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Question

Half of a large chocolate bar is divided into 5 equal pieces, and the other half is divided into 10 equal pieces. If a person eats 2 of the larger pieces and 3 of the smaller pieces, what fraction of the chocolate bar remains uneaten?

Answer Choices

A. $\frac{11}{20}$
B. $\frac{13}{20}$
C. $\frac{9}{20}$
D. $\frac{1}{2}$
E. $\frac{3}{4}$

Steps

Explanation	Calculations	Help
$We let X represent the whole chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Half of a large chocolate bar is divided into 5 equal pieces" into the size of one larger piece.$	$\frac{1}{2} X \times \frac{1}{5} = \frac{1}{10} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the other half is divided into 10 equal pieces" into the size of one smaller piece.$	$\frac{1}{2} X \times \frac{1}{10} = \frac{1}{20} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the larger pieces and 3 of the smaller pieces" into the total eaten amount.$	$2 \times \frac{1}{10} X + 3 \times \frac{1}{20} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the portion from the larger pieces eaten by canceling common factors.$	$2 \times \frac{1}{10} X = \frac{2}{2 \times 5} X = \frac{1}{5} X$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We convert each eaten portion to a common denominator and add.$	$3 \times \frac{1}{20} X = \frac{3}{20} X \frac{1}{5} X = \frac{4}{20} X \frac{4}{20} X + \frac{3}{20} X = \frac{7}{20} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole bar.$	$X - \frac{7}{20} X = \frac{20}{20} X - \frac{7}{20} X \frac{20}{20} X - \frac{7}{20} X = \frac{13}{20} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

B

Question

Half of a large chocolate bar is divided into 5 equal pieces, and the other half is divided into 10 equal pieces. If a person eats 2 of the larger pieces and 3 of the smaller pieces, what fraction of the chocolate bar remains uneaten?

Answer Choices

A. $\frac{11}{20}$
B. $\frac{13}{20}$
C. $\frac{9}{20}$
D. $\frac{1}{2}$
E. $\frac{3}{4}$

Steps

Explanation	Calculations	Help
$We let X represent the whole chocolate bar.$	$X = 1$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Half of a large chocolate bar is divided into 5 equal pieces" into the size of one larger piece.$	$\frac{1}{2} X \times \frac{1}{5} = \frac{1}{10} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the other half is divided into 10 equal pieces" into the size of one smaller piece.$	$\frac{1}{2} X \times \frac{1}{10} = \frac{1}{20} X$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "eats 2 of the larger pieces and 3 of the smaller pieces" into the total eaten amount.$	$2 \times \frac{1}{10} X + 3 \times \frac{1}{20} X$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We simplify the portion from the larger pieces eaten by canceling common factors.$	$2 \times \frac{1}{10} X = \frac{2}{2 \times 5} X = \frac{1}{5} X$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We convert each eaten portion to a common denominator and add.$	$3 \times \frac{1}{20} X = \frac{3}{20} X \frac{1}{5} X = \frac{4}{20} X \frac{4}{20} X + \frac{3}{20} X = \frac{7}{20} X$	Theory & Tactics Method Card FDPR0-B Click to view full details
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole bar.$	$X - \frac{7}{20} X = \frac{20}{20} X - \frac{7}{20} X \frac{20}{20} X - \frac{7}{20} X = \frac{13}{20} X$	Theory & Tactics Method Card TRANS1-D Click to view full details

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Final Answer

B