Fractions · Study guide · Sol Rising

Fractions

Simplify	Divide the top and bottom by the same number: $\frac{18}{24} = \frac{3}{4}$ (both ÷ 6).
Add or subtract	Get a common bottom first: $\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}$ .
Multiply	Straight across: $\frac{2}{3} \times \frac{5}{7} = \frac{10}{21}$ . Cancel first to keep numbers small.
Divide	Flip the second and multiply: $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}$ .
Mixed numbers	$2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}$ . Turn them into this form before multiplying or dividing.
Compare	Cross-multiply: $\frac{3}{7}$ vs $\frac{2}{5}$ → 3 × 5 = 15 vs 2 × 7 = 14, so $\frac{3}{7}$ is bigger.

AFOQT questions on this: Adding fractions · Multiplying fractions · Mixed numbers · Comparing fractions

Drill it

Quick questions on just this skill, to build speed before the practice tests. Type the answers; a clock keeps your time.

Simplifying fractions Write each in lowest terms. $\frac{6}{36}$ = ?
Adding and subtracting fractions Find a common bottom first. $\frac{1}{6} + \frac{5}{8}$ = ?
Multiplying and dividing fractions Straight across, or flip and multiply. $\frac{1}{5} \times \frac{2}{7}$ = ?
Comparing fractions Pick the bigger one. Which is bigger?
Mixed numbers Mixed to improper and back. Write $6 \frac{1}{5}$ as an improper fraction.

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