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What is 212+5132 \frac{1}{2}+5 \frac{1}{3}

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Full solution

Q. What is 212+5132 \frac{1}{2}+5 \frac{1}{3}
  1. Convert to Improper Fractions: Convert mixed numbers to improper fractions. 2122 \frac{1}{2} becomes (2×2+1)/2=52(2\times2 + 1)/2 = \frac{5}{2}, and 5135 \frac{1}{3} becomes (5×3+1)/3=163(5\times3 + 1)/3 = \frac{16}{3}.
  2. Find Common Denominator: Find a common denominator for the fractions 52\frac{5}{2} and 163\frac{16}{3}. The common denominator is 66.
  3. Convert to Common Denominator: Convert fractions to have the common denominator. 52\frac{5}{2} becomes (5×32×3)=156\left(\frac{5\times3}{2\times3}\right) = \frac{15}{6}, and 163\frac{16}{3} becomes (16×23×2)=326\left(\frac{16\times2}{3\times2}\right) = \frac{32}{6}.
  4. Add Fractions: Add the fractions with the common denominator. 156+326=15+326=476.\frac{15}{6} + \frac{32}{6} = \frac{15 + 32}{6} = \frac{47}{6}.
  5. Convert to Mixed Number: Convert the improper fraction back to a mixed number. 476\frac{47}{6} is 77 whole numbers and 56\frac{5}{6} left over, so the mixed number is 7567\frac{5}{6}.

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