![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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
(a)(i) Provide the number in the box $\boxed{}$, such that $\frac{2}{3}\times\boxed{}=\frac{10}{30}$
(ii) The simplest form of the number obtained in $\boxed{}$ is _____.
(b) (i) Provide the number in the box $\boxed{}$, such that $\frac{3}{5}\times\boxed{}=\frac{24}{75}$
(ii) The simplest form of the number obtained in $\boxed{}$ is _____.
To do:
We have to find the missing numbers.
Solution:
(a)
(i) $\frac{2}{3}\times$________$=\frac{10}{30}$
Let the missing number be $\frac{x}{y}$
This implies,
$\frac{2}{3}\times \frac{x}{y}=\frac{10}{30}$
$\frac{2\times x}{3\times y}=\frac{10}{30}$
$2x=10$ and $3y=30$
$x=\frac{10}{2}$ and $y=\frac{30}{3}$
$x=5$ and $y=10$
Therefore, $\frac{5}{10}$ is the number in the box, such that $\frac{2}{3}\times\frac{5}{10}=\frac{10}{30}$.
(ii) The simplest form of $\frac{5}{10}$ is
$\frac{5}{10}=\frac{5\times1}{5\times2}$
$=\frac{1}{2}$
(b)
(i) $\frac{3}{5}\times$______$=\frac{24}{75}$
Let the missing number be $\frac{x}{y}$
This implies,
$\frac{3}{5}\times \frac{x}{y}=\frac{24}{75}$
$\frac{3\times x}{5\times y}=\frac{24}{75}$
$3x=24$ and $5y=75$
$x=\frac{24}{3}$ and $y=\frac{75}{5}$
$x=8$ and $y=15$
Therefore, $\frac{8}{15}$ is the number in the box, such that $\frac{3}{5}\times\frac{8}{15}=\frac{24}{75}$.
(ii) As $\frac{8}{15}$ can't be simplified further since the GCF of the numerator and the denominator is $1$.
Therefore, its simplest form is $\frac{8}{15}$ itself.