The answer is C: [tex]10\text{ }^1/_2[/tex]. Here are the details:
[tex]\text{Equation:}\\ 6\text{ }^1/_3+10\text{ }^1/_2\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Start with the integers.}\\ 6+10=16\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{...then with the fractions, but rewrite them first to make it easier.}\\ ^1/_3+\text{ }^1/_2\stackrel{\text{rewrite}}{\to}\text{ }^2/_6+\text{ }^3/_6=\text{ }^5/_6\stackrel{?}{=}26\text{ }^1/_6\\
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\text{Add 'em up!}\\
16\text{ }^5/_6[/tex]
[tex]\text{Equation:}\\
16\text{ }^5/_6+3\text{ }^5/_6\stackrel{?}{=}26\text{ }^1/_6\\
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\text{Start with the integers.}\\
16+3=19\stackrel{?}{=}26\text{ }^1/_6\\
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\text{...then with the fractions, but rewrite them first to make it easier.}\\
^5/_6+\text{ }^5/_6=\text{ }^{10}/_6\stackrel{\text{rewrite}}{\to}\text{ }^5/_3\stackrel{\text{rewrite}}{\to}1\text{ }^2/_3\stackrel{?}{=}26\text{ }^1/_6\\
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\text{Add 'em up!}\\
20\text{ }^2/_3[/tex]
[tex]\text{Last equation:}\\ 20\text{ }^2/_3+5\text{ }^1/_2\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{Start with the integers.}\\ 20+5=25\stackrel{?}{=}26\text{ }^1/_6\\ \\ \text{...then with the fractions, but rewrite them first to make it easier.}\\ ^2/_3+\text{ }^1/_2\stackrel{\text{rewrite}}{\to}\text{ }^4/_6+\text{ }^3/_6=\text{ }^7/_6\stackrel{\text{rewrite}}{\to}1\text{ }^1/_6\stackrel{?}{=}26\text{ }^1/_6\\
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\text{Add the integer and fraction together.}\\
25+1\text{ }^1/_6\stackrel{?}{=}26\text{ }^1/_6[/tex]
[tex]26\text{ }^1/_6\stackrel{\checkmark}{=}26\text{ }^1/_6[/tex]
