A chocolate bar is divided such that $\frac{1}{4}$ of the bar is broken into 8 equal pieces and the remaining $\frac{3}{4}$ is broken into 12 equal pieces. If a child eats 2 of the larger pieces and 3 of the smaller pieces, what fraction of the chocolate bar remains uneaten?

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Question

A chocolate bar is divided such that of the bar is broken into 8 equal pieces and the remaining is broken into 12 equal pieces. If a child eats 2 of the larger pieces and 3 of the smaller pieces, what fraction of the chocolate bar remains uneaten?

Answer Choices

A. $\frac{7}{32}$
B. $\frac{11}{32}$
C. $\frac{25}{32}$
D. $\frac{21}{32}$
E. $\frac{27}{32}$

Steps

Explanation	Calculations	Help
$We let X represent the entire chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "1/4 of the bar is broken into 8 equal pieces" into the size of one smaller piece.$	$\frac{1}{4} X \times \frac{1}{8} = \frac{1}{32} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the remaining 3/4 is broken into 12 equal pieces" into the size of one larger piece.$	$\frac{3}{4} X \times \frac{1}{12} = \frac{1}{16} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eat 2 of the larger pieces and 3 of the smaller pieces" into the total amount eaten.$	$2 \times \frac{1}{16} X + 3 \times \frac{1}{32} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the portion eaten from the larger pieces.$	$2 \times \frac{1}{16} X = \frac{2}{16} X = \frac{1}{8} X$	Theory & Tactics Method Card FDPR0-E Click to view full details
$We simplify the portion eaten from the smaller pieces.$	$3 \times \frac{1}{32} X = \frac{3}{32} X$	Theory & Tactics Method Card FDPR0-E Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{1}{8} X = \frac{4}{32} X \frac{4}{32} X + \frac{3}{32} X = \frac{7}{32} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole bar.$	$X - \frac{7}{32} X = \frac{32}{32} X - \frac{7}{32} X = \frac{25}{32} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

C

Question

A chocolate bar is divided such that of the bar is broken into 8 equal pieces and the remaining is broken into 12 equal pieces. If a child eats 2 of the larger pieces and 3 of the smaller pieces, what fraction of the chocolate bar remains uneaten?

Answer Choices

A. $\frac{7}{32}$
B. $\frac{11}{32}$
C. $\frac{25}{32}$
D. $\frac{21}{32}$
E. $\frac{27}{32}$

Steps

Explanation	Calculations	Help
$We let X represent the entire chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "1/4 of the bar is broken into 8 equal pieces" into the size of one smaller piece.$	$\frac{1}{4} X \times \frac{1}{8} = \frac{1}{32} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the remaining 3/4 is broken into 12 equal pieces" into the size of one larger piece.$	$\frac{3}{4} X \times \frac{1}{12} = \frac{1}{16} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eat 2 of the larger pieces and 3 of the smaller pieces" into the total amount eaten.$	$2 \times \frac{1}{16} X + 3 \times \frac{1}{32} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the portion eaten from the larger pieces.$	$2 \times \frac{1}{16} X = \frac{2}{16} X = \frac{1}{8} X$	Theory & Tactics Method Card FDPR0-E Click to view full details
$We simplify the portion eaten from the smaller pieces.$	$3 \times \frac{1}{32} X = \frac{3}{32} X$	Theory & Tactics Method Card FDPR0-E Click to view full details
$We convert to a common denominator and add the eaten portions.$	$\frac{1}{8} X = \frac{4}{32} X \frac{4}{32} X + \frac{3}{32} X = \frac{7}{32} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole bar.$	$X - \frac{7}{32} X = \frac{32}{32} X - \frac{7}{32} X = \frac{25}{32} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

C