# Fractions

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## 4/24 Fractions

Remember to always follow the Knowsys Method when approaching math problems: First, read carefully. Then identify the bottom line and assess your options. Next, choose the most efficient method and attack the problem! Finally, loop back to make sure you have the correct answer.

If f(x) = x + ax, and $a=\frac{7}{2}$, what is $f(\frac{3}{2})$?

First, as always, identify the bottom line.

$f(\frac{3}{2})=?$

Next, assess your options. You have variables in the question and numbers in the answer choices, so you could work backward from the answer choices. However, there are also numbers in the question, so you could plug in those numbers to see what that gives you. The second method will be far more efficient.

First, plug in the numbers. $a=\frac{7}{2}$ and $x=\frac{3}{2}$, so plug each of those in where appropriate.

$f(\frac{3}{2})=\frac{3}{2}+\frac{7}{2}(\frac{3}{2})$

Next, following the Order of Operations (PEMDAS), multiply the last two numbers together. When multiplying fractions, simply multiply the numerators and then the denominators.

$f(\frac{3}{2})=\frac{3}{2}+\frac{21}{4}$

Obviously, the next thing to do is to add the fractions together. Remember that when adding fractions, the denominators must match, and you can ONLY add the numerators. You'll need to do something to make the denominators the same.

$f(\frac{3}{2})=\frac{3}{2}(\frac{2}{2})+\frac{21}{4}$

$f(\frac{3}{2})=\frac{6}{4}+\frac{21}{4}$

$f(\frac{3}{2})=\frac{27}{4}$

Now loop back. Is $f(\frac{3}{2})$ what you actually needed to find? Yes, it is! Now look at the answer choices.

$A)\frac{1}{3}$

$B)\frac{3}{2}$

$C)\frac{7}{2}$

$D)\frac{21}{4}$

$E)\frac{27}{4}$