Interpreting Multiplication as Scaling

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you'll understand how scaling works with multiplication. Learn how you can use this to help you build either miniature or larger models of things. You'll see how fractions play a large role in scaling.


When you scale something, you are either making it larger or smaller than the actual thing. For example, a toy car is a smaller scale model of a real car. Everything in the little car is the same amount smaller in the real car. Looking at the two, the only difference is size.


If you wanted to make your own scale model, you can use multiplication to help you.

Using Multiplication

You can think of multiplying as making a measurement smaller or larger as needed. If you multiply by a number less than 1, you'll find the measurement for scale models that are smaller. Multiply by a number larger than 1, and you'll find the measurement for scale models that are larger.

You can always tell, too, by the answer you get. If your answer is larger than your original measurement, then you are finding the measurement for a larger scale model. If your answer is smaller than your original measurement, then you are finding the measurement for a smaller scale model.


If you go a toy store, you'll see a lot of toys that are smaller scale models of their real-life counterparts. You'll see toy cars, toy houses, toy kitchens, etc. All are smaller versions of the real thing.

For model cars, a common scaling is the 1 / 12 scale. This number is referred to as the scaling factor. This means that the model cars are 1 / 12 the size of their real-life counterparts. A model convertible would be 1 / 12 the size of a real convertible. If you multiply a real-world measurement by 1 / 12, you'll see just how much smaller the model is.

If you multiply a real-world measurement of 30 centimeters by 1 / 12, you can see that the model measurement is a lot smaller at 2.5 centimeters.


So, when you use multiplication to help you scale, multiply your real-world measurement by the scaling factor.

If you are making a scale model that is larger, then you'll multiply by a scaling factor that is larger than 1. If your scaling is 2, then your model is twice as big as the real thing.


Remember, scaling factors between 0 and 1 will give you smaller scale models. The smaller the number, the smaller the model. Scaling factors larger than 1 will give you larger scale models.


Let's look at an example.

Say you are an architect, and your clients have asked you to build their future dream house for them. The house hasn't been built yet, but you have already drawn up all the blueprints for the house. You now want to build them a miniature scale model of their future home so they can see that it will be like.

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