sum will be positive/negative,

Determine which of the numbers are a. integers, b. rational numbers, c. irrational numbers, and d. real numbers. List all that apply. $$-17,0.3412, \frac{3}{\pi},-1.010010001 \ldots, \frac{27}{91}, 6.1 \overline{2}$$

Fill in the blank with \(<\) or \(>\) a. On a number line, \(-1\) is to the right of \(-10,\) so \(-1\) \(_____\) -10 b. On a number line, \(-5\) is to the left of \(2,\) so \(-5\) \(______\) 2.

Simplify: \((-7)^{2}-5(2-3)\) a. Perform operations in parentheses. b. Simplify expressions with exponents. c. Multiply. d. Rewrite subtraction as addition of the opposite. e. Add $$(-7)^{2}-5(2-3)$$ $$=(-7)^{2}-(5$$ = _______ -5 (-1) = 49 - _______ = 49 + ______

State whether each "-" is a minus sign or a negative sign. $$-7+(-9)$$

The opposite of a positive number is a \(________\) number. The opposite of a negative number is a \(________\) number.

Simplify. $$\frac{5}{8}-\frac{5}{6}$$

The fraction that represents the quotient \(-63\) and 9 is_______.

Simplify. $$2(3-5)-2$$

State whether each "-" is a minus sign or a negative sign. $$2-(-7)$$

In the expression \(8-(-2),\) the first \(-\operatorname{sign}\) is read as \(_________\) and the second \(-\operatorname{sign}\) is read as \(_______\)

Simplify. $$\frac{1}{9}-\frac{5}{27}$$

Name the operation in each expression, and explain how you determined the operation. a. \(8(-7)\) b. \(8-7 \quad\) c. \(8-(-7)\) \(\begin{array}{lll}\text { d. }-x y & \text { e. } x(-y) & \text { f. }-x-y\end{array}\)

Simplify. $$2-(8-10) \div 2$$

State whether each "-" is a minus sign or a negative sign. $$-6-1$$

The equation \(|-5|=5\) is read "the \(_______\) of negative five is five."

Multiply. $$-4 \cdot 6$$

Simplify. $$-\frac{5}{12}-\frac{3}{8}$$

Simplify. $$4-(-3)^{2}$$

State whether each "-" is a minus sign or a negative sign. $$-4-(-3)$$

Evaluate \(|-y|\) for \(y=-6\) a. Replace \(y\) with \(-\) \(________\) b. The opposite of \(-6\) is 6 c. The absolute value of 6 is 6 \begin{array}{l} |-y| \\ =|-(-6)| \\ =|-| \end{array}

Multiply. $$-7 \cdot 3$$

Simplify. $$-\frac{5}{6}-\frac{5}{9}$$

Simplify. $$-2^{2}-6$$

Rewrite each subtraction as addition of the opposite. $$-9-5=-9+\text{____}$$

Graph the number on the number line. \(-5\) (GRAPH CANT COPY)

Multiply. $$-2(-3)$$

Simplify. $$-\frac{6}{13}+\frac{17}{26}$$

Simplify. $$3 \cdot(6-2) \div 6$$

Rewrite each subtraction as addition of the opposite. $$6-(-4)-3=6\text{_____}+\text{_____}$$

Graph the number on the number line. \(-1\) (GRAPH CANT COPY)

Multiply. $$-5(-1)$$

Simplify. $$-\frac{7}{12}+\frac{5}{8}$$

Simplify. $$4 \cdot(2-7) \div 5$$

Add. $$-3+(-8)$$

Graph the number on the number line. \(-6\) (GRAPH CANT COPY)

Multiply. $$(9)(2)$$

Simplify. $$-\frac{5}{8}-\left(-\frac{11}{12}\right)$$

Simplify. $$2^{3}-(-3)^{2}+2$$

Add. $$-6+(-9)$$

Graph the number on the number line. \(-2\) (GRAPH CANT COPY)

Multiply. $$(3)(8)$$

Simplify. $$-\frac{7}{12}-\left(-\frac{7}{8}\right)$$

Simplify. $$6(8-2) \div 4$$

Add. $$-8+3$$

Graph the number on the number line. \(x,\) for \(x=5\) (GRAPH CANT COPY)