Simplification - Study Mode

[#121] $$frac{{225}}{{836}} imes frac{{152}}{{245}} div 1frac{{43}}{{77}} = ?$$
Correct Answer

(C) $$frac{{3}}{{28}}$$

Explanation

Solution: $$eqalign{
& frac{{225}}{{836}} imes frac{{152}}{{245}} div 1frac{{43}}{{77}} cr
& = frac{{225}}{{836}} imes frac{{152}}{{245}} div frac{{120}}{{77}} cr
& = frac{{225}}{{836}} imes frac{{152}}{{245}} imes frac{{77}}{{120}} cr
& = frac{3}{{28}} cr} $$

[#122] $$frac{3}{2} imes frac{{11}}{5} div left( {frac{{25}}{{44}} imes frac{{11}}{5}}
ight) div frac{{33}}{{15}} = ?$$
Correct Answer

$$frac{{1}}{{2}}$$

Explanation

Solution: $$eqalign{
& frac{3}{2} imes frac{{11}}{5} div left( {frac{{25}}{{44}} imes frac{{11}}{5}}
ight) div frac{{33}}{{15}} cr
& = frac{3}{2} imes frac{{11}}{5} div frac{5}{4} div frac{{33}}{{15}} cr
& = frac{3}{2} imes frac{{11}}{5} imes frac{4}{5} imes frac{{15}}{{33}} cr
& = frac{6}{5} cr
& = 1frac{1}{5} cr} $$

[#123] Simplify : $${ ext{10}}frac{1}{8}{ ext{ of }}frac{{12}}{{15}} div frac{{35}}{{36}}{ ext{ of }}frac{{20}}{{49}}$$
Correct Answer

(D) $$20frac{{103}}{{250}}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& frac{{81}}{8},of,frac{{12}}{{15}} div frac{{35}}{{36}},of,frac{{20}}{{49}} cr
& = frac{{81}}{{10}} div frac{{25}}{{63}} cr
& = frac{{81}}{{10}} imes frac{{63}}{{25}} cr
& = frac{{5103}}{{250}} cr
& = 20frac{{103}}{{250}}, cr} $$

[#124] $$sqrt {frac{{{{left( {0.03}
ight)}^2} + {{left( {0.21}
ight)}^2} + {{left( {0.065}
ight)}^2}}}{{{{left( {0.003}
ight)}^2} + {{left( {0.021}
ight)}^2} + {{left( {0.0065}
ight)}^2}}}} $$
Correct Answer

(B) 10

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& sqrt {frac{{{{left( {0.03}
ight)}^2} + {{left( {0.21}
ight)}^2} + {{left( {0.065}
ight)}^2}}}{{{{left( {0.003}
ight)}^2} + {{left( {0.021}
ight)}^2} + {{left( {0.0065}
ight)}^2}}}} cr
& = sqrt {frac{{0.0009 + 0.0441 + 0.004225}}{{0.000009 + 0.000441 + 0.00004225}}} cr
& = sqrt {frac{{0.049225}}{{0.00049225}}} cr
& = sqrt {100} cr
& = 10 cr} $$

[#125] The sum of $$sqrt {0.01} + sqrt {0.81} + sqrt {1.21} + sqrt {0.0009} = ?$$
Correct Answer

(B) 2.13

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& sqrt {0.01} + sqrt {0.81} + sqrt {1.21} + sqrt {0.0009} cr
& = 0.1 + 0.9 + 1.1 + 0.03 cr
& = 2.13 cr} $$