# Fractions

Yesterday would have been Alan Turing's 100th birthday. Turing was a mathematical genius who laid the foundations for modern day computer science. By the time he was 26 he was performing cryptanalysis for the Government Code and Cypher School in England. He worked on cryptanalysis throughout WWII and developed many crucial new techniques in code breaking. He is best remembered for the invention of the Turing Machine, a theoretical machine that could solve a complex math problem using only simple calculations and a large amount of storage (a precursor to the modern day computer). You can read more about Alan Turing here. He would make a great historical "Excellent Example" for your essay.

## 6/23 Fractions

Read the following SAT test question and then select the correct answer.

You probably notice that this problem looks very straightforward. If you have a calculator and you are comfortable with fractions, you are probably thinking that this problem won't be that difficult. If you don't have a calculator however, (or you don't remember how to enter fractions into your calculator), you might think this isn't such an easy problem. Never forget to follow the Knowsys method for Math Problems. Read the problem carefully and identify the bottom line (in this case, you just need to solve the equation). Next, evaluate your options, think about the various ways that you could solve the problem and then select the best choice. Finally, loop back and verify that the answer you choose correctly answers the bottom line. You could enter all these fractions into a calculator. But, because there are so many fractions it will take quite a while (and there is a good chance that you will make an error when you are entering the numbers). There is actually a much easier (and faster) way to solve this problems. If you just look at the first two fractions

$\frac{1}{2}*\frac{2}{3}$

you should see that you could cancel the 2's. Now, look at the second and third fractions

$\frac{2}{3}*\frac{3}{4}$

in this set, you could cancel the 3's.

If you go through the whole equation and cancel as much as you can, you are simply left with

$\frac{1}{1}*\frac{1}{1}*\frac{1}{1}*\frac{1}{1}*\frac{1}{1}*\frac{1}{7}=\frac{1}{7}$

Now, take a look at the answer choices and see which one matches your prediction.

(A)   $\frac{1}{7}$

(B)   $\frac{3}{7}$

(C)  $\frac{21}{27}$

(D)  $\frac{6}{7}$

(E)  $\frac{7}{8}$

The correct answer choices is (A)

On sat.collegeboard.org 63% of the responses were correct.

For more help with math, visit www.myknowsys.com.