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Simplify. Express your answer as a single fraction in simplest form. \newline23+5ab2\frac{2}{3} + \frac{5ab}{2}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline23+5ab2\frac{2}{3} + \frac{5ab}{2}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions 23\frac{2}{3} and 5ab2\frac{5ab}{2}. The denominators are 33 and 22, so the LCD is the product of these two numbers, which is 66.
  2. Convert fractions: Convert each fraction to an equivalent fraction with the LCD as the denominator.\newlineFor the first fraction, 23\frac{2}{3}, we multiply the numerator and denominator by 22 to get 46\frac{4}{6}.\newlineFor the second fraction, 5ab2\frac{5ab}{2}, we multiply the numerator and denominator by 33 to get 15ab6\frac{15ab}{6}.
  3. Add fractions: Add the two fractions with the common denominator.\newline(46)+(15ab6)=4+15ab6(\frac{4}{6}) + (\frac{15ab}{6}) = \frac{4 + 15ab}{6}
  4. Simplify expression: Simplify the expression, if possible.\newlineIn this case, the numerator 4+15ab4 + 15ab cannot be simplified further because there are no common factors between the number 44 and the term 15ab15ab.

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