Comparing Fractions 📚

[eternity]

wished i would have known this in like 5th grade lol

[calebferguson]

The reason this works is because of how "Getting common denominators" work

To make 10 and 11 have the same base, you usually can multiply them -> 10 * 11 is 110

Now to make each numerator match each base, so the fraction stays the same you multiply each numerator with the other's base:
7 * 11 is 77 -> 77/110
8 * 10 is 80 -> 80/110

but because the denominators are the same, and since we're just comparing, in this example we simply ignore the bottom

[kk]

thanks for showcasing the hack for comparing fractions! Your clear explanation and demonstration make it easier for me to grasp the concept. Impressive breakdown of the fraction comparison hack!

[pgplaysvidya]

the basic explanation is that if the two fractions are equal you get the same number

7/11 and 7/11 - you get 77 and 77

using this, you can apply the inequality preservation

this is, if you multiple an inequality by the same number you preserve the inequality

5 < 7, right?

and 5*5 < 7*5 (25 < 35)

so now you do the thing in the video.

The reason this method works is that by cross-multiplying, you’re effectively scaling both fractions to have the same hypothetical denominator (the product of the two original denominators). This allows you to compare the numerators directly, which represent the scaled values of the fractions. If one scaled numerator is larger than the other, then the corresponding original fraction is larger.

[Jake-ccie]

You can think of it like when a sports team wins a game their winning percentage should always go up unless they already have a 100% winning percentage

[movingon]

More please you explained this very well

[thinkingmom]

Could you please construct a lesson on Gauss-Jordan 2X3. Thanks!

[babusseus]

Another way to imagine this is following the pattern of increasing numerator and denominator infinitely.

As both increase, the value of the fraction will increase up to a limit of 1, while decreasing it will end up at 1/4, since they both have the form of n/n+3.

That means that for every value of n, the smaller n will have a lesser value.

[adrianlindberg]

just imagine adding 1 to the top and bottom infinite times and you notice it gets closer and closer to one

[lucaslzt]

In general I think it's more productive to teach to make the least common denominator for both fractions so you only compare the numerator

[poketube]

7 to 8 is a larger growth percentage than 10 to 11. Thats the fastest way to know

[isjosh]

Compare a/b and c/d

If we find that:
bc > ad
then:
c/d > a/b, when we divide by bd on both sides. This means that if bc > ad then c/d is larger and the reverse also works the same.
Note that this only works if numbers are all positive

[camerond]

They each have a 3 difference and I know that 3/11 is smaller than 3/10

[jonathanparsons]

What I do is I look for differences in the numerator and denominator. I just say "8 is 1 bigger than 7" in the numerator and "11 is 1 bigger than 10" in the denominator. 1/1 = 1, which is obviously greater than 7/10, so 8/11 is larger. This should work for any differences. For example, if you wanted to know if 9/13 was bigger than 7/10, you would do 9-7 = 2 in the numerator, 13-10 = 3 in the denominator. 2/3 is less than 7/10, so 7/10 is larger.

[tncshindiru]

Honestly i noticed something and it seemed to work. If a fraction has a numerator and a denominator that’s exactly 1 more than the other fraction then it’s bigger. For example


So for 7/10 and 8/11 using this logic 8/11 is simply bigger.

[hectorheath]

The remainder 3/11 is clearly less than 3/10.

[SocksWithSandals]

I saw that n/n-3 would tend to 1 in the limit, so the higher n, the bigger ratio.

[thepistolguy]

Turn them to decimals and pick the bigger one that's even easier

[I_love_space.]

I actually use this when adding or subtracting fractions except I add an extra line that crosses through the denominators so that I can get the common denominator for the answer. Basically it’s in the shape of an hour glass without the top part.

[Arcangel]

the derivative of n - 3 / n is positive for all n above 0, therefor n - 3 / n is an increasing function.