Rational numbers can be written as fractions \(a/b\) with \(b\neq 0\). Decimals and mixed numbers are alternative forms of the same values.

Converting fractions and decimals

• Terminating decimal to fraction: \(0.375=\frac{375}{1000}=\frac{3}{8}\).
• Fraction to decimal: divide numerator by denominator.
• Repeating decimal to fraction: \(0.\overline{3}=\frac{1}{3}\).

Add and subtract fractions

Use a common denominator:

\[ \frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}. \]

Multiply and divide fractions

Multiply numerators and denominators. For division, multiply by the reciprocal.

\[ \frac{3}{4}\div\frac{5}{6}=\frac{3}{4}\times\frac{6}{5}=\frac{9}{10}. \]

Mixed numbers

Convert mixed numbers to improper fractions before operations.

Checkpoint: simplify \(1\frac{1}{2}+2\frac{1}{3}\)

\(\frac{3}{2}+\frac{7}{3}=\frac{9}{6}+\frac{14}{6}=\frac{23}{6}=3\frac{5}{6}\).

Checkpoint: write \(0.125\) as a fraction

\(0.125=\frac{125}{1000}=\frac{1}{8}\).