Fractions

Arithmetic: Fractions

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

Read each question carefully.  Then identify the bottom line and assess your options for finding it.  Choose the most efficient method to attack the problem.  Before selecting your answer, loop back to make sure that you solved for the bottom line.

If  $N \times\frac{5}{14} = \frac{5}{14}\times\frac{7}{9}$then N =

Bottom Line:  N = ?

Assess your options: Normally, you would begin working this problem by multiplying the two fractions on the right and then multiplying them by the reciprocal of the fraction on the left in order to find N.  Before you jump into the problem, think about the properties of multiplication and you will see that there is a much faster way to solve the problem.

Attack the problem:  The commutative property of multiplication tells you that order is not important when you are multiplying; 3 × 5 = 5 × 3.  If you rearrange your equation, you will see that $N \times\frac{5}{14} = \frac{7}{9}\times \frac{5}{14}$ .   When you see the same thing, such as a fraction with 5 over 14, on both sides of the equation, you know that you can ignore that information.  No matter what number or variable you have, if it is the same on both sides of the equation, you will eliminate one side when you eliminate the other.  You can check this fact by multiplying both sides by the reciprocal of $\frac{5}{14}$.  If you multiply both sides by $\frac{14}{5}$, the $\frac{5}{14}$ will cancel on each side and you are left with N = $\frac{7}{9}$.

Loop back:  You solved for your bottom line, N, so you should look down at your answer choices.

(A) $\frac{7}{9}$
(B) $\frac{9}{7}$

(C) 5

(D) 7`

(E) 14