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Problem #39 · September 4, 2026

Common fractions

The numerator of a fraction is 5 less than its denominator. If 3 is added to both the numerator and the denominator, the resulting fraction equals 23\frac{2}{3}. Find the original fraction.
  1. A1015\frac{10}{15}
  2. B712\frac{7}{12}
  3. C16\frac{1}{6}
  4. D1621\frac{16}{21}
  5. E127\frac{12}{7}

WORKED EXAMPLE

Solution

If the numerator is xx, the denominator is x+5x+5. By the condition, x+3x+8=23\frac{x+3}{x+8}=\frac{2}{3}; cross-multiplying gives 3(x+3)=2(x+8)3(x+3)=2(x+8), that is, 3x+9=2x+163x+9=2x+16, so x=7x=7. Therefore, the fraction is 712\frac{7}{12}; check: 7+312+3=1015=23\frac{7+3}{12+3}=\frac{10}{15}=\frac{2}{3}.
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