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shusha [124]
3 years ago
14

Is the product of 3⅝ x ⅔ greater than or less than 3⅝? explain without multiplying

Mathematics
2 answers:
almond37 [142]3 years ago
3 0
So the question is
number times 2/3 is greater than or less than the sasme number
so let's say x
x times 2/3 is greater than or less than x
since 2/3 is less than 1, 2/3 is a fraction,
 anything times a fraction will become smaller

therefor
3 and 5/8 times 2/3 is less than 3 and 5/8

the answer is LESS THAN

gizmo_the_mogwai [7]3 years ago
3 0
You are multiplying a number by a fraction, or something that is less than 1. Anytime you multiply a number by a fraction, it will become smaller. Therefore it will be less than.
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To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans  so 100 - 60 = 40 are democrats).

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<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}

Now compute each combination separately:

\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700

and now replace the values:

\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

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3 years ago
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