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For the following problems, simplify the expressions.
$9\left(4-2\right)+6\left(8+2\right)-3\left(1+4\right)$
$26\xf72-10$
$51\xf73\xf77$
$8\left(2\cdot 12\xf713\right)+2\cdot 5\cdot 11-\left[1+4\left(1+2\right)\right]$
$\frac{3}{4}+\frac{1}{12}\left(\frac{3}{4}-\frac{1}{2}\right)$
$\frac{37}{48}$
$48-3\left[\frac{1+17}{6}\right]$
$\frac{\frac{88}{11}+\frac{99}{9}+1}{\frac{54}{9}-\frac{22}{11}}$
$\frac{8\cdot 6}{2}+\frac{9\cdot 9}{3}-\frac{10\cdot 4}{5}$
43
For the following problems, write the appropriate relation symbol $\left(=,<,>\right)$ in place of the $\ast $ .
$22\ast 6$
$9\left[4+3\left(8\right)\right]\ast 6\left[1+8\left(5\right)\right]$
$252>246$
$3\left(1.06+2.11\right)\ast 4\left(11.01-9.06\right)$
For the following problems, state whether the letters or symbols are the same or different.
$a=b\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}b=a$
Represent the sum of $c$ and $d$ two different ways.
$c+d;d+c$
For the following problems, use algebraic notataion.
62 divided by $f$
$\frac{62}{f}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}62\xf7f$
8 times $\left(x+4\right)$
$x+1$ divided by $x-3$
$y+11$ divided by $y+10$ , minus 12
$\left(y+11\right)\xf7\left(y+10\right)-12\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\frac{y+11}{y+10}-12$
zero minus $a$ times $b$
Is every rational number a real number?
For the following problems, locate the numbers on a number line by placing a point at their (approximate) position.
Draw a number line that extends from 10 to 20. Place a point at all odd integers.
Draw a number line that extends from $-10$ to $10$ . Place a point at all negative odd integers and at all even positive integers.
Draw a number line that extends from $-5$ to $10$ . Place a point at all integers that are greater then or equal to $-2$ but strictly less than 5.
Draw a number line that extends from $-10$ to $10$ . Place a point at all real numbers that are strictly greater than $-8$ but less than or equal to 7.
Draw a number line that extends from $-10$ to $10$ . Place a point at all real numbers between and including $-6$ and 4.
For the following problems, write the appropriate relation symbol $(=,<,>).$
$\begin{array}{cc}-1& 1\end{array}$
$\begin{array}{cc}-5& -5\frac{1}{2}\end{array}$
Is there a smallest two digit integer? If so, what is it?
$\text{yes,}\text{\hspace{0.17em}}-99$
Is there a smallest two digit real number? If so, what is it?
For the following problems, what integers can replace $x$ so that the statements are true?
$4\le x\le 7$
$4,\text{\hspace{0.17em}}5,\text{\hspace{0.17em}}6,\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}7$
$-3\le x<1$
$-3<x\le 2$
$-2,\text{\hspace{0.17em}}-1,\text{\hspace{0.17em}}0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}2$
The temperature today in Los Angeles was eighty-two degrees. Represent this temperature by real number.
The temperature today in Marbelhead was six degrees below zero. Represent this temperature by real number.
$-6\xb0$
On the number line, how many units between $-3$ and 2?
$a+b=b+a$ is an illustration of the
$st=ts$ is an illustration of the __________ property of __________.
commutative, multiplication
Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems.
$\left(-8\right)\left(4\right)$
$\left(6\right)\left(-9\right)\left(-2\right)$
$\left(-9\right)\left(6\right)\left(-2\right)\text{\hspace{0.17em}}\text{or\hspace{0.17em}}\left(-9\right)\left(-2\right)\left(6\right)\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\left(6\right)\left(-2\right)\left(-9\right)\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\left(-2\right)\left(-9\right)\left(6\right)$
$\left(x+y\right)\left(x-y\right)$
$\u25b3\cdot \diamond $
$\diamond \text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\u25b3$
Simplify the following problems using the commutative property of multiplication. You need not use the distributive property.
$4axyc4d4e$
$8b\left(a-6\right)9a\left(a-4\right)$
For the following problems, use the distributive property to expand the expressions.
