Exercises to Test Your Understanding of Scaling Using Ratios

Welcome to the practical segment of our journey into scaling with ratios. The best way to master any mathematical concept is through consistent practice. With that in mind, we've prepared a series of exercises to help you solidify your understanding.

Exercise 1: Simple Scaling

Consider a recipe that serves 2 people. If the recipe calls for 3 eggs, how many eggs would you need to serve 8 people?

Exercise 2: Inverse Scaling

Now, let's take the inverse approach. You have a recipe that serves 6 people and requires 4 cups of flour. How much flour would you need if you want to scale down the recipe to serve 3 people?

Exercise 3: Advanced Scaling

Suppose a miniatures artist is creating a model of a 12m tall building at a 1:100 scale. How tall should the model be?

Exercise 4: The Power of Scaling

For this exercise, let's step into the shoes of a physicist. If an object is traveling at a speed of 75 km/h, how far will it travel in 90 minutes?

Exercise 5: Scaling and Proportions

Consider a rectangle with a length of 6 cm and a width of 4 cm. If you increase the length by a factor of 3 and the width by a factor of 2, what is the new area of the rectangle?

Solutions

Before we dive into the solutions, remember the principle we learned in our last tutorial: to scale a quantity, you multiply it by the scaling factor. This principle is key to solving the exercises above.

Solution to Exercise 1

You would need 12 eggs to serve 8 people.

Solution to Exercise 2

You would need 2 cups of flour to serve 3 people.

Solution to Exercise 3

The model of the building should be 0.12m tall.

Solution to Exercise 4

The object will travel 112.5 km in 90 minutes.

Solution to Exercise 5

The new area of the rectangle is 144 cm².

Conclusion

Well done on completing these exercises! Scaling with ratios is a foundational skill in many mathematical disciplines. By understanding and practicing this concept, you've taken a significant step forward in your mathematical journey. Keep practicing and always stay curious!

Scaling with Ratios Tutorials

If you found this ratio information useful then you will likely enjoy the other ratio lessons and tutorials in this section:

• Understanding Rates
• The Relationship Between Ratios and Rates
• Converting Between Rates and Ratios
• Exercises to Test Your Understanding

Next: Ratio Applications: The Golden Ratio