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) $1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}$
=

Question

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" ] } ## 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 $$ \begin{aligned} \text{(1) } \frac{19}{6} - \frac{3}{4} + \frac{7}{8} &= \frac{76}{24} - \frac{18}{24} + \frac{21}{24} = \frac{79}{24} = 3\frac{7}{24} \ \text{(2) } \frac{25}{12} - \frac{3}{2} + \frac{3}{4} &= \frac{25}{12} - \frac{18}{12} + \frac{9}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3} \ \text{(3) } \frac{13}{6} - \frac{7}{12} + \frac{1}{4} &= \frac{26}{12} - \frac{7}{12} + \frac{3}{12} = \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6} \ \text{(4) } \frac{23}{15} - \frac{4}{5} + \frac{1}{3} &= \frac{23}{15} - \frac{12}{15} + \frac{5}{15} = \frac{16}{15} = 1\frac{1}{15} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | (1) | $3\frac{1}{6} - \frac{3}{4} + \frac{7}{8}$ | $3\frac{7}{24}$ | | (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) | $1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}$ | $1\frac{1}{15}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Mixed Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Convert mixed numbers to improper fractions

Find common denominators and calculate

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)	\(1\frac{8}{15} - \frac{4}{5} + \frac{1}{3}\)	\(1\frac{1}{15}\)