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PSAT Math : How to divide fractions

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Example Question #11 : How To Divide Fractions

Define an operation $\ddagger$ as follows:

For all real numbers a ,b ,

$a \ddagger b = \frac{a}{b} - \frac{b}{a}$ .

Evaluate $\frac{3}{4} \ddagger\frac{4}{3}$ .

Possible Answers:

$-1 \frac{31}{144}$

$-3\frac{1}{12}$

$3\frac{1}{12}$

$1 \frac{31}{144}$

Correct answer:

$-1 \frac{31}{144}$

Explanation:

$a \ddagger b = \frac{a}{b} - \frac{b}{a}$ ,

or, equivalently,

$a \ddagger b = (a \div b) - (b \div a)$

$\frac{3}{4} \ddagger\frac{4}{3} =\left (\frac{3}{4} \div \frac{4}{3} \right ) - \left (\frac{4}{3} \div \frac{3}{4} \right )$

$=\left (\frac{3}{4} \times \frac{3}{4} \right ) - \left (\frac{4}{3} \times \frac{4} {3}\right )$

$= \frac{9}{16} -\frac{16}{9}$

From here we need to find a common denominator.

$=\frac{9}{16}\bigg(\frac{9}{9}\bigg)- \frac{16}{9}\bigg(\frac{16}{16}\bigg)$

$= \frac{81}{144} -\frac{256}{144}$

$= -\frac{175}{144}$

$= -1 \frac{31}{144}$

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Example Question #111 : Fractions

Simplify:

$\frac{1+5}{\frac{6}{3+1}}$

Possible Answers:

$\frac{1}{4}$

$\frac{5}{8}$

$\frac{16}{3}$

Correct answer:

Explanation:

Begin by simplifying any additions that need to be done:

$\frac{1+5}{\frac{6}{3+1}}$

becomes

$\frac{6}{\frac{6}{4}}$

Now, remember that the numerator can be rewritten $\frac{6}{1}$ :

$\frac{\frac{6}{1}}{\frac{6}{4}}$

Now, when you divide fractions, you multiply the numerator by the reciprocal of the denominator:

$\frac{6}{1} * \frac{4}{6}$

Cancel the s and you get:

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PSAT Math : How to divide fractions

Study concepts, example questions & explanations for PSAT Math

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Example Question #11 : How To Divide Fractions

Example Question #111 : Fractions

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