Answer:
i know there's a lot of explanation. but it helps u for sure :)
Step-by-step explanation:
1)
[tex]-7 \ and \ \frac{1}{3} = \frac{-7}{1} \ and \ \frac{1}{3}\\\\LCM \ of \ 1 \ and\ 3 = 3\\\\\frac{-21}{3} \ and \ \frac{1}{3}\\\\To \ find \ rational \ numbers \ between \ \frac{-21}{3} \ and \ \frac{1}{3} \ write \ any \ number \ between \ -21 \ and \ 1 \ with \ denominator \ 3. \\\\That \ is, \ \frac{-20}{3}, \frac{-19}{3}, \frac{-18}{3}.....[/tex]
2)
[tex]\frac{5}{9} \ and \ \frac{2}{3}\\\\Similarly \ take \ LCM \ of \ 9 \ and \ 3 = 9\\\\Since \ it \ is \ still \ complicated \ to \ find \ rational \ number \ between \ \frac{5}{9} \ and \ \frac{6}{9},[/tex]
[tex]because \ there \ exists \ no\ natural \ number \ between \ 5 \ and \ 6.[/tex]
[tex]We \ will \ multiply \ numerator \ and \ denominator\ by\ 10. \\\\Therefore\ \frac{5}{9} \ and \ \frac{6}{9} \ becomes \ \frac{50}{90} \ and \ \frac{60}{90}.[/tex]
[tex]Keeping \ denominator \ 90 \ write \ numbers \ from \ 50 \ to \ 60 \ in \ the\ numerator.\\\\That \ is , \frac{51}{90}, \frac{52}{90}, \frac{53}{90}, \frac{54}{90}, .\ .\ .[/tex]
3)
[tex]LCM \ of \ 5 \ and \ 7 = 35\\\\\frac{-2}{5} \ and \ \frac{-3}{7}\ becomes \ \frac{-14}{35} \ and \ \frac{-15}{35}\\\\Now \ multiply \ denominator \ and \ numerator \ by \ 10\\\\\frac{-140}{350} \ and \ \frac{-150}{350}.\\\\Rational \ numbers \ are \frac{-141}{350}, \frac{-142}{350}, \frac{-143}{350}, . \ . \ . \[/tex]
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.
