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Q.1: Find five rational numbers between 1 and 2 .

Q. $1$ : Find five rational numbers between $1$ and $2$ .

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Full solution

Q. Q.

1

: Find five rational numbers between

1

and

2

.

Understand the problem: Understand the problem. $\newline$ We need to find five rational numbers that lie between $1$ and $2$ . Rational numbers can be expressed as fractions where both the numerator and the denominator are integers, and the denominator is not zero.
Choose common denominator: Choose a common denominator to create equal intervals between $1$ and $2$ . A simple way to find numbers between $1$ and $2$ is to consider a common denominator that will allow us to divide the interval between $1$ and $2$ into equal parts. Let's choose $10$ as a common denominator. This means we will look for fractions between $\frac{10}{10}$ and $\frac{20}{10}$ .
Find first rational number: Find the first rational number. The first rational number after $1$ ( $10/10$ ) with a denominator of $10$ is $11/10$ .
Find second rational number: Find the second rational number. $\newline$ The second rational number after $\frac{11}{10}$ is $\frac{12}{10}$ , which can be simplified to $\frac{6}{5}$ .
Find third rational number: Find the third rational number. The third rational number after $\frac{12}{10}$ is $\frac{13}{10}$ .
Find fourth rational number: Find the fourth rational number. $\newline$ The fourth rational number after $\frac{13}{10}$ is $\frac{14}{10}$ , which can be simplified to $\frac{7}{5}$ .
Find fifth rational number: Find the fifth rational number. $\newline$ The fifth rational number after $\frac{14}{10}$ is $\frac{15}{10}$ , which can be simplified to $\frac{3}{2}$ or $1.5$ .
Verify numbers: Verify that all the numbers are between $1$ and $2$ and are in their simplest form. $\newline$ We have the numbers $\frac{11}{10}$ , $\frac{6}{5}$ , $\frac{13}{10}$ , $\frac{7}{5}$ , and $\frac{3}{2}$ . All of these numbers are greater than $1$ and less than $2$ , and they are all in their simplest form.

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