Is 38/576 and 324/315 Proportional?

Are you looking to find out whether 38/576 and 324/315 form a proportion? In this article we'll compare these two to determine if there is a proportional ratio between 38/576 and 324/315. Let's get to it!

Okay, so first off we are referring to this is a proportion, but it can also be considered a ratio. The question we are really asking here is whether 38/576 equals 324/315 in a different proportion. Let's look at it visually and use letters to explain how proportions work:

A / B = C / D

Now these look like fractions and we could call the top number of each a numerator and the bottom number of each the denominator but, when working with proportions we need to refer to them differently.

The numbers in the A and D positions are called the "extremes" and the numbers in the B and C position are called the "means".

So how do we know if 38/576 and 324/315 are proportional to each other? The core defining property of any proportion is that the product of the means is equal to the product of the extremes.

What does that mean? Well in simple terms it means A multiplied by D must equal B multiplied by C. You could also consider these ratios to be fractions and then simplify them down to their lowest terms and compare them. If they are equal, then they are proportional.

Let's first work out if A (38) x D (315) is equal to B (576) x C (324):

38 x 315 = 11970

576 x 324 = 186624

As we can see, 11970 does NOT equal 186624 so we can say that 38/576 and 324/315 are NOT proportional.

Let's also try this by reducing the two fractions/ratios down to their lowest terms and see if the resulting ratio is equal.

38 / 576 = 19/288
324 / 315 = 1 1/35

By reducing the two ratios down to their simplest/lowest form we can see that the simplest form of 38/576 is 19/288 and the simplest form of 324/315 is 1 1/35, so 38/576 and 324/315 are NOT proportional to each other.

That's all there is to it when comparing 38/576 and 324/315 to see if the ratios are proportional. The easiest method is to make sure the product of the "means" is equal to the product of the "extremes" by multiplying A and D and B and C to make the resulting number matches.

Hopefully this tutorial has helped you to understand how to compare fractions and you can use your new found skills to compare whether one fraction is greater than another or not!

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