calculate.

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

$= \frac{\square}{12} + 4\frac{\square}{12} - 3\frac{\square}{12}$

$= 1\frac{\square}{12}$

(2) $\frac{2}{9} + 3\frac{5}{8} - \frac{1}{3}$

$=$

(3) $\frac{7}{9} + 1\frac{1}{3} - \frac{3}{5}$

(4) $3\frac{1}{2} + \frac{7}{10} - \frac{3}{5}$

$=$

(5) $\frac{8}{9} + \frac{3}{4} - \frac{1}{6}$

$=$

Question

calculate.

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

$= \frac{\square}{12} + 4\frac{\square}{12} - 3\frac{\square}{12}$

$= 1\frac{\square}{12}$

(2) $\frac{2}{9} + 3\frac{5}{8} - \frac{1}{3}$

$=$

(3) $\frac{7}{9} + 1\frac{1}{3} - \frac{3}{5}$

(4) $3\frac{1}{2} + \frac{7}{10} - \frac{3}{5}$

$=$

(5) $\frac{8}{9} + \frac{3}{4} - \frac{1}{6}$

$=$

Accepted Answer

{ "quality": "clear", "question_count": 5, "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" ] } ## Find common denominators $$ \begin{aligned} &\text{(1) } \text{LCD}(2, 3, 4) = 12 \ &\text{(2) } \text{LCD}(9, 8, 3) = 72 \ &\text{(3) } \text{LCD}(9, 3, 5) = 45 \ &\text{(4) } \text{LCD}(2, 10, 5) = 10 \ &\text{(5) } \text{LCD}(9, 4, 6) = 36 \end{aligned} $$ ## Convert fractions to common denominators $$ \begin{aligned} &\text{(1) } \frac{1}{2} + 4\frac{2}{3} - 3\frac{3}{4} = \frac{6}{12} + 4\frac{8}{12} - 3\frac{9}{12} \ &\text{(2) } \frac{2}{9} + 3\frac{5}{8} - \frac{1}{3} = \frac{16}{72} + 3\frac{45}{72} - \frac{24}{72} \ &\text{(3) } \frac{7}{9} + 1\frac{1}{3} - \frac{3}{5} = \frac{35}{45} + 1\frac{15}{45} - \frac{27}{45} \ &\text{(4) } 3\frac{1}{2} + \frac{7}{10} - \frac{3}{5} = 3\frac{5}{10} + \frac{7}{10} - \frac{6}{10} \ &\text{(5) } \frac{8}{9} + \frac{3}{4} - \frac{1}{6} = \frac{32}{36} + \frac{27}{36} - \frac{6}{36} \end{aligned} $$ ## Calculate final values $$ \begin{aligned} &\text{(1) } 4\frac{14}{12} - 3\frac{9}{12} = 1\frac{5}{12} \ &\text{(2) } 3\frac{61}{72} - \frac{24}{72} = 3\frac{37}{72} \ &\text{(3) } 1\frac{50}{45} - \frac{27}{45} = 1\frac{23}{45} \ &\text{(4) } 3\frac{12}{10} - \frac{6}{10} = 3\frac{6}{10} = 3\frac{3}{5} \ &\text{(5) } \frac{59}{36} - \frac{6}{36} = \frac{53}{36} = 1\frac{17}{36} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | (1) | $\frac{1}{2} + 4\frac{2}{3} - 3\frac{3}{4}$ | $1\frac{5}{12}$ | | (2) | $\frac{2}{9} + 3\frac{5}{8} - \frac{1}{3}$ | $3\frac{37}{72}$ | | (3) | $\frac{7}{9} + 1\frac{1}{3} - \frac{3}{5}$ | $1\frac{23}{45}$ | | (4) | 3$\frac{1}{2} + \frac{7}{10} - \frac{3}{5}$ | $3\frac{3}{5}$ | | (5) | $\frac{8}{9} + \frac{3}{4} - \frac{1}{6}$ | $1\frac{17}{36}$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Operations" ] }

No.	Problem	Answer
(2)	\(\frac{2}{9} + 3\frac{5}{8} - \frac{1}{3}\)	\(3\frac{37}{72}\)
(3)	\(\frac{7}{9} + 1\frac{1}{3} - \frac{3}{5}\)	\(1\frac{23}{45}\)
(4)	3\(\frac{1}{2} + \frac{7}{10} - \frac{3}{5}\)	\(3\frac{3}{5}\)
(5)	\(\frac{8}{9} + \frac{3}{4} - \frac{1}{6}\)	\(1\frac{17}{36}\)

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QUESTION IMAGE

Question

Explanation:

Find common denominators

Convert fractions to common denominators

Calculate final values

Answer: