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In an inverse proportion, when one quantity increases by a certain factor, the other quantity decreases by the same factor. Keep reading to see a real-life example of this situation. Suppose x and y are variables and k is a constant. Then, y = 8x and y = -2x are examples of direct proportions. However,…

A direct variation, also called direct proportion is a relationship between two variables x and y that can be written as y = kx, k ≠ 0. This situation occurs when the ratio of two variables is constant. When y = kx, we say that y varies directly with x. When z = kt, we…

What is the golden ratio? The short answer is 1.61803398875 and many people call it the divine proportion. The golden ratio was discovered by the Pythagoreans around 500 B.C. The long answer will require some figures and some math. To warm up, we will try to construct an equiangular spiral. Here is how: Draw a…

We will solve “working together word problems” with proportion. It may easier to tackle than algebra. Problem #1: Maria can clean all bathrooms in her house in 5 minutes. Her husband can do the same in 20 minutes. How long will it take them if they work together? One important observation is that an entire task or…

Before studying this lesson about scale drawings, you should review the lesson about solving proportions. Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car or an airplane, we need scale drawings to represent the size like the one you see below…

Learn how to solve multi-step proportions easily with a couple of good examples. Quick review: Suppose you have the following proportion: Numerator #1 / Denominator #1 = Numerator #2 / Denominator #2  After doing cross-multiplication, it is equivalent to  Numerator #1 × Denominator #2 = Numerator #2 × Denominator #1 Example #1 Solve the proportion (x – 5) / 4 = (x + 3) / 6 (x…

Solving proportions by using cross product to find unknown terms is what this lesson is about. We will also show some principles, special techniques or shortcuts that can be used to quickly solve a proportion. Terms to know: Variables such as x, y, or any other letter are used to stand for an unknown number. Unknown…

This lesson about proportions will teach you some very important concepts you need to know. You should review the lesson about ratio before studying this lesson. Take a look at the image below. Try to measure the ratio of arm’s length to height for 5 people that you know. What did you notice? More on this later,…

There is a difference between a ratio and a fraction even though students usually think there is none.  It is true that we can simplify a ratio the same way we simplify a fraction. For example, the ratio 6 to 9 or 6/9 is equivalent to the ratio 2 to 3 or 2/3. However, ratios…