Fractions

Arithmetic: Fractions

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

Use the same process with every SAT question.  Read carefully and identify the bottom line.  Then assess your options for reaching the bottom line and choose the most time efficient method to attack the problem.  When you have an answer, loop back to check that you solved for the bottom line.

$\frac{1}{2}\cdot \frac{2}{3}\cdot \frac{3}{4}\cdot \frac{4}{5}\cdot \frac{5}{6}\cdot \frac{6}{7}=$

Bottom Line: just solve

Assess your options:  When you see a problem like this, get excited!  Some people will multiply all of the numbers, or change the fractions into decimals, but you should recognize a pattern!  Use what you know about fractions to solve this problem in less than 5 seconds.

Attack the problem:   The way you would normally solve the problem is to multiply all of the top numbers and multiply all of the bottom, then simplify the resulting fraction.  There is a faster way!  Although this problem starts out with separate fractions, you can think of the numbers that you are given as factors of the product you would get.  Remember that a number on top of a fraction will cancel if the same number is on the bottom of a fraction. Envision the problem this way:

$\frac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}{2\cdot3\cdot 4\cdot 5\cdot 6\cdot 7 }=$

Then simply eliminate any numbers that are both on top and bottom!  The 2s cancel.  So do the 3s.  Keep going, and what do you have left?

$\frac{1}{7}$

Loop back:  You solved the original equation, so you are ready to look down at the answer choices.

(A) $\frac{1}{7}$
(B) $\frac{3}{7}$
(C) $\frac{21}{27}$
(D) $\frac{6}{7}$
(E) $\frac{7}{8}$

The correct answer is (A).

On sat.collegeboard.org, 60% of the responses were correct.

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