Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find five rational numbers between: $\frac{2}{3}$ and $\frac{4}{5}$.
Given: $\frac{2}{3}$ and $\frac{4}{5}$
To find: We need to find 5 rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.
Solution:
To solve this question, first, we need to convert them into like fractions.
LCM of denominators (3 and 5) is 15. Now we have to change the fractions in such a way that denominators become 15.
To convert into like fractions we will multiply the numerator and denominator of $\frac{4}{5}$ with 3.
$\frac{4}{5} \ =\ \frac{4}{5}\ \times\ \frac{3}{3}\ =\ \frac{12}{15}$
We will multiply numerator and denominator of $\frac{1}{3}$ with 5.
$\frac{2}{3}\ =\ \frac{2}{3}\ \times\ \frac{5}{5}\ =\ \frac{10}{15}$
Now, our numbers are $\frac{10}{15}$ and $\frac{12}{15}$.
Only 1 number is there between 10 and 12. We can find 5 rational numbers between $\frac{10}{15}$ and $\frac{12}{15}$ by multiplying them with ($5\ +\ 1\ =\ 6$).
$\frac{10}{15}\ \times\ \frac{6}{6}\ =\ \frac{60}{90}$
And,
$\frac{12}{15}\ \times\ \frac{6}{6}\ =\ \frac{72}{90}$
Rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ are:
$\frac{61}{90},\ \frac{62}{90},\ \frac{63}{90},\ \frac{64}{90}\ and\ \frac{65}{90}$.
81 Views
