2.1.4 Important Fractions

The following fractions should be memorized for reasons stated in Section 1.2.5. In addition, early problems on the test typically involve converting these fractions to decimals and percentages. So if these conversions were memorized, a lot of time would be saved. Omitted are the “obvious” fractions ($\frac{1}{4}$, $\frac{1}{3}$, $\frac{1}{5}$, etc…).

Fraction	%	Fraction	%	Fraction	% / Decimal
$\frac{1}{6}$	$16\frac{2}{3}\%$	$\frac{1}{7}$	$14\frac{2}{7}\%$	$\frac{1}{8}$	$12\frac{1}{2}\% = 0.125$
$\frac{5}{6}$	$83\frac{1}{3}\%$	$\frac{2}{7}$	$28\frac{4}{7}\%$	$\frac{3}{8}$	$37\frac{1}{2}\% = 0.375$
		$\frac{3}{7}$	$42\frac{6}{7}\%$	$\frac{5}{8}$	$62\frac{1}{2}\% = 0.625$
		$\frac{4}{7}$	$57\frac{1}{7}\%$	$\frac{7}{8}$	$87\frac{1}{2}\% = 0.875$
		$\frac{5}{7}$	$71\frac{3}{7}\%$
		$\frac{6}{7}$	$85\frac{5}{7}\%$

Fraction	%	Fraction	%	Fraction	%	Fraction	%
$\frac{1}{9}$	$11\frac{1}{9}\%$	$\frac{1}{11}$	$9\frac{1}{11}\%$	$\frac{1}{12}$	$8\frac{1}{3}\%$	$\frac{1}{16}$	$6\frac{1}{4}\%$
$\frac{2}{9}$	$22\frac{2}{9}\%$	$\frac{2}{11}$	$18\frac{2}{11}\%$	$\frac{5}{12}$	$41\frac{2}{3}\%$	$\frac{3}{16}$	$18\frac{3}{4}\%$
$\frac{4}{9}$	$44\frac{4}{9}\%$	$\frac{4}{11}$	$36\frac{4}{11}\%$	$\frac{7}{12}$	$58\frac{1}{3}\%$	$\frac{5}{16}$	$31\frac{1}{4}\%$
$\frac{5}{9}$	$55\frac{5}{9}\%$	$\frac{5}{11}$	$45\frac{5}{11}\%$	$\frac{11}{12}$	$91\frac{2}{3}\%$	$\frac{7}{16}$	$43\frac{3}{4}\%$
$\frac{7}{9}$	$77\frac{7}{9}\%$	$\frac{7}{11}$	$63\frac{7}{11}\%$			$\frac{9}{16}$	$56\frac{1}{4}\%$
$\frac{8}{9}$	$88\frac{8}{9}\%$	$\frac{9}{11}$	$81\frac{9}{11}\%$			$\frac{11}{16}$	$68\frac{3}{4}\%$
		$\frac{10}{11}$	$90\frac{10}{11}\%$			$\frac{13}{16}$	$81\frac{1}{4}\%$
						$\frac{15}{16}$	$93\frac{3}{4}\%$

To aid in memorization, it would first help to memorize the first fractions in each column. From here the others can be quickly derived by multiplying the initial fraction by the required integer. For example, if you only had $\frac{1}{11}$ memorized as $9\frac{1}{11}\%$, but you need to know what $\frac{5}{11}$ is, then you could simply multiply by 5:

$5 \times \frac{1}{11} = 5 \times (9\frac{1}{11}\%) = 45\frac{5}{11}\%$

Although memorization of all fractions is ideal, this method will result in correctly answering the question, albeit a lot slower.

Problem Set 2.1.4