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Simplify. Express your answer as a single fraction in simplest form. \newline7q3−35\frac{7q}{3} - \frac{3}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline7q3−35\frac{7q}{3} - \frac{3}{5}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions 7q3\frac{7q}{3} and 35\frac{3}{5}. The denominators are 33 and 55, so the LCD is their least common multiple, which is 1515.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 1515. For the first fraction, multiply both the numerator and the denominator by 55 to get 7q×53×5=35q15\frac{7q \times 5}{3 \times 5} = \frac{35q}{15}. For the second fraction, multiply both the numerator and the denominator by 33 to get 3×35×3=915\frac{3 \times 3}{5 \times 3} = \frac{9}{15}.
  3. Combine fractions: Combine the fractions with the common denominator.\newlineNow that both fractions have the same denominator, we can combine them as follows:\newline(35q15)−(915)=35q−915(\frac{35q}{15}) - (\frac{9}{15}) = \frac{35q - 9}{15}
  4. Check for simplification: Check if the resulting fraction can be simplified further.\newlineThe numerator 35q−935q - 9 and the denominator 1515 do not have any common factors other than 11, so the fraction is already in its simplest form.

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