Add fractions by summing numerators and denominators separately.
An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.
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What is \(\tfrac{1}{2} + \tfrac{1}{3}\)? The trap answer is \(\tfrac{1 + 1}{2 + 3} = \tfrac{2}{5}\). The right answer is \(\tfrac{3}{6} + \tfrac{2}{6} = \tfrac{5}{6}\).
The trap feels natural because you do multiply fractions straight across. But a denominator tells you the size of each piece. You can only add pieces of the same size, so first rename both fractions with a common denominator. Then add the numerators and keep the denominator.
Check habits:
Convert to a common denominator of 24: \(\frac{3}{8} + \frac{7}{12} = \frac{23}{24}\). Adding the numerators and adding the denominators gives \(\frac{1}{2}\). Subtracting instead of adding gives \(-\frac{5}{24}\). Adding the numerators but keeping the first denominator gives \(1\frac{1}{4}\).
Write \(\frac{x}{5} + \frac{x}{6} = 22\) and multiply every term by the LCD \(30\): \(6x + 5x = 660\), so \(11x = 660\) and \(x = 60\). (Adding the denominators, \(\frac{x}{11} = 22\), gives \(242\). Multiplying only the left side by \(30\) gives \(11x = 22\) and \(2\). Stopping before the division gives \(660\).)
Convert to improper fractions with a common denominator and combine: \(6\frac{4}{5} + 1\frac{3}{8} = 8\frac{7}{40}\). Adding only the whole numbers gives \(7\). Adding the numerators and adding the denominators of the fraction parts gives \(7\frac{7}{13}\). Reading each mixed number as the whole number times the fraction gives \(5\frac{7}{40}\).