Is 170/766 and 509/37 Proportional?

Are you looking to find out whether 170/766 and 509/37 form a proportion? In this article we'll compare these two to determine if there is a proportional ratio between 170/766 and 509/37. 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 170/766 equals 509/37 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 170/766 and 509/37 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 (170) x D (37) is equal to B (766) x C (509):

170 x 37 = 6290

766 x 509 = 389894

As we can see, 6290 does NOT equal 389894 so we can say that 170/766 and 509/37 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.

170 / 766 = 85/383
509 / 37 = 13 28/37

By reducing the two ratios down to their simplest/lowest form we can see that the simplest form of 170/766 is 85/383 and the simplest form of 509/37 is 13 28/37, so 170/766 and 509/37 are NOT proportional to each other.

That's all there is to it when comparing 170/766 and 509/37 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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