Simplification - Study Mode

[#161] If $${ ext{A}} = 3frac{1}{4} imes 4frac{1}{4} div 34 - frac{{47}}{{32}} + frac{{47}}{{16}}$$xa0 xa0 xa0 and $${ ext{B}} = 2frac{1}{2} + 5frac{1}{2} div 55 - frac{{11}}{{10}}$$ xa0 xa0 then what is the value of A - B?
Correct Answer

(D) $$frac{3}{8}$$

Explanation

Solution: $$eqalign{
& { ext{A}} = 3frac{1}{4} imes 4frac{1}{4} div 34 - frac{{47}}{{32}} + frac{{47}}{{16}} cr
& { ext{B}} = 2frac{1}{2} + 5frac{1}{2} div 55 - frac{{11}}{{10}} cr
& herefore { ext{A}} - { ext{B}} = left( {3frac{1}{4} imes 4frac{1}{4} div 34 - frac{{47}}{{32}} + frac{{47}}{{16}}}
ight) - left( {2frac{1}{2} + 5frac{1}{2} div 55 - frac{{11}}{{10}}}
ight) cr
& = left( {frac{{13}}{4} imes frac{{17}}{4} imes frac{1}{{34}} - frac{{47}}{{32}} + frac{{47}}{{16}}}
ight) - left( {frac{5}{2} + frac{{11}}{2} imes frac{1}{{55}} - frac{{11}}{{10}}}
ight) cr
& = left( {frac{{13}}{{32}} - frac{{47}}{{32}} + frac{{47}}{{16}}}
ight) - left( {frac{5}{2} + frac{1}{{10}} - frac{{11}}{{10}}}
ight) cr
& = left( {frac{{13 - 47 + 94}}{{32}}}
ight) - left( {frac{{25 + 1 - 11}}{{10}}}
ight) cr
& = frac{{60}}{{32}} - frac{{15}}{{10}} cr
& = frac{{15}}{8} - frac{3}{2} cr
& = frac{{15 - 12}}{8} cr
& = frac{3}{8} cr} $$

[#162] The value of $$0.overline {57} - 0.4overline {32} + 0.3overline 5 $$ xa0 xa0is:
Correct Answer

(B) $$0.4overline {94} $$

Explanation

Solution: $$eqalign{
& 0.overline {57} - 0.4overline {32} + 0.3overline 5 cr
& = 0.overline {57} - 0.4overline {32} + 0.3overline {55} cr
& = frac{{57}}{{99}} - frac{{432 - 4}}{{990}} + frac{{355 - 3}}{{990}} cr
& = frac{{570 - 428 + 352}}{{990}} cr
& = 0.4overline {94} cr} $$

[#163] If 3.352 - (9.759 - x) - 19.64 = 7.052, then what is the value of x?
Correct Answer

(C) 33.099

Explanation

Solution: 3.352 - (9.759 - x) - 19.64 = 7.052 ⇒ 3.352 - 9.759 + x - 19.64 - 7.052 = 0 ⇒ x = 36.451 - 3352 ∴ x = 33.099

[#164] The value of $$frac{8}{9}{ ext{ of}}left( {5frac{1}{4} div 2frac{1}{3}{ ext{ of }}4}
ight) div left( {8 div frac{2}{3}{ ext{ of }}frac{4}{5}}
ight){ ext{of}}left( {8 imes frac{2}{3} div frac{4}{5}}
ight){ ext{is:}}$$
Correct Answer

(C) $$frac{1}{{200}}$$

Explanation

Solution: $$eqalign{
& frac{8}{9}{ ext{ of}}left( {5frac{1}{4} div 2frac{1}{3}{ ext{ of }}4}
ight) div left( {8 div frac{2}{3}{ ext{ of }}frac{4}{5}}
ight){ ext{of}}left( {8 imes frac{2}{3} div frac{4}{5}}
ight) cr
& = frac{8}{9}{ ext{ of}}left( {frac{{21}}{4} div frac{7}{3} imes 4}
ight) div left( {8 div frac{8}{{15}}}
ight){ ext{of}}left( {8 imes frac{2}{3} imes frac{5}{4}}
ight) cr
& = frac{8}{9}{ ext{ of}}left( {frac{{21}}{4} imes frac{3}{{28}}}
ight) div left( {8 imes frac{{15}}{8}}
ight){ ext{of}}left( {frac{{20}}{3}}
ight) cr
& = left( {frac{8}{9} imes frac{9}{{16}}}
ight) div 100 cr
& = frac{1}{{200}} cr} $$

[#165] The value of $$frac{{left{ {left( {{m^2} + {n^2}}
ight)left( {m - n}
ight) - {{left( {m - n}
ight)}^3}}
ight}}}{{left( {{m^2}n - m{n^2}}
ight)}}$$ xa0 xa0 xa0is:
Correct Answer

(C) 2

Explanation

Solution: $$eqalign{
& frac{{left{ {left( {{m^2} + {n^2}}
ight)left( {m - n}
ight) - {{left( {m - n}
ight)}^3}}
ight}}}{{left( {{m^2}n - m{n^2}}
ight)}} cr
& = frac{{left( {m - n}
ight)left[ {{m^2} + {n^2} - {{left( {m - n}
ight)}^2}}
ight]}}{{mnleft( {m - n}
ight)}} cr
& = frac{{{m^2} + {n^2} - {m^2} - {n^2} + 2mn}}{{mn}} cr
& = frac{{2mn}}{{mn}} cr
& = 2{ ext{ Answer}} cr} $$