Respuesta :

sqdancefan

Answer:

  2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

  (8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

Check

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

MrRoyal

Rational numbers are numbers that can be represented as a fraction of two integers. The greatest rational number (r) such that [tex]\frac 8{15} \div r : \frac {18}{35} \div r[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Let the numbers be represented as:

[tex]n_1 = \frac 8{15} \div r[/tex]

[tex]n_2 = \frac {18}{35} \div r[/tex]

To calculate the value of r such that [tex]n_1 : n_2[/tex] is a whole number, we make use of Euclid's algorithm.

Using Euclid's algorithm, the value of r is the common divisor between both fractions

[tex]r = n_1 - n_1[/tex]

[tex]r =\frac 8{15} \div r - \frac {18}{35} \div r[/tex]

Ignore the "r"

[tex]r =\frac 8{15} - \frac {18}{35}[/tex]

Take LCM

[tex]r=\frac {8 \times 7 - 18 \times 3}{105}[/tex]

[tex]r =\frac {2}{105}[/tex]

Hence, the greatest rational number is such that [tex]n_1 : n_2[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Read more about greatest rational numbers at:

https://brainly.com/question/24338971

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