# What is half of Frac 70 70

## Set up terms

In this article I would like to use a few examples to show how to convert (verbal) descriptions into the corresponding **Terms**.

Let's start with four very simple examples based on the terms **total**, **difference**, **product** and **quotient**:

description | term |
---|---|

Sum of x and 11 | x + 11 |

Difference between 7 and a | 7 - a |

Product of 3.1 and a | 3.1 ⋅ a |

Quotient of x and 5 | x: 5 or |

One extends this procedure by using terms like **double of ...** or **The half of …** you can also transform the following descriptions into terms:

description | term |
---|---|

3 times x, reduced by 2 | 3x - 2 |

3 times the difference x - 5 | 3 (x - 5) |

Half of a, increased by 3 | a + 3 |

Half of the sum x + 4 | (x + 4) |

Four times the sum x + 6 | 4 (x + 6) |

The double of a, increased by 10 | 2a + 10 |

After these basic examples we try to combine / nest such descriptions or terms:

description | term |
---|---|

The product of the sum of x and 1 and the difference between 12 and a | (x + 1) ⋅ (12 - a) |

Half of 3 times the sum of x and the 5th part of the difference between a and 2 |

Now **two examples**, in which the setting up of terms in a **Word problem** occurs:

Mr. Schubert pays a basic fee of € 60 for a rental car and € 15 for every kilometer driven. Write the costs for x km as a term.

Solution: 60 € + 0.15⋅x €

For a taxi ride, Ms. Bauer pays € 0.75 for every kilometer driven and a basic fee of € 1.70. Write a term for a x km trip and calculate the costs for a 15 km trip.

Solution: 1.70 € + 0.75⋅x €

1,70 € + 0,75⋅15 € = 1,70 € + 11,25 € = 12,95 €

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