calculate.
(1) $2\frac{1}{2} - \frac{2}{3} - \frac{1}{6}$
$= 2\frac{\square}{6} - \frac{4}{6} - \frac{1}{6}$
$= 1\frac{\square}{6} - \frac{4}{6} - \frac{1}{6}$
$=$

(2) $2\frac{1}{9} - \frac{1}{2} - \frac{1}{3}$
$=$

(3) $3\frac{2}{3} - \frac{5}{6} - \frac{1}{2}$
$=$

(4) $2\frac{7}{9} - \frac{1}{2} - \frac{2}{3}$
$=$

Question

calculate.
(1) $2\frac{1}{2} - \frac{2}{3} - \frac{1}{6}$
$= 2\frac{\square}{6} - \frac{4}{6} - \frac{1}{6}$
$= 1\frac{\square}{6} - \frac{4}{6} - \frac{1}{6}$
$=$

(2) $2\frac{1}{9} - \frac{1}{2} - \frac{1}{3}$
$=$

(3) $3\frac{2}{3} - \frac{5}{6} - \frac{1}{2}$
$=$

(4) $2\frac{7}{9} - \frac{1}{2} - \frac{2}{3}$
$=$

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Subtraction", "Mixed Numbers", "Common Denominator" ], "new_concepts": [], "current_concepts": [ "Fraction Subtraction", "Mixed Numbers", "Common Denominator" ] } ## Find common denominators $$ \begin{aligned} (1)&\quad 2\frac{1}{2} - \frac{2}{3} - \frac{1}{6} = 2\frac{3}{6} - \frac{4}{6} - \frac{1}{6} \ (2)&\quad 2\frac{1}{9} - \frac{1}{2} - \frac{1}{3} = 2\frac{2}{18} - \frac{9}{18} - \frac{6}{18} \ (3)&\quad 3\frac{2}{3} - \frac{5}{6} - \frac{1}{2} = 3\frac{4}{6} - \frac{5}{6} - \frac{3}{6} \ (4)&\quad 2\frac{7}{9} - \frac{1}{2} - \frac{2}{3} = 2\frac{14}{18} - \frac{9}{18} - \frac{12}{18} \end{aligned} $$ ## Regroup mixed numbers where necessary $$ \begin{aligned} (1)&\quad 2\frac{3}{6} - \frac{4}{6} - \frac{1}{6} = 1\frac{9}{6} - \frac{4}{6} - \frac{1}{6} \ (2)&\quad 2\frac{2}{18} - \frac{9}{18} - \frac{6}{18} = 1\frac{20}{18} - \frac{9}{18} - \frac{6}{18} \ (3)&\quad 3\frac{4}{6} - \frac{5}{6} - \frac{3}{6} = 2\frac{10}{6} - \frac{5}{6} - \frac{3}{6} \ (4)&\quad 2\frac{14}{18} - \frac{9}{18} - \frac{12}{18} = 1\frac{32}{18} - \frac{9}{18} - \frac{12}{18} \end{aligned} $$ ## Subtract and simplify $$ \begin{aligned} (1)&\quad 1\frac{9}{6} - \frac{4}{6} - \frac{1}{6} = 1\frac{4}{6} = 1\frac{2}{3} \ (2)&\quad 1\frac{20}{18} - \frac{9}{18} - \frac{6}{18} = 1\frac{5}{18} \ (3)&\quad 2\frac{10}{6} - \frac{5}{6} - \frac{3}{6} = 2\frac{2}{6} = 2\frac{1}{3} \ (4)&\quad 1\frac{32}{18} - \frac{9}{18} - \frac{12}{18} = 1\frac{11}{18} \end{aligned} $$ ## Question 1 $$ \begin{aligned} &2\frac{1}{2} - \frac{2}{3} - \frac{1}{6} \ &= 2\frac{3}{6} - \frac{4}{6} - \frac{1}{6} \ &= 1\frac{9}{6} - \frac{4}{6} - \frac{1}{6} \ &= 1\frac{2}{3} \end{aligned} $$ ## Question 2 $$ \begin{aligned} &2\frac{1}{9} - \frac{1}{2} - \frac{1}{3} \ &= 2\frac{2}{18} - \frac{9}{18} - \frac{6}{18} \ &= 1\frac{20}{18} - \frac{9}{18} - \frac{6}{18} \ &= 1\frac{5}{18} \end{aligned} $$ ## Question 3 $$ \begin{aligned} &3\frac{2}{3} - \frac{5}{6} - \frac{1}{2} \ &= 3\frac{4}{6} - \frac{5}{6} - \frac{3}{6} \ &= 2\frac{10}{6} - \frac{5}{6} - \frac{3}{6} \ &= 2\frac{1}{3} \end{aligned} $$ ## Question 4 $$ \begin{aligned} &2\frac{7}{9} - \frac{1}{2} - \frac{2}{3} \ &= 2\frac{14}{18} - \frac{9}{18} - \frac{12}{18} \ &= 1\frac{32}{18} - \frac{9}{18} - \frac{12}{18} \ &= 1\frac{11}{18} \end{aligned} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Subtraction" ] }

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QUESTION IMAGE

Question

Explanation:

Find common denominators

Regroup mixed numbers where necessary

Subtract and simplify

Answer:

Question 1

Question 2

Question 3

Question 4