Fraction Operations · Pre-Algebra Lesson

By the end of this lesson, you will be able to add, subtract, multiply, and divide fractions and mixed numbers fluently.

$$\frac{3}{4} + \frac{5}{6}: \text{ LCD} = 12 \to \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}$$

Converting: $3\frac{2}{5} = \frac{17}{5}$ (multiply whole by denominator, add numerator)

Subtracting mixed numbers — "borrowing":

$5\frac{1}{4} - 2\frac{3}{4}$: since $\frac{1}{4} < \frac{3}{4}$, borrow 1 from 5:

$4\frac{5}{4} - 2\frac{3}{4} = 2\frac{2}{4} = 2\frac{1}{2}$

Multiply straight across: $\frac{3}{5} \times \frac{4}{7} = \frac{12}{35}$

Cross-cancel first to simplify: $\frac{3}{8} \times \frac{4}{9} = \frac{3}{8} \times \frac{\cancel{4}^1}{\cancel{9}^3} \to$ easier computation

Mixed numbers: convert to improper fractions first.

$2\frac{1}{2} \times 1\frac{1}{3} = \frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = 3\frac{1}{3}$

Keep, Change, Flip (KCF): multiply by the reciprocal.

$\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5} = \frac{18}{20} = \frac{9}{10}$

Mixed numbers: convert to improper first.

$3\frac{1}{2} \div 1\frac{3}{4} = \frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7} = 2$

Adding/subtracting: find LCD; convert; operate on numerators.

Multiplying: multiply across; cross-cancel to simplify.

Dividing: KCF (Keep, Change, Flip) — multiply by the reciprocal.

Mixed numbers: always convert to improper fractions before multiplying or dividing.