Find rational numbers between ( -7 and 1/3) 5/9 and 2/3 ( - 2)/(5) and ( - 3)/(7) ​

Question

Find rational numbers between

( -7 and 1/3)

5/9 and 2/3


`( - 2)/(5) and ( - 3)/(7)`
​

Answer 1

i know there's a lot of explanation. but it helps u for sure :)

Explanation:

1)

`-7 \ and \ (1)/(3) = (-7)/(1) \ and \ (1)/(3)\\\\LCM \ of \ 1 \ and\ 3 = 3\\\\(-21)/(3) \ and \ (1)/(3)\\\\To \ find \ rational \ numbers \ between \ (-21)/(3) \ and \ (1)/(3) \ write \ any \ number \ between \ -21 \ and \ 1 \ with \ denominator \ 3. \\\\That \ is, \ (-20)/(3), (-19)/(3), (-18)/(3).....`

2)

`(5)/(9) \ and \ (2)/(3)\\\\Similarly \ take \ LCM \ of \ 9 \ and \ 3 = 9\\\\Since \ it \ is \ still \ complicated \ to \ find \ rational \ number \ between \ (5)/(9) \ and \ (6)/(9),`

`because \ there \ exists \ no\ natural \ number \ between \ 5 \ and \ 6.`

`We \ will \ multiply \ numerator \ and \ denominator\ by\ 10. \\\\Therefore\ (5)/(9) \ and \ (6)/(9) \ becomes \ (50)/(90) \ and \ (60)/(90).`

`Keeping \ denominator \ 90 \ write \ numbers \ from \ 50 \ to \ 60 \ in \ the\ numerator.\\\\That \ is , (51)/(90), (52)/(90), (53)/(90), (54)/(90), .\ .\ .`

3)

`LCM \ of \ 5 \ and \ 7 = 35\\\\(-2)/(5) \ and \ (-3)/(7)\ becomes \ (-14)/(35) \ and \ (-15)/(35)\\\\Now \ multiply \ denominator \ and \ numerator \ by \ 10\\\\(-140)/(350) \ and \ (-150)/(350).\\\\Rational \ numbers \ are (-141)/(350), (-142)/(350), (-143)/(350), . \ . \ . \`

Tip :

1. Make the denominator same.

2. Multiply numerator and denominator by 10 , 100 or 1000

3. Just write the natural numbers between the 2 numerators keeping denominator same.