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

Question

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Addition", "Fraction Subtraction", "Common Denominator" ], "new_concepts": [], "current_concepts": [ "Fraction Addition", "Fraction Subtraction", "Common Denominator" ] } ## Find common denominators for each expression $$ \begin{aligned} &\text{(1) } \text{LCM}(6, 4, 5) = 60 \ &\text{(2) } \text{LCM}(3, 5, 6) = 30 \ &\text{(3) } \text{LCM}(7, 2, 4) = 28 \ &\text{(4) } \text{LCM}(8, 4, 6) = 24 \ &\text{(5) } \text{LCM}(7, 3, 6) = 42 \end{aligned} $$ ## Convert fractions to equivalent fractions $$ \begin{aligned} &\text{(1) } \frac{10}{60} + \frac{15}{60} - \frac{12}{60} \ &\text{(2) } \frac{20}{30} + \frac{6}{30} - \frac{5}{30} \ &\text{(3) } \frac{16}{28} + \frac{14}{28} - \frac{7}{28} \ &\text{(4) } \frac{9}{24} + \frac{6}{24} - \frac{4}{24} \ &\text{(5) } \frac{24}{42} + \frac{14}{42} - \frac{7}{42} \end{aligned} $$ ## Calculate final values $$ \begin{aligned} &\text{(1) } \frac{10 + 15 - 12}{60} = \frac{13}{60} \ &\text{(2) } \frac{20 + 6 - 5}{30} = \frac{21}{30} = \frac{7}{10} \ &\text{(3) } \frac{16 + 14 - 7}{28} = \frac{23}{28} \ &\text{(4) } \frac{9 + 6 - 4}{24} = \frac{11}{24} \ &\text{(5) } \frac{24 + 14 - 7}{42} = \frac{31}{42} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | (1) | $\frac{1}{6} + \frac{1}{4} - \frac{1}{5}$ | $\frac{13}{60}$ | | (2) | $\frac{2}{3} + \frac{1}{5} - \frac{1}{6}$ | $\frac{7}{10}$ | | (3) | $\frac{4}{7} + \frac{1}{2} - \frac{1}{4}$ | $\frac{23}{28}$ | | (4) | $\frac{3}{8} + \frac{1}{4} - \frac{1}{6}$ | $\frac{11}{24}$ | | (5) | $\frac{4}{7} + \frac{1}{3} - \frac{1}{6}$ | $\frac{31}{42}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Addition" ] }

No.	Problem	Answer
(2)	\(\frac{2}{3} + \frac{1}{5} - \frac{1}{6}\)	\(\frac{7}{10}\)
(3)	\(\frac{4}{7} + \frac{1}{2} - \frac{1}{4}\)	\(\frac{23}{28}\)
(4)	\(\frac{3}{8} + \frac{1}{4} - \frac{1}{6}\)	\(\frac{11}{24}\)
(5)	\(\frac{4}{7} + \frac{1}{3} - \frac{1}{6}\)	\(\frac{31}{42}\)

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QUESTION IMAGE

Question

Explanation:

Find common denominators for each expression

Convert fractions to equivalent fractions

Calculate final values

Answer: