\(\displaystyle 2\frac{3}{4} +2\frac{5}{6}\)

Convert all mixed numbers to improper fractions.

\(\displaystyle 2\frac{3}{4} = \frac{(4\times 2)+3}{4} = \frac{11}{4}\)

\(\displaystyle 2\frac{5}{6} = \frac{(6\times 2)+5}{6} = \frac{17}{6}\)

\(\displaystyle \frac{11}{4} +\frac{17}{6}\)

Because the denominators are not the same, find the LCD of 4 and 6.

Multiples of 4 are 4,8,12, 16.

Multiples of 6 are 6 and 12.

The LCM or the LCD of 4 and 6 is 12.  Then, create equivalent fractions.

\(\displaystyle \frac{11}{4} = \frac{33}{12}\)    Both numerator and denominator were multiplied by 3.

\(\displaystyle \frac{17}{6} =\frac{34}{12}\)      Both numerator and denominator were multiplied by 2.

\(\displaystyle \frac{33}{12} +\frac{34}{12} = \frac{33+34}{12} =\frac{67}{12}\)

\(\displaystyle \frac{67}{12} = 5\frac{7}{12}\)

The sum of the two line segments is \(\displaystyle 5\frac{7}{12} inches.\)

The fraction form of .036 is \(\displaystyle \dpi{100} \frac{36}{1000}\).  None of our answers match this fraction, so we must reduce it.  The easiest way to do so is to divide the top and bottom by 2.

\(\displaystyle \dpi{100} \frac{36}{1000}=\frac{18}{500}\)

We can divide by 2 again:

\(\displaystyle \dpi{100} \frac{18}{500}=\frac{9}{250}\)

This is one of our answers (and also the fraction in its most reduced form).

First add the whole numbers.

\(\displaystyle \dpi{100} 2+5=7\)

Then add the fractions.  In order to this, the fractions need to have a common denominator.  The denominators are 4 and 5, so we need to find the least common multiple of 4 and 5. We can do this by finding all the multiples of the larger number (5) and try to divide each of them by 4.

5: No

10: No

15: No

20: Yes

So the least common multiple is 20.  We can multiply \(\displaystyle \dpi{100} 4\times 5\) to get 20, and \(\displaystyle \dpi{100} 5\times 4\) to get 20.

\(\displaystyle \dpi{100} \frac{1}{4}+\frac{4}{5}=\frac{5\times 1}{5\times 4}+\frac{4\times 4}{4\times 5}=\frac{5}{20}+\frac{16}{20}=\frac{21}{20}\)

We convert \(\displaystyle \dpi{100} \frac{21}{20}\) to \(\displaystyle \dpi{100} 1\frac{1}{20}\) and add it to 7 to get \(\displaystyle \dpi{100} 8\frac{1}{20}\).

Taking 32% of a number is the same as multiplying that number by 0.32. We therefore take the product:

\(\displaystyle 0.32 \cdot 2,000 = 640\)

Let's just pick a number at random, for example \(\displaystyle 100\). 

of this number is \(\displaystyle 25\), which is \(\displaystyle 100\) divided by \(\displaystyle 4\).

We can also work by simplifying the fractional form of . A percent can be written as the number divided by \(\displaystyle 100\).

\(\displaystyle =\frac{25}{100}\)

We can simplify this fraction: \(\displaystyle \frac{25}{100}=\frac{5}{20}=\frac{1}{4}\).

Either way, we get the same answer.

To find out what percent a part \(\displaystyle P\) is of a whole \(\displaystyle W\), evaluate the expression 

\(\displaystyle \frac{P}{W} \cdot 100 = \frac{3,300}{12,000} \cdot 100 = 27.5\) 

If \(\displaystyle 65\) is \(\displaystyle 12.5\%\) of a number, \(\displaystyle N\), then we can set up an equation. First, we convert \(\displaystyle 12.5\%\) to a decimal, \(\displaystyle 0.125\). Then, we can formulate the equation below.

\(\displaystyle 65 = 0.125N\)

Solve for \(\displaystyle N\) by dividing both sides of the equation by \(\displaystyle 0.125\).

\(\displaystyle \frac{0.125N}{0.125}=\frac{65}{0.125}\)

\(\displaystyle N = 520\)

First find the percentage amount for each choice by multiplying the number by the percentage amount

a. \(\displaystyle 90\ast .10=9\)

b. \(\displaystyle 160\ast .5=8\)

c. \(\displaystyle 50\ast .20=10\)

d. \(\displaystyle 40 \ast .30= 12\)

Then compare the amounts to find the largest.

The answer is (d) 12.

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{75}{N}= \frac{60}{100}\)

\(\displaystyle N \cdot 60 = 75 \cdot 100 = 7,500\)

\(\displaystyle N \cdot 60 \div 60 = 7,500\div 60\)

\(\displaystyle N = 125\)

Rewrite 120% as a decimal by writing 120 with a decimal point, then shifting it two spaces left:

\(\displaystyle 120.0\% = 1.20 = 1.2\)

Multiply this by 120:

\(\displaystyle 120 \times 1.2 = 144\)