Questions & Answers
Question
Answers
Related Questions
Find five rational numbers between $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$
Answer
![Verified]()
Verified
Verified
Hint- As we know that rational numbers are represented as $\dfrac{{\text{p}}}{q}$ . And we have to find more rational numbers between $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$ So, we multiply the numerator and denominator by the same number.
“Complete step-by-step answer:”
Given numbers are $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$
So, we have to find five numbers, we will multiply the given numbers by $\dfrac{6}{6}$
Let the number ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$
Now, multiply A by $\dfrac{6}{6}$ , we obtain
${\text{A = }}\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}}$
And, multiply B by $\dfrac{6}{6}$ , we obtain
${\text{B = }}\dfrac{4}{5} \times \dfrac{6}{6} = \dfrac{{24}}{{30}}$
So, between $\dfrac{{18}}{{30}}{\text{ and }}\dfrac{{24}}{{30}}$ , we have to find rational numbers
Here, $\dfrac{{18}}{{30}} > \dfrac{{19}}{{30}} > \dfrac{{20}}{{30}} > \dfrac{{21}}{{30}} > \dfrac{{22}}{{30}} > \dfrac{{23}}{{30}} > \dfrac{{24}}{{30}}$
Hence five rational numbers between ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$ are
$\dfrac{{19}}{{30}},\dfrac{{20}}{{30}},\dfrac{{21}}{{30}},\dfrac{{22}}{{30}},\dfrac{{23}}{{30}}$
Note- To solve these types of questions, basic definitions of numbers, their properties must be remembered. Some definitions such as Irrational numbers have decimal expansion that neither terminate nor periodic and cannot be expressed as fraction for any integers. This question can also be done by continuous finding the average of the given number first and then the average of numbers obtained.
“Complete step-by-step answer:”
Given numbers are $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$
So, we have to find five numbers, we will multiply the given numbers by $\dfrac{6}{6}$
Let the number ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$
Now, multiply A by $\dfrac{6}{6}$ , we obtain
${\text{A = }}\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}}$
And, multiply B by $\dfrac{6}{6}$ , we obtain
${\text{B = }}\dfrac{4}{5} \times \dfrac{6}{6} = \dfrac{{24}}{{30}}$
So, between $\dfrac{{18}}{{30}}{\text{ and }}\dfrac{{24}}{{30}}$ , we have to find rational numbers
Here, $\dfrac{{18}}{{30}} > \dfrac{{19}}{{30}} > \dfrac{{20}}{{30}} > \dfrac{{21}}{{30}} > \dfrac{{22}}{{30}} > \dfrac{{23}}{{30}} > \dfrac{{24}}{{30}}$
Hence five rational numbers between ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$ are
$\dfrac{{19}}{{30}},\dfrac{{20}}{{30}},\dfrac{{21}}{{30}},\dfrac{{22}}{{30}},\dfrac{{23}}{{30}}$
Note- To solve these types of questions, basic definitions of numbers, their properties must be remembered. Some definitions such as Irrational numbers have decimal expansion that neither terminate nor periodic and cannot be expressed as fraction for any integers. This question can also be done by continuous finding the average of the given number first and then the average of numbers obtained.
×
Sorry!, This page is not available for now to bookmark.
Like this
Liked
-
LIVECourses
-
Crash Courses 2021
-
Vedantu Pro
-
Vedantu Assist
-
Class 12
-
-
JEE
-
JEE Main & Advanced 2021
-
JEE Main & Advanced 2022
-
JEE Main & Advanced 2023
-
-
NEET
-
NEET 2021
-
NEET 2022
-
NEET 2023
-
-
NDA
-
CBSE
-
Commerce
-
Class 11
-
Class 12
-
-
ICSE
-
Maharashtra Board
-
Micro Courses
-
-
Reading & Spoken English -
FREEMaster Classes
-
PREMIUM1-on-1 Classes
-
Study Material
-
NCERT Solutions
-
Previous Year Papers
-
Mock Tests
-
Sample Papers
-
Reference Book Solutions
-
ICSE Solutions
-
School Syllabus
-
Revision Notes
-
Important Questions
-
Math Formula Sheets
-
-
More
Book your FREE Online counselling session
Share your contact information
Your FREE Online counselling session has been booked!
Vedantu academic counsellor will be calling you shortly for your Online Counselling session.
DONE
Please try again later
OK
NCERT Book Solutions
Reference Book Solutions
Toll Free:
1800-120-456-456
Mobile:
+91 988-660-2456
Toll Free:
1800-120-456-456
Mobile:
+91 988-660-2456
(Mon-Sun: 9am - 11pm IST)
Questions?
Chat with us
