Question

Find four rational numbers between 2/3 and 3/5.

Answer 1

Answer: The four rational numbers between 2/3 and 3/5 are:

649/1125, 699/1125, 749/1125, 799/1125

To find four rational numbers between 2/3 and 3/5, we can first find a common denominator for the two fractions, which is 15. Then we can rewrite the fractions as:

2/3 = 10/15

3/5 = 9/15

Next, we can find four rational numbers between 10/15 and 9/15 by dividing the difference between the two fractions by 5 and adding the resulting value to the smaller fraction, as follows:

(9/15 - 10/15)/5 = -1/75

10/15 + (-1/75) = 799/1125

10/15 + 2(-1/75) = 749/1125

10/15 + 3(-1/75) = 699/1125

10/15 + 4(-1/75) = 649/1125

Therefore, the four rational numbers between 2/3 and 3/5 are:

649/1125, 699/1125, 749/1125, 799/1125

Learn more about rational numbers here

https://brainly.in/question/135903

Learn more about denominator here

https://brainly.in/question/358434

#SPJ2

Answer 2

The four rational numbers are $\frac{19}{30} ,\frac{13}{20} , \frac{37}{60} , \frac{77}{120} .$

• When referring to the set, the word "rational" relates to the fact that a rational number is a ratio of two integers. "Rational" is frequently used as a word to shorten "rational number" in mathematics. When the word rational is used, it sometimes refers to numbers whose coefficients are rational.
• For instance, a rational point is a point whose coordinates are rational numbers; a rational matrix is a matrix of rational numbers and a rational polynomial may be a polynomial with rational coefficients, though the term "polynomial over the rationals" is generally preferred to avoid confusion between "rational expression" and "rational function" (a polynomial is a rational expression and defines a rational function, even if its coefficients are not rational).
• A rational curve, however, is a curve that can be parameterized by rational functions rather than a curve defined over the rationals.

Here, according to the given information, we are given that,

The two rational numbers are, $\frac{2}{3}$ and $\frac{3}{5} .$

Now, the rational numbers between these two numbers are,

• $\frac{\frac{2}{3} +\frac{3}{5} }{2} = \frac{\frac{19}{15} }{2} = \frac{19}{30} .$
• $\frac{\frac{2}{3} +\frac{19}{30} }{2} = \frac{\frac{39}{30} }{2} = \frac{39}{60} = \frac{13}{20} .$
• $\frac{\frac{19}{30} +\frac{3}{5} }{2} = \frac{\frac{37}{30} }{2} = \frac{37}{60} .$
• $\frac{\frac{13}{20} +\frac{19}{30} }{2} = \frac{\frac{39+38}{60} }{2} = \frac{77}{120} .$

Hence, the four rational numbers are $\frac{19}{30} ,\frac{13}{20} , \frac{37}{60} , \frac{77}{120} .$

Learn more here

brainly.in/question/138158

#SPJ3