robin and freddy eat cookies from a jar robin ate 3/16of the cookies the fraction of cookies eaten by freddy turns out to be multiplication inverse of the fraction eaten by robin determine the fraction of cookies freddy eat
Answers
Answer:
Given
:
\sf{Sum~of~two~rational~numbers={\dfrac{2}{5}}}Sum of two rational numbers=
5
2
\sf{One~of~the~number~is~{\dfrac{-4}{7}}}One of the number is
7
−4
\bf{{\underline{To~find}}:}
To find
:
\sf{The~other~number}The other number
\bf{{\underline{Solution}}:}
Solution
:
\sf{Let~the~number~be~~‛x’}Let the number be ‛x’
\sf{~~~~~~~~~~ x+{\dfrac{-4}{7}}={\dfrac{2}{5}}} x+
7
−4
=
5
2
\sf\implies{x={\dfrac{2}{5}}-{\dfrac{-4}{7}}}⟹x=
5
2
−
7
−4
\sf\implies{x={\dfrac{(2×7)-(-4×5)}{35}}~~~~~~(LCM=35)}⟹x=
35
(2×7)−(−4×5)
(LCM=35)
\sf\implies{x={\dfrac{14-(-20)}{35}}}⟹x=
35
14−(−20)
\sf\implies{x={\dfrac{14+20}{35}}}⟹x=
35
14+20
\sf\implies{x=\purple{\underline{\boxed{\bf~{\dfrac{34}{35}}~}}}}⟹x=
35
34
\bf\therefore{{\underline{Required~answer}}:}∴
Required answer
:
\sf{Unknown~number,~~x~~is~{\purple{\bf {\dfrac{34}{35}}}}}Unknown number, x is
35
34
\bf{{\underline{Verification}}:}
Verification
:
\sf{~~~~ {\dfrac{-4}{7}}+{\dfrac{34}{35}}}
7
−4
+
35
34
\sf{={\dfrac{(5×-4)+34}{35}}~~~~~~(LCM=35)}=
35
(5×−4)+34
(LCM=35)
\sf{={\dfrac{-20+34}{35}}}=
35
−20+34
\sf{={\dfrac{14}{35}}}=
35
14
\sf{={\dfrac{\cancel{14}~~^{2}}{\cancel{35}~~^{5}}}~~~~~~~~~~~~Taking~7~as~common~factor}=
35
5
14
2
Taking 7 as common factor
\bf{={\purple{\bf {\dfrac{2}{5}}}}=RHS}=
5
2
=RHS
{}
\bf{Hence~verified~!}Hence verified !