Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.

Rational numbers are numbers that can be represented as a fraction of two integers. The greatest rational number (r) such that is a whole number is

Let the numbers be represented as:

To calculate the value of r such that 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

Ignore the "r"

Take LCM

Hence, the greatest rational number is such that is a whole number is

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  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.

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step-by-step explanation: