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

(2) $\frac{1}{2} - \frac{2}{5} + \frac{3}{8}$
=

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

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

(5) $\frac{3}{8} - \frac{2}{9} + \frac{2}{3}$
=

Question

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

(2) $\frac{1}{2} - \frac{2}{5} + \frac{3}{8}$
=

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

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

(5) $\frac{3}{8} - \frac{2}{9} + \frac{2}{3}$
=

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Subtraction", "Common Denominator", "Fraction Addition", "Order of Operations" ], "new_concepts": [], "current_concepts": [ "Fraction Subtraction", "Common Denominator", "Fraction Addition", "Order of Operations" ] } ## Find common denominators for each expression $$ \begin{aligned} &\text{For (1): } \text{LCM}(6, 2, 8) = 24\ &\text{For (2): } \text{LCM}(2, 5, 8) = 40\ &\text{For (3): } \text{LCM}(3, 2, 3) = 6\ &\text{For (4): } \text{LCM}(8, 3, 6) = 24\ &\text{For (5): } \text{LCM}(8, 9, 3) = 72 \end{aligned} $$ ## Convert fractions to equivalent fractions $$ \begin{aligned} &\text{For (1): } \frac{5}{6} - \frac{1}{2} + \frac{3}{8} = \frac{20}{24} - \frac{12}{24} + \frac{9}{24}\ &\text{For (2): } \frac{1}{2} - \frac{2}{5} + \frac{3}{8} = \frac{20}{40} - \frac{16}{40} + \frac{15}{40}\ &\text{For (3): } \frac{2}{3} - \frac{1}{2} + \frac{1}{3} = \frac{4}{6} - \frac{3}{6} + \frac{2}{6}\ &\text{For (4): } \frac{3}{8} - \frac{1}{3} + \frac{5}{6} = \frac{9}{24} - \frac{8}{24} + \frac{20}{24}\ &\text{For (5): } \frac{3}{8} - \frac{2}{9} + \frac{2}{3} = \frac{27}{72} - \frac{16}{72} + \frac{48}{72} \end{aligned} $$ ## Perform addition and subtraction from left to right $$ \begin{aligned} &\text{For (1): } \frac{20 - 12 + 9}{24} = \frac{17}{24}\ &\text{For (2): } \frac{20 - 16 + 15}{40} = \frac{19}{40}\ &\text{For (3): } \frac{4 - 3 + 2}{6} = \frac{3}{6} = \frac{1}{2}\ &\text{For (4): } \frac{9 - 8 + 20}{24} = \frac{21}{24} = \frac{7}{8}\ &\text{For (5): } \frac{27 - 16 + 48}{72} = \frac{59}{72} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | (1) | $\frac{5}{6} - \frac{1}{2} + \frac{3}{8}$ | $\frac{17}{24}$ | | (2) | $\frac{1}{2} - \frac{2}{5} + \frac{3}{8}$ | $\frac{19}{40}$ | | (3) | $\frac{2}{3} - \frac{1}{2} + \frac{1}{3}$ | $\frac{1}{2}$ | | (4) | $\frac{3}{8} - \frac{1}{3} + \frac{5}{6}$ | $\frac{7}{8}$ | | (5) | $\frac{3}{8} - \frac{2}{9} + \frac{2}{3}$ | $\frac{59}{72}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Operations" ] }

No.	Problem	Answer
(2)	\(\frac{1}{2} - \frac{2}{5} + \frac{3}{8}\)	\(\frac{19}{40}\)
(3)	\(\frac{2}{3} - \frac{1}{2} + \frac{1}{3}\)	\(\frac{1}{2}\)
(4)	\(\frac{3}{8} - \frac{1}{3} + \frac{5}{6}\)	\(\frac{7}{8}\)
(5)	\(\frac{3}{8} - \frac{2}{9} + \frac{2}{3}\)	\(\frac{59}{72}\)

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QUESTION IMAGE

Question

Explanation:

Find common denominators for each expression

Convert fractions to equivalent fractions

Perform addition and subtraction from left to right

Answer: