Question

find three rational numbers between 2/5 and 3/7​

Answer 1

Answer:

Here we need to find rational numbers between two other rational numbers.

Step 1: We need to find the LCM of the denominator to make them equal.

$\begin{array}{r| l}7 & 5,7 \\ \cline{2-2} 5 & 5,1 \\ \cline{2-2} &1,1 \end{array} \\ \\ So \: LCM \: of \: 5 \: and \: 7 \: is \: 35$

Step 2: Make the denominators equal.

$\frac{2\times7 }{5\times7 }=\frac{14}{35}\\ \\ \frac{3\times5 }{7\times5 } =\frac{15}{35}$

Step 3: Now you can multiply any number to the numerator and denominator. Here I am gonna multiply 4

$\frac{14\times4 }{35\times4 } = \frac{56}{140} \\ \\ \frac{15\times4 }{35\times4 } =\frac{60}{140}$

$\therefore The \: rational \: numbers \: between \\ \frac{2}{5} \: and \: \frac{3}{7} \: are \: \frac{57}{140}, \: \frac{58}{140} \ and \ \frac{59}{140}$

☆Additional Information ☆

What are rational numbers?

Numbers that can be represented in p/q form where q≠ 0 is known as rational numbers.

About the properties of rational numbers?

Closure Property - Rational Numbers are closed under Addition, Subtraction, and Multiplication for Rational numbers.

Commutative Propert - Rational Numbers are commutative under Addition and Multiplication for Rational numbers.

Associative Property - Rational Numbers are associative under Addition and Multiplication for Rational numbers.

Distributive Property - There are two types of distributive properties. They are -

Distributive Property over Addition - a × (b + c) = a × b + a × c

Distributive Property over Subtraction - a × (b - c) = a × b - a × c

Answer 2

Step-by-step explanation:

L.C.M of 5 and 7 is 35

=2/5=2*7/5*7=14/35

=3/7=3*5/7*5=15/35

by multiplying the numerator and denominator of 14/35 and 15/35 by 4.

= 14/35=14*4/35*4=56/140

=15/35=15*4/35*4=60/140

therefore,

the three rational numbers =57/140, 58/140, 59/140