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a14−2a7+3a2\frac{a}{14}-\frac{2a}{7}+\frac{3a}{2}

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Q. a14−2a7+3a2\frac{a}{14}-\frac{2a}{7}+\frac{3a}{2}
  1. Find Common Denominator: Step Title: Find a Common Denominator\newlineConcise Step Description: To combine the fractions, find a common denominator that is a multiple of all the individual denominators.\newlineStep Calculation: The least common multiple (LCM) of 1414, 77, and 22 is 1414.\newlineStep Output: Common Denominator: 1414
  2. Rewrite with Common Denominator: Step Title: Rewrite Fractions with Common Denominator\newlineConcise Step Description: Rewrite each fraction so that they all have the common denominator of 1414.\newlineStep Calculation: \newline- The first fraction is already over 1414, so it remains a14\frac{a}{14}.\newline- The second fraction, 2a7\frac{2a}{7}, is multiplied by 22\frac{2}{2} to get 4a14\frac{4a}{14}.\newline- The third fraction, 3a2\frac{3a}{2}, is multiplied by 77\frac{7}{7} to get 21a14\frac{21a}{14}.\newlineStep Output: Fractions with common denominator: a14\frac{a}{14}, 4a14\frac{4a}{14}, 21a14\frac{21a}{14}
  3. Combine Fractions: Step Title: Combine the Fractions\newlineConcise Step Description: Combine the fractions by adding or subtracting the numerators and keeping the common denominator.\newlineStep Calculation: \newlineCombine the fractions: (a14)−(4a14)+(21a14)(\frac{a}{14}) - (\frac{4a}{14}) + (\frac{21a}{14})\newlineStep Output: Combined fraction: (a−4a+21a)/14(a - 4a + 21a)/14
  4. Simplify Numerator: Step Title: Simplify the Numerator\newlineConcise Step Description: Simplify the numerator by combining like terms.\newlineStep Calculation: \newlineSimplify the expression: a−4a+21aa - 4a + 21a\newlineStep Output: Simplified numerator: 18a18a
  5. Write Final Expression: Step Title: Write the Final Simplified Expression\newlineConcise Step Description: Write the final simplified expression with the simplified numerator over the common denominator.\newlineStep Calculation: \newlineThe final simplified expression is 18a14\frac{18a}{14}.\newlineStep Output: Final simplified expression: 18a14\frac{18a}{14}
  6. Reduce if Possible: Step Title: Reduce the Fraction if Possible\newlineConcise Step Description: Check if the fraction can be reduced by finding the greatest common divisor (GCD) of the numerator and the denominator.\newlineStep Calculation: \newlineThe GCD of 18a18a and 1414 is 22.\newlineDivide both the numerator and the denominator by 22 to reduce the fraction.\newlineStep Output: Reduced fraction: (18a/2)/(14/2)(18a/2)/(14/2)
  7. Final Answer: Step Title: Final Answer\newlineConcise Step Description: Write down the final answer after reducing the fraction.\newlineStep Calculation: \newlineThe final answer is 9a7\frac{9a}{7}.\newlineStep Output: Final answer: 9a7\frac{9a}{7}

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