Question

Find five rational number between 1/3 and 2/3

Answer 1

Answer:

Five rational numbers between  $\frac{1}{3} , \frac{2}{3}$  are   $\frac{1}{2} , \frac{4}{9}, \frac{5}{9}, \frac{5}{12}, \frac{7}{12}$

Step-by-step explanation:

Given rational numbers are $\frac{1}{3} , \frac{2}{3}$

To find five rational numbers between the given two rational numbers

Solution:

The rational numbers between any two rational numbers is the same as the rational number between their equivalent fractions.

The equivalent fractions of a rational number are obtained by multiplying the numerator and denominator with the same number

The equivalent fractions of  $\frac{1}{3} , \frac{2}{3}$ are ( $\frac{1X2}{3X2} , \frac{2X2}{3X2}$), ($\frac{1X3}{3X3} , \frac{2X3}{3X3}$),  ($\frac{1X4}{3X4} , \frac{2X4}{3X4}$)

The equivalent fractions of  $\frac{1}{3} , \frac{2}{3}$ are  $(\frac{2}{6} , \frac{4}{6})$, $(\frac{3}9} , \frac{6}{9})$,  $(\frac{4}{12} , \frac{8}{12})$

The rational number between  $\frac{1}{3} , \frac{2}{3}$ can be a rational number in any two of these equivalent fractions

The rational number between  $(\frac{2}{6} , \frac{4}{6})$ = $\frac{3}{6}$

Rational number between $(\frac{3}9} , \frac{6}{9})$ = $\frac{4}{9} , \frac{5}{9}$

Rational number between  $(\frac{4}{12} , \frac{8}{12})$ = $\frac{5}{12}, \frac{6}{12}, \frac{7}{12}$

Rational number between  $\frac{1}{3} , \frac{2}{3}$  =  $\frac{3}{6}$ , $\frac{4}{9} , \frac{5}{9}$, $\frac{5}{12}, \frac{6}{12}, \frac{7}{12}$

= $\frac{1}{2} , \frac{4}{9}, \frac{5}{9}, \frac{5}{12}, \frac{1}{2}, \frac{7}{12},$

=  $\frac{1}{2} , \frac{4}{9}, \frac{5}{9}, \frac{5}{12}, \frac{7}{12}$

Five rational numbers between  $\frac{1}{3} , \frac{2}{3}$  =  $\frac{1}{2} , \frac{4}{9}, \frac{5}{9}, \frac{5}{12}, \frac{7}{12}$

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Answer 2

Answer:

$\frac{10}{27} ,\frac{11}{27},\frac{12}{27},\frac{13}{27} and \frac{14}{27}$ are the rational number between  $\frac{1}{3}$ and $\frac{2}{3}$.

Step-by-step explanation:

Explanation:

Given that, $\frac{1}{3}$ and $\frac{2}{3}$

Rational number - A rational number can be stated mathematically as the ratio or fraction $\frac{p}{q}$ of two numbers, where p and q are the numerator and denominator, respectively.

According to the question we need to find the five rational number lying between  $\frac{1}{3}$ and $\frac{2}{3}$.

Step 1:

We have, $\frac{1}{3}$ and $\frac{2}{3}$

On multiplying both numerator and denominator of the given numbers by 9.

⇒ $\frac{1}{3}$ × $\frac{9}{9}$ = $\frac{9}{27}$ and $\frac{2}{3}$ × $\frac{9}{9}$ = $\frac{18}{27}$

So, the rational number between $\frac{9}{27}$ and $\frac{18}{27}$ are $\frac{10}{27} ,\frac{11}{27},\frac{12}{27},\frac{13}{27},\frac{14}{27},\frac{15}{27}$.

Final answer:

Hence, $\frac{10}{27} ,\frac{11}{27},\frac{12}{27},\frac{13}{27} and \frac{14}{27}$ are the rational number between  $\frac{1}{3}$ and $\frac{2}{3}$.

#SPJ2