Question

calculate.
(1) \\(3\frac{1}{6} - \frac{3}{4} + \frac{7}{8}\\)
=
(2) \\(2\frac{1}{12} - 1\frac{1}{2} + \frac{3}{4}\\)
=
(3) \\(2\frac{1}{6} - \frac{7}{12} + \frac{1}{4}\\)
=
(4) \\(1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}\\)
=

Explanation:

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<reasoning>

Convert mixed numbers to improper fractions

\[

$$\begin{aligned} \text{(1) } 3\frac{1}{6} &= \frac{19}{6} \\ \text{(2) } 2\frac{1}{12} &= \frac{25}{12}, \quad 1\frac{1}{2} = \frac{3}{2} \\ \text{(3) } 2\frac{1}{6} &= \frac{13}{6} \\ \text{(4) } 1\frac{8}{15} &= \frac{23}{15} \end{aligned}$$

\]

Find common denominators and calculate

\[

$$\begin{aligned} \text{(1) } \frac{19}{6} - \frac{3}{4} + \frac{7}{8} &= \frac{76}{24} - \frac{18}{24} + \frac{21}{24} = \frac{79}{24} = 3\frac{7}{24} \\ \text{(2) } \frac{25}{12} - \frac{3}{2} + \frac{3}{4} &= \frac{25}{12} - \frac{18}{12} + \frac{9}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3} \\ \text{(3) } \frac{13}{6} - \frac{7}{12} + \frac{1}{4} &= \frac{26}{12} - \frac{7}{12} + \frac{3}{12} = \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6} \\ \text{(4) } \frac{23}{15} - \frac{4}{5} + \frac{1}{3} &= \frac{23}{15} - \frac{12}{15} + \frac{5}{15} = \frac{16}{15} = 1\frac{1}{15} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Problem	Answer
(2)	\(2\frac{1}{12} - 1\frac{1}{2} + \frac{3}{4}\)	\(1\frac{1}{3}\)
(3)	\(2\frac{1}{6} - \frac{7}{12} + \frac{1}{4}\)	\(1\frac{5}{6}\)
(4)	\(1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}\)	\(1\frac{1}{15}\)

</answer>

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Answer:

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<reasoning>

Convert mixed numbers to improper fractions

\[

$$\begin{aligned} \text{(1) } 3\frac{1}{6} &= \frac{19}{6} \\ \text{(2) } 2\frac{1}{12} &= \frac{25}{12}, \quad 1\frac{1}{2} = \frac{3}{2} \\ \text{(3) } 2\frac{1}{6} &= \frac{13}{6} \\ \text{(4) } 1\frac{8}{15} &= \frac{23}{15} \end{aligned}$$

\]

Find common denominators and calculate

\[

$$\begin{aligned} \text{(1) } \frac{19}{6} - \frac{3}{4} + \frac{7}{8} &= \frac{76}{24} - \frac{18}{24} + \frac{21}{24} = \frac{79}{24} = 3\frac{7}{24} \\ \text{(2) } \frac{25}{12} - \frac{3}{2} + \frac{3}{4} &= \frac{25}{12} - \frac{18}{12} + \frac{9}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3} \\ \text{(3) } \frac{13}{6} - \frac{7}{12} + \frac{1}{4} &= \frac{26}{12} - \frac{7}{12} + \frac{3}{12} = \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6} \\ \text{(4) } \frac{23}{15} - \frac{4}{5} + \frac{1}{3} &= \frac{23}{15} - \frac{12}{15} + \frac{5}{15} = \frac{16}{15} = 1\frac{1}{15} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Problem	Answer
(2)	\(2\frac{1}{12} - 1\frac{1}{2} + \frac{3}{4}\)	\(1\frac{1}{3}\)
(3)	\(2\frac{1}{6} - \frac{7}{12} + \frac{1}{4}\)	\(1\frac{5}{6}\)
(4)	\(1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}\)	\(1\frac{1}{15}\)

</answer>

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