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Pre-Algebra

Apply proportional reasoning to solve problems involving scales to find actual distances on a map.

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After completing this tutorial, you will be able to complete the following:

- Explain scale drawing.
- Explain scale.
- Apply proportional reasoning to solve problems involving scales to find actual distances on a map.

Scale drawing, scale and scale factor

A scale drawing is a drawing of an object whose dimensions are proportional to the actual dimensions of an object. The scale tells how the drawing's dimensions and the actual dimensions are related, and is expressed as a ratio. When this ratio of a drawing's dimensions and the actual dimensions is written as a fraction without units, it is called scale factor.

If a problem asks for you to find and write the scale, you would write the size of the scale model first then the actual size.

This can be expressed as 1 cm : 50 km or

Using proportions to solve problems involving scale.You can use proportional reasoning to solve problems involving scale.For example, a boat is 3 inches in size and the scale is 1 in. : 5ft. To find the actual size of the boat, setup a proportion

Therefore, the value of x, is 15 ft, which is the actual size of the boat

The following key vocabulary terms will be used throughout this Activity Object:

- actual distance - the real-world size or distance of an object
- map - a drawing that shows proportional distances from one location to another
- proportion - an equation when it states equality between two ratios
- ratio - a comparison of two numbers or quantities
- scale - the ratio that tells how a drawing's dimensions and the actual dimensions are related
- scale drawing - a drawing whose dimensions are proportional to the actual dimensions of an object
- scale factor - when the ratio of a drawing's dimensions and the actual dimensions is written as a fraction without units
- scale model - a model of an object in which the dimensions are proportional to the actual dimensions of the object

Approximate Time | 27 Minutes |

Pre-requisite Concepts | measurement, proportion |

Course | Pre-Algebra |

Type of Tutorial | Concept Development |

Key Vocabulary | actual distance, map, proportion |