Fractions and Decimals

Fraction rules

Equivalent fractions

\frac{a}{b} = \frac{a \times k}{b \times k}

b ≠ 0, k ≠ 0

Simplest form

\frac{a}{b} = \frac{a \div GCF (a, b)}{b \div GCF (a, b)}

Mixed number to improper fraction

W \frac{n}{d} = \frac{W \times d + n}{d}

Add or subtract, like denominators

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

Add or subtract, unlike denominators

\frac{a}{b} \pm \frac{c}{d} = \frac{a d \pm b c}{b d}

Multiply

\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}

Divide (keep, change, flip)

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c}

Compare by cross-multiplying

\frac{a}{b} > \frac{c}{d} \Leftrightarrow a d > b c

b > 0, d > 0

One repeating digit

0 . \overset{―}{a} = \frac{a}{9}

a is a digit

Two repeating digits

0 . \overset{―}{a b} = \frac{a b}{99}

ab is a 2-digit block

Three repeating digits

0 . \overset{―}{a b c} = \frac{a b c}{999}

abc is a 3-digit block

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