 Questions & Answers    Question Answers

# Find five rational numbers between $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$  Answer 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.
Bookmark added to your notes.
View Notes
Rational Numbers Between Two Rational Numbers  Difference Between Rational and Irrational Numbers  Rational and Irrational Numbers  CBSE Class 8 Maths Chapter 1 - Rational Numbers Formulas  Rational Numbers  Rational Numbers and Their Properties  Operations on Rational Numbers  Decimal Expansion of Rational Numbers  Rational Numbers on a Number line  CBSE Class 7 Maths Chapter 9 - Rational Numbers Formulas  