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523−112=n5\frac{2}{3} - 1\frac{1}{2} = n

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Add and subtract mixed numbersright chevron icon

Full solution

Q. 523−112=n5\frac{2}{3} - 1\frac{1}{2} = n
  1. Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier calculation.\newline523=(5×3+2)/3=1735 \frac{2}{3} = (5 \times 3 + 2)/3 = \frac{17}{3}\newline112=(1×2+1)/2=321 \frac{1}{2} = (1 \times 2 + 1)/2 = \frac{3}{2}
  2. Subtract Fractions: Subtract the two fractions.\newlineTo subtract, find a common denominator. The least common multiple of 33 and 22 is 66.\newlineConvert 173\frac{17}{3} to a fraction with denominator 66: (173)×(22)=346\left(\frac{17}{3}\right) \times \left(\frac{2}{2}\right) = \frac{34}{6}\newlineConvert 32\frac{3}{2} to a fraction with denominator 66: (32)×(33)=96\left(\frac{3}{2}\right) \times \left(\frac{3}{3}\right) = \frac{9}{6}\newlineNow subtract: 346−96=256\frac{34}{6} - \frac{9}{6} = \frac{25}{6}
  3. Convert Back to Mixed Number: Convert the improper fraction back to a mixed number. 256=4\frac{25}{6} = 4 remainder 11, so it's 4164 \frac{1}{6}.

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