Answer:
[tex] { \boxed{ \bold{ \huge{ { \boxed{ \sf{ \frac{1}{2} }}}}}}}[/tex]
Step-by-step explanation:
Let the missing fraction be x
[tex] \star \: \: \: \sf{x - \frac{3}{10} = \frac{1}{5}} [/tex]
Solve for x.
L.C.M of 1 and 10 = 10
[tex] \longmapsto{ \sf{ \frac{x \times 10 - 3}{10} = \frac{1}{5} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{10x - 3}{10} = \frac{1}{5} }}[/tex]
Do cross multiplication
[tex] \longmapsto {\sf{5(10x - 3) = 10 \times 1}}[/tex]
Distribute 5 through the parentheses
[tex] \longmapsto{ \sf{50x - 15 = 10}}[/tex]
Move 15 to right hand side and change it's sign
[tex] \longmapsto{ \sf{50x = 10 + 15}}[/tex]
Add the numbers: 10 and 15
[tex] \longmapsto{ \sf{50x = 25}}[/tex]
Divide both sides by 50
[tex] \longmapsto{ \sf{ \frac{50x}{50} = \frac{25}{50}}} [/tex]
[tex] \longmapsto{ \purple{ \boxed{ \sf{ x = \frac{1}{2} }}}}[/tex]
The missing fraction is [tex] \sf{ \frac{1}{2} }[/tex]
Hope I helped!
Best regards! :D
~TheAnimeGirl
