Question

ten rational number between 5/3 and 7/15​

Answer 1

Given:

Two rational numbers -

$\bf \bullet \: \dfrac{5}{3} \\ \\ \\ \bf \bullet \: \dfrac{7}{15}$

What To Find:

We have to find

• Ten rational numbers between these two numbers.

How To Find:

To find them we have to

• Make the denominator of two given rational numbers the same by taking the LCM of them
• Then see whether the numbers between them are more than needed as asked in the question.
• If yes, we have found the number of rational numbers between them.
• If no, we have to proceed with the same steps by taking the numbers greater than we took the last time.

Solution:

Find the LCM of 3 and 15 ie,

$\rm \implies 15$

Multiply the 1st rational numbers,

$\rm \implies \dfrac{5}{3} \times \dfrac{5}{5} = \dfrac{25}{15}$

Multiply the 2nd rational numbers,

$\rm \implies \dfrac{7}{15} \times \dfrac{1}{1} = \dfrac{7}{15}$

Find the rational numbers between them,

$\rm \implies \dfrac{8}{15} \: ; \dfrac{9}{15} \: ; \dfrac{10}{15} \: ; \dfrac{11}{15} \: ; \dfrac{12}{15} \: ; \dfrac{13}{15} \: ; \dfrac{14}{15} \: ; \dfrac{15}{15} \: ; \dfrac{16}{15} \: ; \dfrac{17}{15} \: \: and \: so \: on.$

Final Answer:

Thus, the ten rational numbers are -

$\bf \hookrightarrow \: \dfrac{8}{15} \: ; \dfrac{9}{15} \: ; \dfrac{10}{15} \: ; \dfrac{11}{15} \: ; \dfrac{12}{15} \: ; \dfrac{13}{15} \: ; \dfrac{14}{15} \: ; \dfrac{15}{15} \: ; \dfrac{16}{15} \: ; \dfrac{17}{15}$