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Two-thirds of a pie is cut into 9 equal slices, and the remaining one-third is cut into 4 equal slices. If a person eats 2 of the larger slices and 1 of the smaller slices, what fraction of the pie remains uneaten?

Explanation	Calculations	Help
$We let the whole pie be X.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Two-thirds of a pie is cut into 9 equal slices" into an expression for one larger slice.$	$\frac{2}{3} X \times \frac{1}{9} = \frac{2}{27} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the remaining one-third is cut into 4 equal slices" into an expression for one smaller slice.$	$\frac{1}{3} X \times \frac{1}{4} = \frac{1}{12} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the larger slices and 1 of the smaller slices" into the sum of the eaten portions.$	$2 \times \frac{2}{27} X + 1 \times \frac{1}{12} X = \frac{4}{27} X + \frac{1}{12} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{4}{27} X = \frac{16}{108} X \frac{1}{12} X = \frac{9}{108} X \frac{16}{108} X + \frac{9}{108} X = \frac{25}{108} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole pie.$	$X - \frac{25}{108} X = \frac{108}{108} X - \frac{25}{108} X \frac{83}{108} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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A

Two-thirds of a pie is cut into 9 equal slices, and the remaining one-third is cut into 4 equal slices. If a person eats 2 of the larger slices and 1 of the smaller slices, what fraction of the pie remains uneaten?

Explanation	Calculations	Help
$We let the whole pie be X.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Two-thirds of a pie is cut into 9 equal slices" into an expression for one larger slice.$	$\frac{2}{3} X \times \frac{1}{9} = \frac{2}{27} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the remaining one-third is cut into 4 equal slices" into an expression for one smaller slice.$	$\frac{1}{3} X \times \frac{1}{4} = \frac{1}{12} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the larger slices and 1 of the smaller slices" into the sum of the eaten portions.$	$2 \times \frac{2}{27} X + 1 \times \frac{1}{12} X = \frac{4}{27} X + \frac{1}{12} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{4}{27} X = \frac{16}{108} X \frac{1}{12} X = \frac{9}{108} X \frac{16}{108} X + \frac{9}{108} X = \frac{25}{108} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole pie.$	$X - \frac{25}{108} X = \frac{108}{108} X - \frac{25}{108} X \frac{83}{108} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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A