Is 15/8 or 17/6 greater?

Is 15/8 or 17/6 greater?

Postby Guest » Tue Nov 07, 2017 8:00 pm

Is 15/8 or 17/6 greater?
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Re: Is 15/8 or 17/6 greater?

Postby Guest » Wed Nov 08, 2017 11:35 am

LCM(6, 8) = 24

[tex]\frac{15}{8} = \frac{45}{24}[/tex]

[tex]\frac{17}{6} = \frac{68}{24}[/tex]

[tex]\frac{17}{6} > \frac{15}{8}[/tex]
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Re: Is 15/8 or 17/6 greater?

Postby HallsofIvy » Sat Mar 09, 2019 3:34 pm

Equivalently, assume for the moment that [tex]\frac{15}{8}> \frac{17}{6}[/tex]. Since the denominators are both positive, we can multiply both sides by 8 and 6 without changing the direction of the inequality: (15)(6)> (17)(8) or 90> 136. That is NOT true so our original assumption, that [tex]\frac{15}{8}> \frac{17}{6}[/tex], is NOT true. Those are also not equal so we must have [tex]\frac{15}{8}< \frac{17}{6}[/tex].

A formal proof of that inequality would reverse that calculation. From the obviously true "90< 136", divide both sides by the (positive) numbers 8 and 6 to get [tex]\frac{90}{(8)(6)}< \frac{136}{(8)(6)}[/tex] or [tex]\frac{15}{8}< \frac{17}{6}[/tex].

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Re: Is 15/8 or 17/6 greater?

Postby Math_Books_Author » Sun Mar 10, 2019 12:33 am

The fastest way to compare fractions is to multiply the numerators of the fractions with the denominators of each other, and write the products on the sides where the NUMERATORS came from. Whichever product is greater, the fraction on that side is greater.

Case in point: [tex]\frac{15}{8}[/tex] versus [tex]\frac{17}{6}[/tex]

15 x 6 = 90, and 17 x 8 = 136

Since 90 < 136, therefore [tex]\frac{15}{8}[/tex] < [tex]\frac{17}{6}[/tex]

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Re: Is 15/8 or 17/6 greater?

Postby Guest » Tue Apr 20, 2021 3:23 pm

In any fraction, a/b, the fraction increases as a increases and increases as as b decreases.

Going from 15/8 to 17/6 the numerator increases from 15 to 17 and the denominator decreases from 8 to 6, Therefore 17/6 is larger than 15/8.
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Re: Is 15/8 or 17/6 greater?

Postby Guest » Fri May 21, 2021 1:27 pm

The simplest way to do this is to observe that 15/8= 1 and 7/8 while 17/6= 2 and 5/6.
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Re: Is 15/8 or 17/6 greater?

Postby Guest » Sun Jul 18, 2021 10:44 am

LCM(8, 6) = 24 [tex]\Rightarrow[/tex]

[tex]\frac{15}{8}[/tex] * [tex]\frac{3}{3}[/tex] = [tex]\frac{45}{24}[/tex]

[tex]\frac{17}{6}[/tex] * [tex]\frac{4}{4}[/tex] = [tex]\frac{68}{24}[/tex] [tex]\Rightarrow[/tex]

45 < 68 [tex]\Rightarrow[/tex]

[tex]\frac{15}{8}[/tex] < [tex]\frac{17}{6}[/tex]
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Re: Is 15/8 or 17/6 greater?

Postby Guest » Tue Jul 20, 2021 8:01 am

15/8 can be written as (15 x 3)/(8 x 3) = 45/24

17/6 can be written as (17 x 4)/(6 x 4) = 68/24

Clearly 68 is greater than 45, thus 68/24 > 45/24

So, 17/6 is greater than 15/8.
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