Question

Find five rational numbers between 1/4 and 1/3​

Answer 1

Answer:

1/4 = 3/12 < *7/28* < 4/12 = 1/3

Let x,y be rational numbers, then x = a/b and y = c/d for a,b,c,d in integers, let n and m be positive integers:

(ma/b + nc/d)/(m+n) is a weighted mean of x and y,

(mad+bnc )/bd(m+n) is a rational number between x and y for any m,n in positive integers

a=1,b=4 and c=1,d=3

(3m+4n)/12(m+n) gives you a rational number number between 1/4 and 1/3 for any positive integers m,n

Answer 2

Answer:

$Rational \: Number \: between \: \frac{30}{120} \: and \: \frac{40}{120} \: are \: \\ \frac{31}{120} \\ \\ \frac{32}{120} = \frac{4}{15} \\ \\ \frac{33}{120 } \\ \\ \frac{34}{120} = \frac{17}{60} \\ \\ \frac{35}{120} = \frac{7}{24}$

Step-by-step explanation:

${1}^{st} Rational \: Number = \frac{1}{4} \\ \\ {2}^{nd} Rational \: Number = \frac{1}{3} \\ \\ {1}^{st} Rational \: Number = \frac{1}{4} \times \frac{30}{30} = \frac{30}{120} \\ \\ {2}^{nd} \: Rational \: Number = \frac{1}{3} \times \frac{40}{40} = \frac{40}{120} \\ \\ \\ \\ \\ Rational \: Number \: between \: \frac{30}{120} \: and \: \frac{40}{120} \: are \: \\ \frac{31}{120} \\ \\ \frac{32}{120} = \frac{4}{15} \\ \\ \frac{33}{120 } \\ \\ \frac{34}{120} = \frac{17}{60} \\ \\ \frac{35}{120} = \frac{7}{24}$

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