Is 675/78 and 331/214 Proportional?

Are you looking to find out whether 675/78 and 331/214 form a proportion? In this article we'll compare these two to determine if there is a proportional ratio between 675/78 and 331/214. 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 675/78 equals 331/214 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 675/78 and 331/214 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 (675) x D (214) is equal to B (78) x C (331):

675 x 214 = 144450

78 x 331 = 25818

As we can see, 144450 does NOT equal 25818 so we can say that 675/78 and 331/214 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.

675 / 78 = 8 17/26
331 / 214 = 1 117/214

By reducing the two ratios down to their simplest/lowest form we can see that the simplest form of 675/78 is 8 17/26 and the simplest form of 331/214 is 1 117/214, so 675/78 and 331/214 are NOT proportional to each other.

That's all there is to it when comparing 675/78 and 331/214 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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