Question

1. calculate.

(1) \\(9\frac{2}{7} - \frac{3}{7} + \frac{4}{7}\\)
=

(2) \\(9\frac{2}{7} + \frac{4}{7} - \frac{3}{7}\\)
=

(3) \\(3\frac{1}{7} - \frac{3}{7} + \frac{5}{7}\\)
=

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

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

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

1. fill in the blanks. from the above, the pairs of problems with the same answer are (1) & , (3) & , and (5) & .

Explanation:

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<reasoning>

Calculate expressions (1) to (6)

\[

$$\begin{aligned} (1)\quad & 9\frac{2}{7} - \frac{3}{7} + \frac{4}{7} = 8\frac{9}{7} - \frac{3}{7} + \frac{4}{7} = 8\frac{6}{7} + \frac{4}{7} = 8\frac{10}{7} = 9\frac{3}{7} \\ (2)\quad & 9\frac{2}{7} + \frac{4}{7} - \frac{3}{7} = 9\frac{6}{7} - \frac{3}{7} = 9\frac{3}{7} \\ (3)\quad & 3\frac{1}{7} - \frac{3}{7} + \frac{5}{7} = 2\frac{8}{7} - \frac{3}{7} + \frac{5}{7} = 2\frac{5}{7} + \frac{5}{7} = 2\frac{10}{7} = 3\frac{3}{7} \\ (4)\quad & 3\frac{1}{7} + \frac{5}{7} - \frac{3}{7} = 3\frac{6}{7} - \frac{3}{7} = 3\frac{3}{7} \\ (5)\quad & 2\frac{1}{7} + \frac{5}{7} - 1\frac{4}{7} = 2\frac{6}{7} - 1\frac{4}{7} = 1\frac{2}{7} \\ (6)\quad & 2\frac{1}{7} - 1\frac{4}{7} + \frac{5}{7} = 1\frac{8}{7} - 1\frac{4}{7} + \frac{5}{7} = \frac{4}{7} + \frac{5}{7} = \frac{9}{7} = 1\frac{2}{7} \end{aligned}$$

\]

Match pairs with identical answers

\[

$$\begin{aligned} \text{Answer for (1) and (2): } & 9\frac{3}{7} \\ \text{Answer for (3) and (4): } & 3\frac{3}{7} \\ \text{Answer for (5) and (6): } & 1\frac{2}{7} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(1) \(9\frac{2}{7} - \frac{3}{7} + \frac{4}{7} = 9\frac{3}{7}\)

(2) \(9\frac{2}{7} + \frac{4}{7} - \frac{3}{7} = 9\frac{3}{7}\)

(3) \(3\frac{1}{7} - \frac{3}{7} + \frac{5}{7} = 3\frac{3}{7}\)

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

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

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

Question 2

From the above, the pairs of problems with the same answer are (1) & <blank>(2)</blank>, (3) & <blank>(4)</blank>, and (5) & <blank>(6)</blank>.
</answer>

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Answer:

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<reasoning>

Calculate expressions (1) to (6)

\[

$$\begin{aligned} (1)\quad & 9\frac{2}{7} - \frac{3}{7} + \frac{4}{7} = 8\frac{9}{7} - \frac{3}{7} + \frac{4}{7} = 8\frac{6}{7} + \frac{4}{7} = 8\frac{10}{7} = 9\frac{3}{7} \\ (2)\quad & 9\frac{2}{7} + \frac{4}{7} - \frac{3}{7} = 9\frac{6}{7} - \frac{3}{7} = 9\frac{3}{7} \\ (3)\quad & 3\frac{1}{7} - \frac{3}{7} + \frac{5}{7} = 2\frac{8}{7} - \frac{3}{7} + \frac{5}{7} = 2\frac{5}{7} + \frac{5}{7} = 2\frac{10}{7} = 3\frac{3}{7} \\ (4)\quad & 3\frac{1}{7} + \frac{5}{7} - \frac{3}{7} = 3\frac{6}{7} - \frac{3}{7} = 3\frac{3}{7} \\ (5)\quad & 2\frac{1}{7} + \frac{5}{7} - 1\frac{4}{7} = 2\frac{6}{7} - 1\frac{4}{7} = 1\frac{2}{7} \\ (6)\quad & 2\frac{1}{7} - 1\frac{4}{7} + \frac{5}{7} = 1\frac{8}{7} - 1\frac{4}{7} + \frac{5}{7} = \frac{4}{7} + \frac{5}{7} = \frac{9}{7} = 1\frac{2}{7} \end{aligned}$$

\]

Match pairs with identical answers

\[

$$\begin{aligned} \text{Answer for (1) and (2): } & 9\frac{3}{7} \\ \text{Answer for (3) and (4): } & 3\frac{3}{7} \\ \text{Answer for (5) and (6): } & 1\frac{2}{7} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(1) \(9\frac{2}{7} - \frac{3}{7} + \frac{4}{7} = 9\frac{3}{7}\)

(2) \(9\frac{2}{7} + \frac{4}{7} - \frac{3}{7} = 9\frac{3}{7}\)

(3) \(3\frac{1}{7} - \frac{3}{7} + \frac{5}{7} = 3\frac{3}{7}\)

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

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

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

Question 2

From the above, the pairs of problems with the same answer are (1) & <blank>(2)</blank>, (3) & <blank>(4)</blank>, and (5) & <blank>(6)</blank>.
</answer>

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