calculate.

(1) $\frac{1}{2} + \frac{1}{3} - \frac{1}{4}$
$= \frac{6}{12} + \frac{\box}{12} - \frac{\box}{12}$
$= \frac{\box}{12}$

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

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

(4) $\frac{1}{3} + \frac{1}{7} - \frac{1}{6}$
$=$

(5) $\frac{1}{2} + \frac{2}{3} - \frac{3}{5}$
$=$

Question

calculate.

(1) $\frac{1}{2} + \frac{1}{3} - \frac{1}{4}$
$= \frac{6}{12} + \frac{\box}{12} - \frac{\box}{12}$
$= \frac{\box}{12}$

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

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

(4) $\frac{1}{3} + \frac{1}{7} - \frac{1}{6}$
$=$

(5) $\frac{1}{2} + \frac{2}{3} - \frac{3}{5}$
$=$

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 $$ \begin{aligned} &\text{(1) } \text{LCD}(2, 3, 4) = 12 \implies \frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{6}{12} + \frac{4}{12} - \frac{3}{12}\ &\text{(2) } \text{LCD}(3, 4, 6) = 12 \implies \frac{1}{3} + \frac{1}{4} - \frac{1}{6} = \frac{4}{12} + \frac{3}{12} - \frac{2}{12}\ &\text{(3) } \text{LCD}(3, 4, 5) = 60 \implies \frac{1}{3} + \frac{1}{4} - \frac{1}{5} = \frac{20}{60} + \frac{15}{60} - \frac{12}{60}\ &\text{(4) } \text{LCD}(3, 7, 6) = 42 \implies \frac{1}{3} + \frac{1}{7} - \frac{1}{6} = \frac{14}{42} + \frac{6}{42} - \frac{7}{42}\ &\text{(5) } \text{LCD}(2, 3, 5) = 30 \implies \frac{1}{2} + \frac{2}{3} - \frac{3}{5} = \frac{15}{30} + \frac{20}{30} - \frac{18}{30} \end{aligned} $$ ## Perform addition and subtraction $$ \begin{aligned} &\text{(1) } \frac{6 + 4 - 3}{12} = \frac{7}{12}\ &\text{(2) } \frac{4 + 3 - 2}{12} = \frac{5}{12}\ &\text{(3) } \frac{20 + 15 - 12}{60} = \frac{23}{60}\ &\text{(4) } \frac{14 + 6 - 7}{42} = \frac{13}{42}\ &\text{(5) } \frac{15 + 20 - 18}{30} = \frac{17}{30} \end{aligned} $$ | No. | Answer | |---|---| | (1) | $\frac{6}{12} + \frac{4}{12} - \frac{3}{12} = \frac{7}{12}$ | | (2) | $\frac{5}{12}$ | | (3) | $\frac{23}{60}$ | | (4) | $\frac{13}{42}$ | | (5) | $\frac{17}{30}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Arithmetic", "Fraction Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Find common denominators

Perform addition and subtraction

Answer:

No.	Answer
(2)	\(\frac{5}{12}\)
(3)	\(\frac{23}{60}\)
(4)	\(\frac{13}{42}\)
(5)	\(\frac{17}{30}\)