If you have ever drawn your own copy of a figure that you liked or you have used a map, then you have worked with enlargements and reductions!

Enlargement — to make a document or image bigger.

Reduction — to make a document or image smaller.

A photocopier or various computer software allows a copy of a document or image to be made bigger (enlarged) or shrunk (reduced) to a smaller size. These enlargements (bigger sizes) and reductions (smaller sizes) require the person to tell the photocopier or software how many times the document is to be enlarged or reduced.

Scale Factor

The ratio of the size in a drawing (or model) to the size of the real thing.

The scale factor (sometimes called the scale ratio) tells how many times bigger or smaller a document needs to be changed.

Scale uses proportions and ratios to make the enlargements or reductions. You might want your image or document to be twice as big, or you might want it only 1.1 times as big.

In the example below, the scale factor is 3.5. That means that the second letter "F" is 3.5 times bigger than the first one. So, how did we get those numbers? It's easy — all you need to do is multiply the original scale numbers (in the small letter "F") by 3.5 to scale the object up by 3.5 to enlarge it.

Example: 4" logo

Example: 1" logo (1/4 of its original size)

So how are scale and ratio related? Let's look again at the definition of scale.

In the drawing above, the scale shows the ratio of the drawing, which is 1:10. Therefore, anything with the size of "1" would have a size of "10" in the real world, so a measurement of 150 mm on the drawing would be 1,500 mm on the real horse.

The trick with ratios is to always multiply or divide the numbers by the same value . When you want to enlarge something, you multiply (make it bigger). When you want to reduce something, you divide (make it smaller).

Now let's take a look at a real-world example of where you might need to use ratios in your own life.