Add, subtract, multiply, and divide fractions and mixed numbers.
Free, timed SHSAT practice sets on fraction & mixed-number arithmetic— every question includes a full worked explanation, and there's no account required.
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Pick the rule for the operation first.
Mixed numbers: change them to improper fractions first, \(5\frac{1}{4} = \frac{21}{4}\). This avoids borrowing errors in problems like \(5\frac{1}{4} - 2\frac{5}{6}\).
A big fraction bar also means divide. Work out the top and the bottom on their own, then divide.
Common traps: flipping the wrong fraction, and losing a negative sign.
Convert to improper fractions with a common denominator and combine: \(4\frac{5}{6} - 4\frac{3}{4} = \frac{1}{12}\). Subtracting only the whole numbers gives \(0\). Subtracting the numerators and adding the denominators of the fraction parts gives \(\frac{1}{5}\). Reading each mixed number as the whole number times the fraction gives \(\frac{1}{3}\).
Multiply by the reciprocal to divide: \(-1\frac{1}{4} \div 1\frac{1}{8} = -1\frac{1}{9}\). Multiplying straight across without flipping the second fraction gives \(-1\frac{13}{32}\). Flipping both fractions gives \(-\frac{32}{45}\). Getting the sign of the answer wrong gives \(1\frac{1}{9}\).
Top: \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\). Bottom: \(1 - \frac{1}{4} = \frac{3}{4}\). Divide: \(\frac{5}{6} \div \frac{3}{4} = \frac{5}{6} \times \frac{4}{3} = \frac{10}{9} = 1\frac{1}{9}\). (Multiplying the top by the bottom instead of dividing gives \(\frac{5}{8}\). Adding the top as \(\frac{1 + 1}{2 + 3} = \frac{2}{5}\) gives \(\frac{8}{15}\). Dividing the bottom by the top gives \(\frac{9}{10}\).)