Question

(5) \\(2\frac{1}{6} + \frac{1}{4} - \frac{7}{12}\\)

=

(7) \\(5\frac{1}{3} - \frac{3}{4} - \frac{1}{6}\\)

=

(6) \\(2\frac{3}{5} - \frac{1}{10} + \frac{1}{2}\\)

=

(8) \\(15\frac{5}{14} - \frac{1}{2} + \frac{3}{7}\\)

=

Explanation:

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"current_concepts": [
"Fraction Subtraction",
"Mixed Numbers",
"Common Denominator",
"Fraction Addition",
"Order of Operations"
]
}
</pre_analysis>

<reasoning>

Solve Question 5

\[

$$\begin{aligned} 2\frac{1}{6} + \frac{1}{4} - \frac{7}{12} &= \frac{13}{6} + \frac{1}{4} - \frac{7}{12} \\ &= \frac{26}{12} + \frac{3}{12} - \frac{7}{12} \\ &= \frac{29}{12} - \frac{7}{12} \\ &= \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6} \end{aligned}$$

\]

Solve Question 6

\[

$$\begin{aligned} 2\frac{3}{5} - \frac{1}{10} + \frac{1}{2} &= \frac{13}{5} - \frac{1}{10} + \frac{1}{2} \\ &= \frac{26}{10} - \frac{1}{10} + \frac{5}{10} \\ &= \frac{25}{10} + \frac{5}{10} \\ &= \frac{30}{10} = 3 \end{aligned}$$

\]

Solve Question 7

\[

$$\begin{aligned} 5\frac{1}{3} - \frac{3}{4} - \frac{1}{6} &= \frac{16}{3} - \frac{3}{4} - \frac{1}{6} \\ &= \frac{64}{12} - \frac{9}{12} - \frac{2}{12} \\ &= \frac{55}{12} - \frac{2}{12} \\ &= \frac{53}{12} = 4\frac{5}{12} \end{aligned}$$

\]

Solve Question 8

\[

$$\begin{aligned} 15\frac{5}{14} - 5\frac{1}{2} + \frac{3}{7} &= \frac{215}{14} - \frac{11}{2} + \frac{3}{7} \\ &= \frac{215}{14} - \frac{77}{14} + \frac{6}{14} \\ &= \frac{138}{14} + \frac{6}{14} \\ &= \frac{144}{14} = \frac{72}{7} = 10\frac{2}{7} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

\[2\frac{5}{6}\] (or \(\frac{11}{6}\))

Question 6

\[3\]

Question 7

\[4\frac{5}{12}\] (or \(\frac{53}{12}\))

Question 8

\[10\frac{2}{7}\] (or \(\frac{72}{7}\))
</answer>

<post_analysis>
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</post_analysis>

Answer:

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"current_concepts": [
"Fraction Subtraction",
"Mixed Numbers",
"Common Denominator",
"Fraction Addition",
"Order of Operations"
]
}
</pre_analysis>

<reasoning>

Solve Question 5

\[

$$\begin{aligned} 2\frac{1}{6} + \frac{1}{4} - \frac{7}{12} &= \frac{13}{6} + \frac{1}{4} - \frac{7}{12} \\ &= \frac{26}{12} + \frac{3}{12} - \frac{7}{12} \\ &= \frac{29}{12} - \frac{7}{12} \\ &= \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6} \end{aligned}$$

\]

Solve Question 6

\[

$$\begin{aligned} 2\frac{3}{5} - \frac{1}{10} + \frac{1}{2} &= \frac{13}{5} - \frac{1}{10} + \frac{1}{2} \\ &= \frac{26}{10} - \frac{1}{10} + \frac{5}{10} \\ &= \frac{25}{10} + \frac{5}{10} \\ &= \frac{30}{10} = 3 \end{aligned}$$

\]

Solve Question 7

\[

$$\begin{aligned} 5\frac{1}{3} - \frac{3}{4} - \frac{1}{6} &= \frac{16}{3} - \frac{3}{4} - \frac{1}{6} \\ &= \frac{64}{12} - \frac{9}{12} - \frac{2}{12} \\ &= \frac{55}{12} - \frac{2}{12} \\ &= \frac{53}{12} = 4\frac{5}{12} \end{aligned}$$

\]

Solve Question 8

\[

$$\begin{aligned} 15\frac{5}{14} - 5\frac{1}{2} + \frac{3}{7} &= \frac{215}{14} - \frac{11}{2} + \frac{3}{7} \\ &= \frac{215}{14} - \frac{77}{14} + \frac{6}{14} \\ &= \frac{138}{14} + \frac{6}{14} \\ &= \frac{144}{14} = \frac{72}{7} = 10\frac{2}{7} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

\[2\frac{5}{6}\] (or \(\frac{11}{6}\))

Question 6

\[3\]

Question 7

\[4\frac{5}{12}\] (or \(\frac{53}{12}\))

Question 8

\[10\frac{2}{7}\] (or \(\frac{72}{7}\))
</answer>

<post_analysis>
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"knowledge_point": [
"Mathematics",
"Arithmetic",
"Fraction Operations"
]
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