Simplification - Study Mode
[#171] $$eqalign{
& { ext{Simplify if,}} cr
& { ext{I = }}frac{3}{5} div frac{5}{6}{ ext{,}} cr
& { ext{II = 3}} div left[ {left( {4 div 5}
ight) div 6}
ight]{ ext{,}} cr
& { ext{III = }}left[ {3 div left( {4 div 5}
ight)}
ight] div 6,, cr
& { ext{IV = 3}} div { ext{4}}left( {5 div 6}
ight) cr
& { ext{then }} cr} $$
Correct Answer
I and II are equal
Explanation
Solution: $$eqalign{
& { ext{According to question,}} cr
& { ext{I = }}frac{3}{5} div frac{5}{6} cr
& { ext{I = }}frac{3}{5} imes frac{6}{5} = frac{18}{{25}} cr
& cr
& { ext{II = 3}} div left[ {frac{4}{5} imes frac{1}{6}}
ight] cr
& { ext{II = 3}} imes frac{{30}}{4} cr
& { ext{II = }}frac{{45}}{2} cr
& cr
& { ext{III = }}left[ {3 div left( {4 div 5}
ight)}
ight] div 6, cr
& { ext{III = }}left[ {3 imes frac{5}{4}}
ight] imes frac{1}{6}, cr
& { ext{III = }}frac{5}{8} cr
& cr
& { ext{IV = 3}} div { ext{4}}left( {5 div 6}
ight) cr
& { ext{IV = 3}} div { ext{4}} imes frac{5}{6} cr
& { ext{IV = 3}} imes frac{6}{{20}} cr
& { ext{IV = }}frac{9}{{10}} cr } $$
[#172] Simplify : -7m -[3n -{8m -(4n - 10m)}]
Correct Answer
(B) 11m - 7n
Explanation
Solution: $$eqalign{
& { ext{ = }}, - 7m - left[ {3n - left{ {8m - left( {4n - 10m}
ight)}
ight}}
ight],,, cr
& = , - 7m - left[ {3n - left{ {8m - 4n + 10m}
ight}}
ight], cr
& = - 7m - left[ {3n - 18m + 4n}
ight] cr
& = - 7m - left[ {7n - 18m}
ight] cr
& = - 7m - 7n + 18m,,, cr
& = ,11m - 7n,, cr} $$
[#173] If a + 2b = 6 and ab = 4, then what is $$frac{2}{a} + frac{1}{b} = ?$$
Correct Answer
(C) $$frac{3}{2}$$
Explanation
Solution: $$eqalign{
& frac{2}{a} + frac{1}{b} cr
& = frac{{2b + a}}{{ab}} cr
& = frac{6}{4} cr
& = frac{3}{2} cr} $$
[#174] Simplify the value of $$frac{{{ ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9 + 0}}{ ext{.2}} imes { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.2 + 0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} - { ext{3}} imes 0.9 imes { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.3}}}}{{{ ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9 + 0}}{ ext{.2}} imes { ext{0}}{ ext{.2 + 0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} - 0.9 imes { ext{0}}{ ext{.2}} - { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.3}} - 0.3 imes 0.9}} = ?$$
Correct Answer
(A) 1.4
Explanation
Solution: According to question, $$frac{{{ ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9 + 0}}{ ext{.2}} imes { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.2 + 0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} - { ext{3}} imes 0.9 imes { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.3}}}}{{{ ext{0}}{ ext{.9}} imes { ext{0}}{ ext{.9 + 0}}{ ext{.2}} imes { ext{0}}{ ext{.2 + 0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} - 0.9 imes { ext{0}}{ ext{.2}} - { ext{0}}{ ext{.2}} imes { ext{0}}{ ext{.3}} - 0.3 imes 0.9}}$$ As we know that $${a^3} + {b^3} + {c^3} - 3abc = $$ xa0 xa0 $$left( {a + b + c}
ight)$$ xa0 $$left( {{a^2} + {b^2} + {c^2} - ab - bc - ca}
ight)$$ $$ = frac{{{{(0.9)}^3} + {{(0.2)}^3} + {{(0.3)}^3} - 3 imes 0.9 imes 0.2 imes 0.3}}{{{{(0.9)}^2} + {{(0.2)}^2} + {{(0.3)}^2} - 0.9 imes 0.2 - 0.2 imes 0.3 - 0.3 imes 0.9}}$$ $$ = frac{{left( {0.9 + 0.2 + 0.3}
ight)left[ {{{(0.9)}^2} + {{(0.2)}^2} + {{(0.3)}^2} - 0.9 imes 0.2 - 0.2 imes 0.3 - 0.3 imes 0.9}
ight]}}{{{{(0.9)}^2} + {{(0.2)}^2} + {{(0.3)}^2} - 0.9 imes 0.2 - 0.2 imes 0.3 - 0.3 imes 0.9}}$$ $$eqalign{
& = 0.9 + 0.2 + 0.3 cr
& = 1.4 cr} $$
[#175] Simplify : $$frac{{1 + frac{1}{2}}}{{1 - frac{1}{2}}} div frac{4}{7}left( {frac{2}{5} + frac{3}{{10}}}
ight)$$ xa0 xa0 $${ ext{of}}$$ $$frac{{frac{1}{2} + frac{1}{3}}}{{frac{1}{2} - frac{1}{3}}}$$
Correct Answer
(C) $$frac{3}{2}$$
Explanation
Solution: $$eqalign{
& { ext{According to question,}} cr
& frac{{1 + frac{1}{2}}}{{1 - frac{1}{2}}} div frac{4}{7}left( {frac{2}{5} + frac{3}{{10}}}
ight){ ext{of }}frac{{frac{1}{2} + frac{1}{3}}}{{frac{1}{2} - frac{1}{3}}} cr
& = frac{{frac{3}{2}}}{{frac{1}{2}}} div frac{4}{7}left( {frac{{20 + 15}}{{50}}}
ight) imes frac{{frac{5}{6}}}{{frac{1}{6}}} cr
& = frac{3}{2} imes frac{2}{1} div frac{4}{7} imes frac{{35}}{{50}} imes frac{5}{6} imes frac{6}{1} cr
& = frac{3}{2} imes frac{2}{1} div 2 cr
& = frac{3}{2} imes 2 div frac{1}{2} cr
& = frac{3}{2} cr} $$