How to simplify fractions within fractions with variables?

Problem: Simplify fraction within fraction with variables

4ab/15cd |
---|

2a/5d |

Solution.

1. Rewrite the fraction as a division.

4ab/15cd | = |
---|---|

2a/5d |

4ab | ÷ | 2a |
---|---|---|

15cd | 5d |

2. Divide the two fractions.

To divide two fractions multiply the first fraction by the the reciprocal of the second fraction.

See Rules for dividing fractions.

We have

4ab | ÷ | 2a | = |
---|---|---|---|

15cd | 5d |

4ab | * | 5d | = |
---|---|---|---|

15cd | 2a |

4ab * 5d | = |
---|---|

15cd * 2a |

2a * 2b * 5d | = |
---|---|

3c * 5d * 2a |

2a * 2b * 5d | = |
---|---|

3c * 5d * 2a |

2b |
---|

3c |

3. The answer is

4ab/15cd | = | 2b |
---|---|---|

2a/5d | 3c |

The problem is solved.