Number & Algebra
Fractions and decimals
Convert between fractions, terminating decimals, and repeating decimals; add, subtract, multiply, and divide rational numbers and mixed numbers.
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
\(0.125=\frac{125}{1000}=\frac{1}{8}\).
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