$a\left(b+3c\right)$
$\left(8m+5n\right)6p$
$\left(a+2\right)\left(b+2c\right)$
$10{a}_{z}\left({b}_{z}+c\right)$
For the following problems, write the expressions using exponential notation.
$\left(y+2\right)$ cubed.
$\left(a+2b\right)$ squared minus $\left(a+3b\right)$ to the fourth.
${\left(a+2b\right)}^{2}-{\left(a+3b\right)}^{4}$
$x$ cubed plus 2 times $\left(y-x\right)$ to the seventh.
$2\cdot 2\cdot 2\cdot 2$
$\left(-8\right)\left(-8\right)\left(-8\right)\left(-8\right)xxxyyyyy$
${\left(-8\right)}^{4}{x}^{3}{y}^{5}$
$\left(x-9\right)\left(x-9\right)+\left(3x+1\right)\left(3x+1\right)\left(3x+1\right)$
$2zzyzyyy+7zzyz{\left(a-6\right)}^{2}\left(a-6\right)$
$2{y}^{4}{z}^{3}+7y{z}^{3}{\left(a-6\right)}^{3}$
For the following problems, expand the terms so that no exponents appear.
${x}^{3}$
${7}^{3}{x}^{2}$
${\left(4b\right)}^{2}$
$4b\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}4b$
${(6{a}^{2})}^{3}{(5c-4)}^{2}$
${({x}^{3}+7)}^{2}{({y}^{2}-3)}^{3}(z+10)$
$\left(xxx+7\right)\left(xxx+7\right)\left(yy-3\right)\left(yy-3\right)\left(yy-3\right)\left(z+10\right)$
Choose values for $a$ and $b$ to show that
Choose value for $x$ to show that
(a) any value except zero
(b) only zero
Simplify the following problems.
${4}^{2}+8$
${1}^{8}+{0}^{10}+{3}^{2}({4}^{2}+{2}^{3})$
$\frac{{3}^{4}+1}{{2}^{2}+{4}^{2}+{3}^{2}}$
$\frac{{6}^{2}+{3}^{2}}{{2}^{2}+1}+\frac{{\left(1+4\right)}^{2}-{2}^{3}-{1}^{4}}{{2}^{5}-{4}^{2}}$
10
${a}^{4}{a}^{3}$
$4{a}^{3}{b}^{2}{c}^{8}\cdot 3a{b}^{2}{c}^{0}$
$(3xy{z}^{2})(2{x}^{2}{y}^{3})(4{x}^{2}{y}^{2}{z}^{4})$
${\left(10xy\right)}^{2}$
${({a}^{4}{b}^{7}{c}^{7}{z}^{12})}^{9}$
${\left(\frac{3}{4}{x}^{8}{y}^{6}{z}^{0}{a}^{10}{b}^{15}\right)}^{2}$
$\frac{9}{16}{x}^{16}{y}^{12}{a}^{20}{b}^{30}$
$\frac{{x}^{8}}{{x}^{5}}$
$\frac{14{a}^{4}{b}^{6}{c}^{7}}{2a{b}^{3}{c}^{2}}$
$7{a}^{3}{b}^{3}{c}^{5}$
$\frac{11{x}^{4}}{11{x}^{4}}$
${a}^{3}{b}^{7}\cdot \frac{{a}^{9}{b}^{6}}{{a}^{5}{b}^{10}}$
$\frac{{\left({x}^{4}{y}^{6}{z}^{10}\right)}^{4}}{{\left(x{y}^{5}{z}^{7}\right)}^{3}}$
${x}^{13}{y}^{9}{z}^{19}$
$\frac{{\left(2x-1\right)}^{13}{\left(2x+5\right)}^{5}}{{\left(2x-1\right)}^{10}\left(2x+5\right)}$
${\left(\frac{3{x}^{2}}{4{y}^{3}}\right)}^{2}$
$\frac{9{x}^{4}}{16{y}^{6}}$
$\frac{{\left(x+y\right)}^{9}{\left(x-y\right)}^{4}}{{\left(x+y\right)}^{3}}$
${a}^{n+2}{a}^{n+4}$
$\frac{18{x}^{4n+9}}{2{x}^{2n+1}}$
${({a}^{2n}{b}^{3m}{c}^{4p})}^{6r}$
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