Remember that fractions are:

$\displaystyle \frac{part}{whole}$

So, the triangle has a total of 8 parts, and 3 are shaded in. Therefore the fraction of the area that is shaded is $\displaystyle \frac{3}{8}$.

The first place value after the decimal is the tenths place, so $\displaystyle 0.6$ is six-tenths, or $\displaystyle \frac{6}{10}$.

The question asks for the percentage of people who chose chocolate over vanilla. If 8 people out of 32 preferred vanilla over chocolate, then $\displaystyle 32-8=24$ people preferred chocolate over vanilla. 

$\displaystyle \frac{24}{32}=.75*100=75$

35% can be written as $\displaystyle \frac{35}{100}=.35$.

$\displaystyle .35*300=105$

When converting a fraction to a decimal, divide the denominator by the numerator. Divide 23 by 79. The quotient is 0.291129...  The question asked you to round to the nearest hundredths place, so the correct choice is: 0.29.

You don't have to figure out the exact decimal values of the fractions in order to solve this problem. Written as a mixed number, $\displaystyle \frac{15}{7}=2\frac{1}{7}$.

You can see that $\displaystyle 2.09$ is the lowest number, because $\displaystyle .09$ is less than $\displaystyle \frac{1}{10}$, and $\displaystyle \frac{1}{8}$ and $\displaystyle \frac{1}{7}$ are greater than $\displaystyle \frac{1}{10}$.

Next comes $\displaystyle 2\frac{1}{8}$, because a larger denominator means a smaller number (if, of course, the numerator is the same).

Then comes $\displaystyle \frac{15}{7}$, and finally $\displaystyle 222\%$, which in decimal form (remember: "percent" = "per hundred") equals $\displaystyle 2.22$, which is clearly greater than $\displaystyle 2\frac{1}{5}$.

Since 3 is greater than half of 5, we know that $\displaystyle \frac{3}{5}$ is greater than $\displaystyle \frac{1}{2}$.

That eliminates $\displaystyle \frac{1}{2}$,  $\displaystyle \frac{5}{11}$, and $\displaystyle \frac{4}{9}$, which are all less than or equal to $\displaystyle \frac{1}{2}$.

That leaves $\displaystyle \frac{7}{9}$, which is between $\displaystyle \frac{3}{5}$ and $\displaystyle \frac{9}{10}$.

For this problem, you will need to find a common denominator for the fraction part of the mixed numbers:

$\displaystyle 13\frac{1}{8}-8\frac{3}{4}= 13\frac{1}{8}- 8\frac{6}{8}$

Next, we want for the fraction in the mixed number we are subtracting from to be larger than the other fraction. We can do this by "taking" $\displaystyle 1$ (or $\displaystyle \frac{8}{8}$) from the $\displaystyle 13$ and add it to the $\displaystyle \frac{1}{8}$. This gives us:

$\displaystyle 12\frac{9}{8}-8\frac{6}{8}$.

This should look less threatening now. Simply subtract the whole numbers and the fractions, and you are left with: $\displaystyle 4\frac{3}{8}$.

The expression is equal to sixty-six one-hundredths, so write it as a fraction and reduce as follows:

$\displaystyle 0.66 = \frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50}$

Divide 5 by 4:

$\displaystyle 5 \div 4 = 1.25$