Simplification - Study Mode

[#66] The value of $$0.overline {45} imes 1.overline {22} $$ xa0 is:
Correct Answer

(D) $$0.overline 5 $$

Explanation

Solution: $$eqalign{
& 0.overline {45} imes 1.overline {22} cr
& = frac{{45}}{{99}} imes frac{{122 - 1}}{{99}} cr
& = frac{{45}}{{99}} imes frac{{121}}{{99}} cr
& = frac{5}{9} cr
& = 0.overline 5 { ext{ Answer}} cr} $$

[#67] The value of $$22.overline 4 + 11.5overline {67} - 33.5overline 9 $$ xa0 xa0 is:
Correct Answer

(B) $$0.4overline {12} $$

Explanation

Solution: $$eqalign{
& 22.overline 4 + 11.5overline {67} - 33.5overline 9 cr
& = 22 + frac{4}{9} + 11 + frac{{567 - 5}}{{990}} - 33 - frac{{59 - 5}}{{90}} cr
& = 33 - 33 + frac{4}{9} + frac{{562}}{{990}} - frac{{54}}{{90}} cr
& = frac{{40}}{{90}} - frac{{54}}{{90}} + frac{{562}}{{990}} cr
& = frac{{ - 14}}{{90}} + frac{{562}}{{990}} cr
& = frac{{ - 154 + 562}}{{990}} cr
& = frac{{408}}{{990}} cr
& = 0.4overline {12} cr} $$

[#68] Find the value of $$309 div left[ {left( {frac{3}{2}}
ight){ ext{of}}left( {25 + 35}
ight) - 12frac{3}{4}}
ight]$$
Correct Answer

(D) 4

Explanation

Solution: $$eqalign{
& 309 div left[ {left( {frac{3}{2}}
ight){ ext{of}}left( {25 + 35}
ight) - 12frac{3}{4}}
ight] cr
& = 309 div left[ {frac{3}{2} imes 60 - frac{{51}}{4}}
ight] cr
& = 309 div left[ {90 - frac{{51}}{4}}
ight] cr
& = 309 imes frac{4}{{360 - 51}} cr
& = 4 cr} $$

[#69] If a = -12, b = -6 and c = 18, then what is the value of $$frac{{2{ ext{abc}}}}{9}.$$
Correct Answer

(B) 288

Explanation

Solution: $$eqalign{
& frac{{2{ ext{abc}}}}{9} cr
& = frac{{2 imes - 12 imes - 6 imes 18}}{9} cr
& = 288 cr} $$

[#70] If $$M = frac{3}{7} div frac{6}{5} imes frac{2}{3} + frac{1}{5} imes frac{3}{2}$$ xa0 xa0 xa0and $$N = frac{2}{5} imes frac{5}{6} div frac{1}{3} + frac{3}{5} imes frac{2}{3} div frac{3}{5},$$ xa0 xa0 xa0then what is the value of $$frac{M}{N}$$?
Correct Answer

(C) $$frac{{113}}{{350}}$$

Explanation

Solution: $$eqalign{
& M = frac{3}{7} div frac{6}{5} imes frac{2}{3} + frac{1}{5} imes frac{3}{2} cr
& = frac{3}{7} imes frac{5}{6} imes frac{2}{3} + frac{3}{{10}} cr
& = frac{5}{{21}} + frac{3}{{10}} cr
& = frac{{50 + 63}}{{210}} cr
& = frac{{113}}{{210}} cr
& N = frac{2}{5} imes frac{5}{6} div frac{1}{3} + frac{3}{5} imes frac{2}{3} div frac{3}{5} cr
& = frac{2}{5} imes frac{5}{6} imes frac{3}{1} + frac{3}{5} imes frac{2}{3} imes frac{5}{3} cr
& = 1 + frac{2}{3} cr
& = frac{5}{3} cr
& frac{M}{N} = frac{{113}}{{210}} div frac{5}{3} cr
& = frac{{113}}{{210}} imes frac{3}{5} cr
& = frac{{113}}{{350}} cr} $$