Simplification - Study Mode

[#206] $$frac{3}{7},{ ext{of}},455 + frac{5}{8},{ ext{of}},456 = ?$$
Correct Answer

(D) 480

Explanation

Solution: $$eqalign{
& { ext{Given Expression,}} cr
& {frac{3}{7} imes 455 + frac{5}{8} imes 456} cr
& = left( {3 imes 65 + 5 imes 57}
ight) cr
& = 195 + 285 cr
& = 480 cr} $$

[#207] $$6frac{5}{6} imes 5frac{1}{3} imes 17frac{2}{3} imes 4frac{1}{2} = ?$$
Correct Answer

$$112frac{1}{3}$$

Explanation

Solution: $$eqalign{
& {frac{{41}}{6} imes frac{{16}}{3} + frac{{53}}{3} imes frac{9}{2}} cr
& = {frac{{328}}{9} + frac{{159}}{2}} cr
& = frac{{656 + 1431}}{{18}} cr
& = frac{{2087}}{{18}} cr
& = 115frac{{17}}{{18}} cr} $$

[#208] $$4frac{4}{5} div 6frac{2}{5} = ?$$
Correct Answer

(A) $$frac{3}{4}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression}} cr
& frac{{24}}{5} div frac{{32}}{5} cr
& = frac{{24}}{5} imes frac{5}{{32}} cr
& = frac{3}{4} cr} $$

[#209] $${ ext{If }}x = frac{1}{{2 + frac{1}{2}}}{ ext{ then }}frac{1}{x} = ?$$
Correct Answer

(B) $$frac{5}{2}$$

Explanation

Solution: $$eqalign{
& x = frac{1}{{2 + frac{1}{2}}} = frac{2}{5} cr
& Rightarrow frac{1}{x} = frac{5}{2} cr} $$

[#210] Simplify the following: $$frac{{{{left( {0.1}
ight)}^2} + {{left( {0.01}
ight)}^2} + {{left( {0.009}
ight)}^2} + 2left[ {0.1 imes 0.01 + 0.01 imes 0.009 + 0.009 imes 0.1}
ight]}}{{0.01 + 0.001 + 0.0009}}$$
Correct Answer

(D) 1.19

Explanation

Solution: $$eqalign{
& frac{{{{left( {0.1}
ight)}^2} + {{left( {0.01}
ight)}^2} + {{left( {0.009}
ight)}^2} + 2left[ {0.1 imes 0.01 + 0.01 imes 0.009 + 0.009 imes 0.1}
ight]}}{{0.01 + 0.001 + 0.0009}} cr
& = frac{{10{{left( {0.1 + 0.01 + 0.009}
ight)}^2}}}{{left( {0.1 + 0.01 + 0.009}
ight)}} cr
& = 10 imes 0.119 cr
& = 1.19{ ext{ Answer}} cr} $$