Which Of the following is a rational number between 2/3 and 3/4
Answers
Answer:
The rational number between 2/3 and 3/4 is 17/24
To find:
rational number between 2/3 and 3/4
Solution:
Given numbers are 2/3 and 3/4
Rational number: Rational is a number that can be written in terms of “numerator” upon the “denominator”, but denominator should not be equal to zero. The numerator and denominator are the integers.
Rational number is in the form of p/q, here q≠0
Where p is the “numerator” and q is the “denominator”
The formula to find the rational number between two numbers is \frac {(a+b)}{2}
2
(a+b)
\begin{gathered}\begin{array} { l } { \text { Here } a = \frac { 2 } { 3 } } \\\\ { \mathrm { b } = \frac { 3 } { 4 } } \\\\ { = \frac { ( \frac { 2 } { 3 } + \frac { 3 } { 4 } ) } { 2 } } \end{array}\end{gathered}
Here a=
3
2
b=
4
3
=
2
(
3
2
+
4
3
)
\begin{gathered}\begin{array} { l } { = \frac { ( \frac { 8 + 9 } { 12 } ) } { 2 } } \\\\ { = \frac { 17 } { 24 } } \end{array}\end{gathered}
=
2
(
12
8+9
)
=
24
17
Therefore, the rational number between 2/3 and 3/4 is 17/24
LCM of 3 and 4 = 60
So, to make the denominators same multiply
2/3 × 20/20 = 40/60
And,
3/4 × 15/15 = 45/60
Hence, 41/60,42/60,43/60,44/60 are the rational numbers that lies between 2/3 and 3/4.
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