Question

Find three rational number between 2/3 and 4/5​

Answer 1

Answer:

Answer Expert Verified

the rational numbers = 61 / 90 62 /90 63 /90 64/90 65/90 66/90 67 /90 ....

Answer 2

ɢɪᴠᴇɴ :-

• $\sf Two\: numbers\:are\:given\:to\:us.$
• $\sf Two\: numbers\:are\:\dfrac{2}{3}\&\:\dfrac{4}{5}.$

ᴛᴏ ғɪɴᴅ:-

• $\sf Three\: Rational\:numbers\: between\:them.$

ᴀɴsᴡᴇʀ:-

Given two numbers are ,

• $\blue{\tt First\: number\:as\:\dfrac{2}{3}}.$
• $\blue{\tt Second\: number\:as\:\dfrac{4}{5}}.$

$\underline{\bf{\red{\blue{\mapsto}\:Steps\:of\: solving:-}}}$

$\sf{\green{\orange{\leadsto}\:Step\:1:-}}$ Find the LCM of their denominators.

$\sf{\green{\orange{\leadsto}\:Step\:2:-}}$ Convert the fractions into like fractions.

$\sf{\green{\orange{\leadsto}\:Step\:3:-}}$ Multiply the like fractions by the number one more than the number of fractions we are required to find.

$\sf{\green{\orange{\leadsto}\:Step\:4:-}}$ Write the consecutive next fractions after smaller fraction and convert them into simplest form.

____________________________________

$\underline{\bf{\red{\blue{\mapsto}\:Here\:we\: go:-}}}$

Here the denominators of fractions are ,

• $\blue{\tt Denominator\:of\: first\: fraction=3}$
• $\blue{\tt Denominator\:of\: second\: fraction=5}$

$\bf\boxed{\purple{ \mathbb{ LCM\:of\:3\&\:5=3\times5=15}}}$

$\sf{\red{\longrightarrow} Now,\:we\:may\: write\:them\:as:-}$

$\tt\pink{\dag}\:\dfrac{2}{3}=\dfrac{2\times5}{3\times5}=\green{\dfrac{10}{15}}$

$\tt\pink{\dag}\:\dfrac{4}{5}=\dfrac{4\times3}{3\times5}=\green{\dfrac{12}{15}}$

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Here we are required to find 3 rational numbers , So Multiply them by 4 .

$\sf{\red{\longrightarrow} Multiply\:them\:by\:4:}$

$\tt\green{\dag}\:\dfrac{10}{15}=\dfrac{10\times4}{15\times4}=\pink{\dfrac{40}{60}}$

$\tt\green{\dag}\:\dfrac{12}{15}=\dfrac{12\times4}{15\times4}=\pink{\dfrac{48}{60}}$

$\bf Hence\: required\:numbers \:are:-$

$\boxed{\red{\bf\longmapsto \dfrac{41}{60},\dfrac{43}{60},\dfrac{47}{60}}}$