There are several ways to solve equations with fractions.

The easiest way is to multiply the whole equation by the lowest common multiple (lcm) of the denominators (bottom parts) of the fraction. This will eliminate the fractions and the equation can then be solved normally.

**Example**

Solve the following equation for a:

11a - 2 | = | 12a + 1 |

6 | 7 |

**Answer**

11a - 2 | = | 12a + 1 |

6 | 7 |

Multiply both sides by the lcm of 6 and 7 which is 42.

Put brackets around the numerators (top parts).

42 × | (11a - 2) | = | 42 × | (12a + 1) |

6 | 7 |

Reduce the fractions

7 |
(11a - 2) | = | 6 |
(12a + 1) |

Simplify

7 (11a - 2) = 6 (12a + 1)

Multiply out the brackets

77a - 14 = 72a + 6

Add 14 to both sides

77a - 14 + 14 = 72a + 6 + 14

Simplify

77a = 72a + 20

Subtract 72a from both sides

77a -72a = 72a + 20 - 72a

Simplify

5a = 20

Divide both sides by 5

5a ÷ 5 = 20 ÷ 5

Simplify

**a = 4
**