evaluate

8 3/4 + 12.25-5 1/2

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- May 6th 2008, 01:57 PM #1

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- May 6th 2008, 02:00 PM #2

- May 6th 2008, 02:08 PM #3

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- May 6th 2008, 02:20 PM #4

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- May 6th 2008, 04:31 PM #6
Moo is right: you didn't state the problem clearly. From that choice of answers, I assume you mean 8

*and*3/4, and 5*and*1/2, and not 8*(3/4) and 5*(1/2). You have to be careful about this sort of thing, because this unfortunate notation that we have for mixed fractions can be ambiguous. So, try to make sure people understand what you are asking.

I will demonstrate how to evaluate this type of expression. Instead of solving your particular problem, I'll take you through another example, so that you can have the satisfaction of solving that one yourself.

Consider this problem: Evaluate $\displaystyle 2\frac56 + 4\frac12 - 3\frac49$.

Now, in this case the fractions next to the whole numbers are to be added, and not multiplied, so to avoid confusion I will rewrite this problem as:

$\displaystyle \left(2+\frac56\right) + \left(4+\frac12\right) - \left(3+\frac49\right)$

The first step is to convert these "mixed fractions" into "improper fractions" (but don't get hung up on the word "improper"--there's nothing wrong with having a numerator larger than a denominator). To do this conversion, transform the whole number into a fraction by multiplying and dividing it by the denominator of the fractional part and then combine the two together, like this:

$\displaystyle \left(2+\frac56\right) + \left(4+\frac12\right) - \left(3+\frac49\right)$

$\displaystyle =\left(

{\color{red}

\frac{ {\color{black}2}\cdot6}{6} } + \frac56

\right)

+\left(

{\color{red}

\frac{ {\color{black}4}\cdot2}{2} } + \frac12

\right)

-\left(

{\color{red}

\frac{ {\color{black}3}\cdot9}{9} } + \frac49

\right)

$

$\displaystyle =\left(\frac{\color{red}12}{6}+\frac56\right) + \left(\frac{\color{red}8}{2}+\frac12\right) - \left(\frac{\color{red}27}{9}+\frac49\right)$

$\displaystyle =\left(\frac{\color{red}12 + 5}{6}\right) + \left(\frac{\color{red}8 + 1}{2}\right) - \left(\frac{\color{red}27 + 4}{9}\right)$

$\displaystyle =\left(\frac{\color{red}17}{6}\right) + \left(\frac{\color{red}9}{2}\right) - \left(\frac{\color{red}31}{9}\right)$

$\displaystyle =\frac{17}6 + \frac92 - \frac{31}9$

Now, to add these fractions together, we need to find a common denominator. So, we find the least common multiple of 6, 2, and 9:

$\displaystyle 6\cdot3 = 18$

$\displaystyle 2\cdot9 = 18$

$\displaystyle 9\cdot2 = 18$

Now, multiply the numerator and denominator of each fraction by the necessary amount to get a common denominator:

$\displaystyle \frac{17}6\cdot{\color{red}\frac33} + \frac92\cdot{\color{red}\frac99} - \frac{31}9\cdot{\color{red}\frac22}$

$\displaystyle =\frac{17\color{red}\cdot3}{6\color{red}\cdot3} + \frac{9\color{red}\cdot9}{2\color{red}\cdot9} - \frac{31\color{red}\cdot2}{9\color{red}\cdot2}$

$\displaystyle =\frac{51}{18} + \frac{81}{18} - \frac{62}{18}$

$\displaystyle =\frac{\color{red}51 + 81 - 62}{18}$

$\displaystyle =\frac{70}{18}$

Now simplify:

$\displaystyle \frac{70}{18} = \frac{35}9$

Did that help? Now you try!