1) $5\frac{5}{6} + 2\frac{2}{3}$
2) $2\frac{1}{2} \div 1\frac{5}{6}$
3) 35 is 20% of what amount?
4) what is the % of increase from 30 to 120?
5) $2^3 + (8-5)^2 - 3$
6) $3abc + 26ab^2 - 10abc + 13$
7) $(x+5)(x-6)$
8) $\frac{2(5+x) - 3(5+x)}{5+x}$
9) $(3x+4) + (2x+2)$
10) $\frac{18x^2 + 6x}{3x}$

Question

Accepted Answer

{ "quality": "clear", "question_count": 10, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mixed Number Arithmetic", "Percentage Calculations", "Combining Like Terms", "Polynomial Expansion", "Algebraic Simplification" ], "new_concepts": [ "Order of Operations", "Rational Expression Simplification" ], "current_concepts": [ "Mixed Number Arithmetic", "Percentage Calculations", "Order of Operations", "Combining Like Terms", "Polynomial Expansion", "Algebraic Simplification", "Rational Expression Simplification" ] } ## Solve arithmetic and percentage questions (1 to 4) $$ \begin{aligned} &\text{Q1: } 5\frac{5}{6} + 2\frac{2}{3} = \frac{35}{6} + \frac{8}{3} = \frac{35 + 16}{6} = \frac{51}{6} = \frac{17}{2} = 8\frac{1}{2}\ &\text{Q2: } 2\frac{1}{2} \div 1\frac{5}{6} = \frac{5}{2} \div \frac{11}{6} = \frac{5}{2} \times \frac{6}{11} = \frac{15}{11} = 1\frac{4}{11}\ &\text{Q3: } 35 = 0.20 \times x \implies x = \frac{35}{0.2} = 175\ &\text{Q4: } \frac{120 - 30}{30} \times 100\% = \frac{90}{30} \times 100\% = 300\% \end{aligned} $$ ## Solve algebraic expressions (5 to 7) $$ \begin{aligned} &\text{Q5: } 2^3 + (8-5)^2 - 3 = 8 + 3^2 - 3 = 8 + 9 - 3 = 14\ &\text{Q6: } 3abc + 26ab^2 - 10abc + 13 = -7abc + 26ab^2 + 13\ &\text{Q7: } (x+5)(x-6) = x^2 - 6x + 5x - 30 = x^2 - x - 30 \end{aligned} $$ ## Solve algebraic simplifications (8 to 10) $$ \begin{aligned} &\text{Q8: } \frac{2(5+x) - 3(5+x)}{5+x} = \frac{-(5+x)}{5+x} = -1 \quad (x e -5)\ &\text{Q9: } (3x+4) + (2x+2) = 5x + 6\ &\text{Q10: } \frac{18x^2 + 6x}{3x} = \frac{6x(3x + 1)}{3x} = 2(3x + 1) = 6x + 2 \quad (x e 0) \end{aligned} $$ | No. | Answer | |---|---| | 1 | $8\frac{1}{2}$ | | 2 | $1\frac{4}{11}$ | | 3 | $175$ | | 4 | $300\%$ | | 5 | $14$ | | 6 | $-7abc + 26ab^2 + 13$ | | 7 | $x^2 - x - 30$ | | 8 | $-1$ | | 9 | $5x + 6$ | | 10 | $6x + 2$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

No.	Answer
2	\(1\frac{4}{11}\)
3	\(175\)
4	\(300\%\)
5	\(14\)
6	\(-7abc + 26ab^2 + 13\)
7	\(x^2 - x - 30\)
8	\(-1\)
9	\(5x + 6\)
10	\(6x + 2\)

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Question

Explanation:

Solve arithmetic and percentage questions (1 to 4)

Solve algebraic expressions (5 to 7)

Solve algebraic simplifications (8 to 10)

Answer: