Question

calculate.

(1) \\(2\frac{1}{3} - 1\frac{1}{2} - \frac{7}{10}\\)
=

(2)* \\(3\frac{1}{10} - \frac{4}{5} - \frac{1}{2}\\)
=

(3) \\(3\frac{1}{6} - \frac{2}{3} - \frac{3}{4}\\)
=

(4) \\(8\frac{1}{15} - \frac{5}{6} - \frac{9}{10}\\)
=

Explanation:

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<reasoning>

Solve Question 1

\[

$$\begin{aligned} 2\frac{1}{3} - 1\frac{1}{2} - \frac{7}{10} &= \frac{7}{3} - \frac{3}{2} - \frac{7}{10} \\ &= \frac{70}{30} - \frac{45}{30} - \frac{21}{30} \\ &= \frac{25}{30} - \frac{21}{30} = \frac{4}{30} = \frac{2}{15} \end{aligned}$$

\]

Solve Question 2

\[

$$\begin{aligned} 3\frac{1}{10} - \frac{4}{5} - \frac{1}{2} &= \frac{31}{10} - \frac{8}{10} - \frac{5}{10} \\ &= \frac{23}{10} - \frac{5}{10} \\ &= \frac{18}{10} = \frac{9}{5} = 1\frac{4}{5} \end{aligned}$$

\]

Solve Question 3

\[

$$\begin{aligned} 3\frac{1}{6} - \frac{2}{3} - \frac{3}{4} &= \frac{19}{6} - \frac{4}{6} - \frac{3}{4} \\ &= \frac{15}{6} - \frac{3}{4} = \frac{5}{2} - \frac{3}{4} \\ &= \frac{10}{4} - \frac{3}{4} = \frac{7}{4} = 1\frac{3}{4} \end{aligned}$$

\]

Solve Question 4

\[

$$\begin{aligned} 8\frac{1}{15} - \frac{5}{6} - \frac{9}{10} &= \frac{121}{15} - \frac{25}{30} - \frac{27}{30} \\ &= \frac{242}{30} - \frac{25}{30} - \frac{27}{30} \\ &= \frac{217}{30} - \frac{27}{30} = \frac{190}{30} = \frac{19}{3} = 6\frac{1}{3} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\[
\frac{2}{15}
\]

Question 2

\[
1\frac{4}{5}
\]

Question 3

\[
1\frac{3}{4}
\]

Question 4

\[
6\frac{1}{3}
\]
</answer>

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Answer:

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"Fraction Subtraction",
"Mixed Numbers",
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</pre_analysis>

<reasoning>

Solve Question 1

\[

$$\begin{aligned} 2\frac{1}{3} - 1\frac{1}{2} - \frac{7}{10} &= \frac{7}{3} - \frac{3}{2} - \frac{7}{10} \\ &= \frac{70}{30} - \frac{45}{30} - \frac{21}{30} \\ &= \frac{25}{30} - \frac{21}{30} = \frac{4}{30} = \frac{2}{15} \end{aligned}$$

\]

Solve Question 2

\[

$$\begin{aligned} 3\frac{1}{10} - \frac{4}{5} - \frac{1}{2} &= \frac{31}{10} - \frac{8}{10} - \frac{5}{10} \\ &= \frac{23}{10} - \frac{5}{10} \\ &= \frac{18}{10} = \frac{9}{5} = 1\frac{4}{5} \end{aligned}$$

\]

Solve Question 3

\[

$$\begin{aligned} 3\frac{1}{6} - \frac{2}{3} - \frac{3}{4} &= \frac{19}{6} - \frac{4}{6} - \frac{3}{4} \\ &= \frac{15}{6} - \frac{3}{4} = \frac{5}{2} - \frac{3}{4} \\ &= \frac{10}{4} - \frac{3}{4} = \frac{7}{4} = 1\frac{3}{4} \end{aligned}$$

\]

Solve Question 4

\[

$$\begin{aligned} 8\frac{1}{15} - \frac{5}{6} - \frac{9}{10} &= \frac{121}{15} - \frac{25}{30} - \frac{27}{30} \\ &= \frac{242}{30} - \frac{25}{30} - \frac{27}{30} \\ &= \frac{217}{30} - \frac{27}{30} = \frac{190}{30} = \frac{19}{3} = 6\frac{1}{3} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\[
\frac{2}{15}
\]

Question 2

\[
1\frac{4}{5}
\]

Question 3

\[
1\frac{3}{4}
\]

Question 4

\[
6\frac{1}{3}
\]
</answer>

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