2.8 Exercise supplement

$12+7\left(4+3\right)$

$9\left(4-2\right)+6\left(8+2\right)-3\left(1+4\right)$

$6\left[1+8\left(7+2\right)\right]$

$26÷2-10$

$\frac{\left(4+17+1\right)+4}{14-1}$

$51÷3÷7$

$\left(4+5\right)\left(4+6\right)-\left(4+7\right)$

$8\left(2\cdot 12÷13\right)+2\cdot 5\cdot 11-\left[1+4\left(1+2\right)\right]$

$\frac{3}{4}+\frac{1}{12}\left(\frac{3}{4}-\frac{1}{2}\right)$

$48-3\left[\frac{1+17}{6}\right]$

$\frac{29+11}{6-1}$

$\frac{\frac{88}{11}+\frac{99}{9}+1}{\frac{54}{9}-\frac{22}{11}}$

$\frac{8\cdot 6}{2}+\frac{9\cdot 9}{3}-\frac{10\cdot 4}{5}$

$22\ast 6$

$9\left[4+3\left(8\right)\right]\ast 6\left[1+8\left(5\right)\right]$

$3\left(1.06+2.11\right)\ast 4\left(11.01-9.06\right)$

$2\ast 0$

>and ≮

$a=b\text{and}b=a$

Represent the sum of $c$ and $d$ two different ways.

8 plus 9

62 divided by $f$

8 times $\left(x+4\right)$

6 times $x$ , minus 2

$x+1$ divided by $x-3$

$y+11$ divided by $y+10$ , minus 12

zero minus $a$ times $b$

Is every natural number a whole number?

Is every rational number a real number?

2

$3.6$

$-1\frac{3}{8}$

0

$-4\frac{1}{2}$

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.

$\begin{array}{cc}-3& 0\end{array}$

$\begin{array}{cc}-1& 1\end{array}$

$\begin{array}{cc}-8& -5\end{array}$

$\begin{array}{cc}-5& -5\frac{1}{2}\end{array}$

Is there a smallest two digit integer? If so, what is it?

Is there a smallest two digit real number? If so, what is it?

$4\le x\le 7$

$-3\le x<1$

$-3<x\le 2$

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.

On the number line, how many units between $-3$ and 2?

On the number line, how many units between $-4$ and 0?

$a+b=b+a$ is an illustration of the property of addition.

$st=ts$ is an illustration of the __________ property of __________.

$y+12$

$a+4b$

$6x$

$2\left(a-1\right)$

$\left(-8\right)\left(4\right)$

$\left(6\right)\left(-9\right)\left(-2\right)$

$\left(x+y\right)\left(x-y\right)$

$△\cdot \diamond$

$8x3y$

$16ab2c$

$4axyc4d4e$

$3(x+2)5(x-1)0(x+6)$

$8b\left(a-6\right)9a\left(a-4\right)$

$3\left(a+4\right)$

$a\left(b+3c\right)$

$2g\left(4h+2k\right)$

$\left(8m+5n\right)6p$

$3y\left(2x+4z+5w\right)$

$\left(a+2\right)\left(b+2c\right)$

$\left(x+y\right)\left(4a+3b\right)$

$10a_z\left(b_z+c\right)$

$x$ to the fifth.

$\left(y+2\right)$ cubed.

$\left(a+2b\right)$ squared minus $\left(a+3b\right)$ to the fourth.

$x$ cubed plus 2 times $\left(y-x\right)$ to the seventh.

$aaaaaaa$

$2\cdot 2\cdot 2\cdot 2$

$\left(-8\right)\left(-8\right)\left(-8\right)\left(-8\right)xxxyyyyy$

$\left(x-9\right)\left(x-9\right)+\left(3x+1\right)\left(3x+1\right)\left(3x+1\right)$

$2zzyzyyy+7zzyz{\left(a-6\right)}^2\left(a-6\right)$

$x^3$

$3x^3$

$7^3{x}^2$

${\left(4b\right)}^2$

${(6a^2)}^3{(5c-4)}^2$

${(x^3+7)}^2{(y^2-3)}^3(z+10)$

Choose values for $a$ and $b$ to show that

1. ${\left(a+b\right)}^2$ is not always equal to $a^2+b^2$ .
2. ${\left(a+b\right)}^2$ may be equal to $a^2+b^2$ .

Choose value for $x$ to show that

1. ${\left(4x\right)}^2$ is not always equal to $4x^2$ .
2. ${\left(4x\right)}^2$ may be equal to $4x^2$ .

$4^2+8$

$6^3+5\left(30\right)$

$1^8+0^{10}+3^2(4^2+2^3)$

${12}^2+0.3{\left(11\right)}^2$

$\frac{3^4+1}{2^2+4^2+3^2}$

$\frac{6^2+3^2}{2^2+1}+\frac{{\left(1+4\right)}^2-2^3-1^4}{2^5-4^2}$

$a^4{a}^3$

$2b^{5}2b^3$

$4a^3{b}^2{c}^8\cdot 3a{b}^2{c}^0$

$(6x^4{y}^{10})(x{y}^3)$

$(3xy{z}^2)(2x^2{y}^3)(4x^2{y}^2{z}^4)$

${\left(3a\right)}^4$

${\left(10xy\right)}^2$

${(x^2{y}^4)}^6$

${(a^4{b}^7{c}^7{z}^{12})}^9$

${\left(\frac{3}{4}{x}^8{y}^6{z}^0{a}^{10}{b}^{15}\right)}^2$

$\frac{x^8}{x^5}$

$\frac{14a^4{b}^6{c}^7}{2a{b}^3{c}^2}$

$\frac{11x^4}{11x^4}$

$x^4\cdot \frac{x^{10}}{x^3}$

$a^3{b}^7\cdot \frac{a^9{b}^6}{a^5{b}^{10}}$

$\frac{{\left(x^4{y}^6{z}^{10}\right)}^4}{{\left(x{y}^5{z}^7\right)}^3}$

$\frac{{\left(2x-1\right)}^{13}{\left(2x+5\right)}^5}{{\left(2x-1\right)}^{10}\left(2x+5\right)}$

${\left(\frac{3x^2}{4y^3}\right)}^2$

$\frac{{\left(x+y\right)}^9{\left(x-y\right)}^4}{{\left(x+y\right)}^3}$

$x^n\cdot x^m$

$a^{n+2}{a}^{n+4}$

$6b^{2n+7}\cdot 8b^{5n+2}$

$\frac{18x^{4n+9}}{2x^{2n+1}}$

${(x^{5t}{y}^{4r})}^7$

${(a^{2n}{b}^{3m}{c}^{4p})}^{6r}$

$\frac{u^w}{u^k}$