Question

calculate.
(1) \\(1\frac{1}{2} - \frac{7}{10} + \frac{2}{5}\\)
(2) \\(3\frac{1}{6} - \frac{2}{3} + \frac{1}{4}\\)
(3) \\(1\frac{7}{15} - \frac{2}{5} + \frac{2}{3}\\)
(4) \\(2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}\\)

Explanation:

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<reasoning>

Solve Question 1

\[

$$\begin{aligned} 1\frac{1}{2} - \frac{7}{10} + \frac{2}{5} &= \frac{3}{2} - \frac{7}{10} + \frac{4}{10} \\ &= \frac{15}{10} - \frac{7}{10} + \frac{4}{10} \\ &= \frac{8}{10} + \frac{4}{10} \\ &= \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5} \end{aligned}$$

\]

Solve Question 2

\[

$$\begin{aligned} 3\frac{1}{6} - \frac{2}{3} + \frac{1}{4} &= \frac{19}{6} - \frac{4}{6} + \frac{1}{4} \\ &= \frac{15}{6} + \frac{1}{4} \\ &= \frac{5}{2} + \frac{1}{4} \\ &= \frac{10}{4} + \frac{1}{4} = \frac{11}{4} = 2\frac{3}{4} \end{aligned}$$

\]

Solve Question 3

\[

$$\begin{aligned} 1\frac{7}{15} - \frac{2}{5} + \frac{2}{3} &= \frac{22}{15} - \frac{6}{15} + \frac{10}{15} \\ &= \frac{16}{15} + \frac{10}{15} \\ &= \frac{26}{15} = 1\frac{11}{15} \end{aligned}$$

\]

Solve Question 4

\[

$$\begin{aligned} 2\frac{1}{2} - \frac{5}{8} + \frac{1}{4} &= \frac{5}{2} - \frac{5}{8} + \frac{2}{8} \\ &= \frac{20}{8} - \frac{5}{8} + \frac{2}{8} \\ &= \frac{15}{8} + \frac{2}{8} \\ &= \frac{17}{8} = 2\frac{1}{8} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Problem	Answer
(2)	\(3\frac{1}{6} - \frac{2}{3} + \frac{1}{4}\)	\(2\frac{3}{4}\)
(3)	\(1\frac{7}{15} - \frac{2}{5} + \frac{2}{3}\)	\(1\frac{11}{15}\)
(4)	\(2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}\)	\(2\frac{1}{8}\)

</answer>

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Answer:

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<reasoning>

Solve Question 1

\[

$$\begin{aligned} 1\frac{1}{2} - \frac{7}{10} + \frac{2}{5} &= \frac{3}{2} - \frac{7}{10} + \frac{4}{10} \\ &= \frac{15}{10} - \frac{7}{10} + \frac{4}{10} \\ &= \frac{8}{10} + \frac{4}{10} \\ &= \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5} \end{aligned}$$

\]

Solve Question 2

\[

$$\begin{aligned} 3\frac{1}{6} - \frac{2}{3} + \frac{1}{4} &= \frac{19}{6} - \frac{4}{6} + \frac{1}{4} \\ &= \frac{15}{6} + \frac{1}{4} \\ &= \frac{5}{2} + \frac{1}{4} \\ &= \frac{10}{4} + \frac{1}{4} = \frac{11}{4} = 2\frac{3}{4} \end{aligned}$$

\]

Solve Question 3

\[

$$\begin{aligned} 1\frac{7}{15} - \frac{2}{5} + \frac{2}{3} &= \frac{22}{15} - \frac{6}{15} + \frac{10}{15} \\ &= \frac{16}{15} + \frac{10}{15} \\ &= \frac{26}{15} = 1\frac{11}{15} \end{aligned}$$

\]

Solve Question 4

\[

$$\begin{aligned} 2\frac{1}{2} - \frac{5}{8} + \frac{1}{4} &= \frac{5}{2} - \frac{5}{8} + \frac{2}{8} \\ &= \frac{20}{8} - \frac{5}{8} + \frac{2}{8} \\ &= \frac{15}{8} + \frac{2}{8} \\ &= \frac{17}{8} = 2\frac{1}{8} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Problem	Answer
(2)	\(3\frac{1}{6} - \frac{2}{3} + \frac{1}{4}\)	\(2\frac{3}{4}\)
(3)	\(1\frac{7}{15} - \frac{2}{5} + \frac{2}{3}\)	\(1\frac{11}{15}\)
(4)	\(2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}\)	\(2\frac{1}{8}\)

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