a) $\displaystyle 11^{2}$ $\displaystyle = 11\cdot11=121$

b) The smallest prime number larger than $\displaystyle 100$ is $\displaystyle 101$.

c) $\displaystyle 95$ percent of $\displaystyle 120$

 $\displaystyle 120\cdot.95=114$

Therefore (b) is smaller than (c) which is smaller than (a).

Always do the operations in parantheses first, then multiplication, then addition.

a) $\displaystyle (2+7)\cdot8 = 9\cdot8 = 72$

b) $\displaystyle 2+(7\cdot8) = 2+56 =58$

c) $\displaystyle (2\cdot8)+7 = 16+7 = 23$

Therefore (a) is greater than (b), which is greater than (c) .

Multiply each fraction by the number to find each value:

a) $\displaystyle \frac{2}{3}$ of $\displaystyle 36$

$\displaystyle \frac{36\cdot2}{3}=24$

b) $\displaystyle \frac{5}{2}$ of $\displaystyle 36$

$\displaystyle \frac{36\cdot5}{2}=90$

c) $\displaystyle \frac{5}{6}$ of $\displaystyle 72$

$\displaystyle \frac{72\cdot5}{6}=60$

Therefore (a) is less than (c), which is less than (b).

Always do the operations in parantheses first, then exponents, multiplication, and last addition.

a) $\displaystyle 6+(2\cdot3)$ $\displaystyle =6+6=12$

b) $\displaystyle (6+2)\cdot3$ $\displaystyle =8\cdot3=24$

c) $\displaystyle (6+3)^2$ $\displaystyle = 9^2 = 81$

Compute each value in order to compare them:

a) $\displaystyle .6 \cdot .4$ $\displaystyle =.24$

b) $\displaystyle .6 \cdot4$ $\displaystyle =2.4$

c) $\displaystyle 6 \cdot .4$ $\displaystyle =2.4$

Therefore (b) and (c) are equal, and they are greater than (a).

Rewrite the first fraction with a denominator of $\displaystyle 10$ in order to compare more easily:

a) $\displaystyle \frac{1}{5}=\frac{2}{10}$

b) $\displaystyle \frac{3}{10}$

c) $\displaystyle \frac{1}{10}$

It becomes clear that (b) is the greatest, followed by (a), then (c).

Calculate the percents in order to compare them:

a) $\displaystyle 30$ percent of $\displaystyle 100$

$\displaystyle 100\cdot.30=30$

b) $\displaystyle 60$ percent of $\displaystyle 50$

$\displaystyle 50\cdot.60=30$

c) $\displaystyle 60$ percent of $\displaystyle 200$

$\displaystyle 200\cdot.60=120$

Therefore (a) and (b) are equal, and less than (c).

Calculate the exponents to compare the values:

a) $\displaystyle 2^5$ $\displaystyle =2\cdot2\cdot2\cdot2\cdot2=32$

b) $\displaystyle 3^3$ $\displaystyle =3\cdot3\cdot3=27$

c) $\displaystyle 4^2$ $\displaystyle =4\cdot4=16$

Therefore (a) is greater than (b), which is greater than (c).

Simplify each expression to see if they are equal:

a) $\displaystyle 7x$ (already simplified)

b) $\displaystyle 2(x+5x)$ $\displaystyle =2x+10x=12x$

c) $\displaystyle 2x+5x$ $\displaystyle =7x$

Therefore (a) and (c) are equal, but (b) is different.

Convert each expression into a decimal in order to compare them:

a) $\displaystyle .\bar{66}$

b) $\displaystyle .6$

c)$\displaystyle .65$

Therefore (a) is the largest.