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) $2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}$
=

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Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Subtraction", "Mixed Numbers", "Common Denominator", "Fraction Addition", "Order of Operations" ], "new_concepts": [], "current_concepts": [ "Fraction Subtraction", "Mixed Numbers", "Common Denominator", "Fraction Addition", "Order of Operations" ] } ## 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 $$ \begin{aligned} 3\frac{1}{6} - \frac{2}{3} + \frac{1}{4} &= \frac{19}{6} - \frac{2}{3} + \frac{1}{4} \ &= \frac{38}{12} - \frac{8}{12} + \frac{3}{12} \ &= \frac{30}{12} + \frac{3}{12} \ &= \frac{33}{12} = \frac{11}{4} = 2\frac{3}{4} \end{aligned} $$ ## 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 $$ \begin{aligned} 2\frac{1}{2} - \frac{5}{8} + \frac{1}{4} &= \frac{5}{2} - \frac{5}{8} + \frac{2}{8} \ &= \frac{20}{8} - \frac{5}{8} + \frac{2}{8} \ &= \frac{15}{8} + \frac{2}{8} \ &= \frac{17}{8} = 2\frac{1}{8} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | (1) | $1\frac{1}{2} - \frac{7}{10} + \frac{2}{5}$ | $1\frac{1}{5}$ | | (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) | $2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}$ | $2\frac{1}{8}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Operations" ] }

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Explanation:

Solve Question 1

Solve Question 2

Solve Question 3

Solve Question 4

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)	\(2\frac{1}{2} - \frac{5}{8} + \frac{1}{4}\)	\(2\frac{1}{8}\)