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Simplify. Express your answer as a single fraction in simplest form. \newline4qr3−q5\frac{4qr}{3} - \frac{q}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline4qr3−q5\frac{4qr}{3} - \frac{q}{5}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe denominators are 33 and 55, so the LCD is 3×5=153 \times 5 = 15.
  2. Rewrite fractions: Rewrite each fraction with the LCD as the new denominator.\newlineFor the first fraction, multiply both the numerator and the denominator by 55 to get (4qr×5)/(3×5)(4qr \times 5) / (3 \times 5).\newlineFor the second fraction, multiply both the numerator and the denominator by 33 to get (q×3)/(5×3)(q \times 3) / (5 \times 3).
  3. Perform multiplications: Perform the multiplications.\newline(4qr×5)/(3×5)=(20qr)/15(4qr \times 5) / (3 \times 5) = (20qr) / 15\newline(q×3)/(5×3)=(3q)/15(q \times 3) / (5 \times 3) = (3q) / 15
  4. Combine fractions: Combine the fractions over the common denominator.\newline(20qr)/15−(3q)/15=(20qr−3q)/15(20qr) / 15 - (3q) / 15 = (20qr - 3q) / 15
  5. Factor out qq: Factor out the common factor qq from the numerator.20qr−3q15=q(20r−3)15\frac{20qr - 3q}{15} = \frac{q(20r - 3)}{15}
  6. Check for simplification: Check if any further simplification is possible.\newlineThere are no common factors between the numerator and the denominator, so the fraction is in its simplest form.

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