Is 853/419 and 180/172 Proportional?

Are you looking to find out whether 853/419 and 180/172 form a proportion? In this article we'll compare these two to determine if there is a proportional ratio between 853/419 and 180/172. 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 853/419 equals 180/172 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 853/419 and 180/172 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 (853) x D (172) is equal to B (419) x C (180):

853 x 172 = 146716

419 x 180 = 75420

As we can see, 146716 does NOT equal 75420 so we can say that 853/419 and 180/172 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.

853 / 419 = 2 15/419
180 / 172 = 1 2/43

By reducing the two ratios down to their simplest/lowest form we can see that the simplest form of 853/419 is 2 15/419 and the simplest form of 180/172 is 1 2/43, so 853/419 and 180/172 are NOT proportional to each other.

That's all there is to it when comparing 853/419 and 180/172 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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