Is 15/8 or 17/6 greater?

Is 15/8 or 17/6 greater?

Is 15/8 or 17/6 greater?
Guest

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

LCM(6, 8) = 24

$$\frac{15}{8} = \frac{45}{24}$$

$$\frac{17}{6} = \frac{68}{24}$$

$$\frac{17}{6} > \frac{15}{8}$$
Guest

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

Equivalently, assume for the moment that $$\frac{15}{8}> \frac{17}{6}$$. 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 $$\frac{15}{8}> \frac{17}{6}$$, is NOT true. Those are also not equal so we must have $$\frac{15}{8}< \frac{17}{6}$$.

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 $$\frac{90}{(8)(6)}< \frac{136}{(8)(6)}$$ or $$\frac{15}{8}< \frac{17}{6}$$.

HallsofIvy

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

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: $$\frac{15}{8}$$ versus $$\frac{17}{6}$$

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

Since 90 < 136, therefore $$\frac{15}{8}$$ < $$\frac{17}{6}$$

Math_Books_Author

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

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.
Guest

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

The simplest way to do this is to observe that 15/8= 1 and 7/8 while 17/6= 2 and 5/6.
Guest

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

Guest wrote:The simplest way to do this is to observe that 15/8= 1 and 7/8 while 17/6= 2 and 5/6.

Hello. in any fraction, a / b, the fraction increases as a increases and increases as b decreases.
this is the path to the solution

benevideslauren67

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

benevideslauren67 wrote:
Guest wrote:The simplest way to do this is to observe that 15/8= 1 and 7/8 while 17/6= 2 and 5/6.

Hello. in any fraction, a / b, the fraction increases as a increases and increases as b decreases worktime.
this is the path to the solution

\displaystyle \frac{15}{8}
8
15

versus \displaystyle \frac{17}{6}
6
17

benevideslauren67

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