# Properties and Operations of Fractions

Let a, b, and c be real numbers, variables, or algebraic expressions such that b /= 0 and d /= 0.

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Term | Expression | Examples |
---|---|---|

Equivalent Fractions | a/b = c/d if and only if ad = bc | 1/2 = 2/4 |

Rules of Signs | -(a/b) = (-a)/b = a/(-b) and (-a)/(-b) = a/b | -(3/4) = (-3)/4 = 3/(-4) and (-3)/(-4) = 3/4 |

Generate Equivalent Fractions | a/b = ac/bc, c /= 0 | x/2 = (x*3)/(2*3) = 3x/6 |

Add or subtract like denominators | a/b +/- c/b = (a +/- c)/b | 1/2 + 5x/2 = (1 + 5x)/2 |

Add or subtract with unlike denominators | a/b +/- c/d = (ad +/- bc)/bd | 1/2 + 3/5 = ((5)1)/((5)2) + ((2)3)/((2)5) = ((5)1 + (2)3)/((5)(2)) = (5 + 6)/10 = 11/10 |

Multiply fractions | a/b * c/d = ac/bd | 3/5 * 1/3 = ((3)1)/(5(3)) = ((3)1)/((3)5) = 3/15 = 1/5 |

Divide fractions | (a/b)/(c/d) = a/b * d/c = ad/bc, c /= 0 | (3/5)/(1/3) = 3/5 * 3/1 = (3*3)/(5*1) = 9/5 |