Free Practice Questions for Simplification in Maths

$\frac{72+\frac{3}{8} \text { of } 56-8}{95-\frac{5}{2} of(25-21)}$
$\Rightarrow \frac{72+21-8}{95-\frac{5}{2} of(4)}$
$\Rightarrow \frac{83}{95-10}=\frac{85}{85}=1$

We can write it as:
$
\begin{aligned}
&\frac{6}{11}=0.545 \\
&\frac{13}{18}=0.72 \\
&\frac{15}{22}=0.68 \\
&\frac{19}{36}=0.52 \\
&\frac{25}{33}=0.75
\end{aligned}
$
Clearly, $\frac{25}{33}$ is the largest fraction.

$\frac{\frac{1}{4} \div \frac{1}{2} \times 1 \frac{1}{3}}{\frac{3}{4} o f 8 \div 2}+6 \div 3 \times 2$
$\Rightarrow \frac{\frac{1}{2} \times \frac{4}{3}}{6 \div 2}+2 \times 2$
$\Rightarrow \frac{\frac{2}{3}}{3}+4$
$\Rightarrow \frac{2}{9}+4$
$\Rightarrow \frac{2+36}{9}=\frac{38}{9} 4 \frac{2}{9}$

$\begin{aligned} & 2 \div 2 \text { of } \frac{1}{2}+2.5 \times 2 \div 5 \times \frac{3}{5} \text { of } \frac{1}{3}-0.5\left(2.5-\frac{1}{2} \times 2 \div \frac{1}{2}\right) \\ \Rightarrow & 2 \div 1+2.5 \times 2 \div 5 \times \frac{3}{15}-0.5\left(2.5-\frac{1}{2} \times 4\right) \\ \Rightarrow & 2+5 \div 1-0.25 \\ \Rightarrow & 7-0.25 \\ \Rightarrow & 6.75 \end{aligned}$

Let the number be x.
Now,

72 × 28 = 36 × 4 × x   

⇒ 2016 = 144 x x 

⇒ x = (2016/144) = 14

Now, when we check options -
(A) 14 is a multiple of 7.

(B) 14 is not a prime number.
(C) 14 is greater than 10.
(D) 14 is a multiple of 2 so it is an even number.
(E) 56 = 4 × 14, therefore 14 is the factor of 56.

So, A, D and E are correct.

Factors of the numbers -

36 = 1, 2, 3, 4, 6,9, 12, 18, 36 

48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48  

56 = 1, 2, 4, 7, 8, 14, 56  

24 = 1, 2, 3, 4, 6, 8, 12, 24

Clearly, 36 is a multiple of 3, 4, 6 and it has total of 9 factors.

Total money saved by Asha in a week = (50 + 100 + 80) - 60 = 230 - 60 = 170
Price of Mobile = 5,950
The number of weeks required = 5950/170 = 35

Price of letter weight35 g=20 g+additional15 g=5+2=7
Price of parcel weight250 g=50 g+additional200 g

=50 g+ additional (4×50)g =5+4×3=17

Price of parcel weighting300 g=50 g+ additional250 g

=50 g+ additional (5×50)g =5+5×3=20

Total postal charge=5+7+17+20=49

We know that one quadrant is 1/4.

So, $18 \frac{3}{4}=\frac{18 \times 4+3}{4}=\frac{75}{4} \div \frac{1}{4}$=75

$\Rightarrow 3 \times 6+8-6 \div 3+9$
$=18+8-2+9$
$=35-2$
$=33$

$\Rightarrow 3+\left\{1+\frac{1}{3}-(3-4 \div 3)+\frac{1}{4}+\frac{2}{3}\right\}$
$=3+\left\{\frac{3+1}{3}-\left(3-\frac{4}{3}\right)+\frac{3+8}{12}\right\}$
$=3+\left\{\frac{4}{3}-\left(\frac{9-4}{3}\right)+\frac{11}{12}\right\}$
$=3+\left\{\frac{4}{3}-\frac{5}{3}+\frac{11}{12}\right\}$
$=3+\left\{\frac{16-20+11}{12}\right\}$
$=3+\frac{7}{12}$
$=\frac{36+7}{12}$
$=\frac{43}{12}$

$= 104 \div 39$ of $\frac{2}{3}+1 \frac{2}{5} \times 12 \frac{1}{7}-\frac{3}{4}$
$= 104 \div 26+\frac{7}{5} \times \frac{85}{7}-\frac{3}{4}$
$= 4+17-\frac{3}{4}$
$= \frac{16+68-3}{4}$
$=\frac{81}{4}$
$= 20 \frac{1}{4}$

$\Rightarrow \frac{(5+9)-2+24 \text { of } 6 \div 4 \times 12}{-24 \div(-8) \times(-2)+3}$
$\Rightarrow \frac{14-2+144 \div 4 \times 12}{3 \times(-2)+3}$
$\Rightarrow \frac{14-2+36 \times 12}{-6+3}$
$\Rightarrow \frac{14-2+432}{-3}$
$\Rightarrow \frac{444}{-3}$
$\Rightarrow-148$

$\Rightarrow \frac{\frac{5}{6} \div \frac{5}{2} \times 3-1 \text { of } 2}{1+3 \div \frac{1}{3} \times 6-2}$
$=\frac{\frac{5}{6} \times \frac{2}{5} \times 3-2}{1+3 \times 3 \times 6-2}$
$=\frac{1-2}{1+54-2}$
$=\frac{-1}{53}$

$\Rightarrow[8+8-2 \times(2+81)-45 \div 9+(27 \div 9+5 \times 3-19)]$
$=[8+8-2 \times 83-5+(3+15-19)]$
$=[16-166-5-1]$
$=[16-172]$
$=-156$

$\Rightarrow$ Using BODMAS concept
$
=\frac{3 \text { of } 5 \frac{1}{2}+6 \div 5-2 \text { of } 3 \div 4}{1+\frac{3}{1+\frac{1}{4}} \text { of } 5-3 \frac{1}{3} \text { of } 2 \div 5}
$
$
=\frac{3 \text { of } \frac{11}{2}+6 \div 5-2 \text { of } 3 \div 4}{1+\frac{3 \times 4}{5} \text { of } 5-\frac{10}{3} \text { of } 2 \div 5}
$
$
\begin{aligned}
&=\frac{\frac{33}{2}+\frac{6}{5}-\frac{6}{4}}{1+12-\frac{4}{3}} \\
&=\frac{\frac{33}{2}+\frac{6}{5}-\frac{6}{4}}{1+12-\frac{4}{3}}=\frac{\frac{330-6}{20}}{\frac{35}{3}}=\frac{243}{175}
\end{aligned}
$

$\Rightarrow$ Using BODMAS concept

$=96-4$ of $(18-13)+4 \times 7$
$=96-4$ of $5+4 \times 7$
$=96-20+28$
$
=104
$

$\Rightarrow \frac{7}{8} \div 4 \frac{2}{3}$ of $1 \frac{1}{4}-1 \frac{1}{4} \times 1 \frac{1}{5}+(0 . \overline{53} \div 0.5 \overline{8}) \times 2 \frac{3}{4}$
$=\frac{7}{8} \div \frac{14}{3}$ of $\frac{5}{4}-\frac{5}{4} \times \frac{6}{5}+\left(\frac{53}{99} \div \frac{(58-5)}{90}\right) \times \frac{11}{4}$
$=\frac{7}{8} \div \frac{70}{12}-\frac{3}{2}+\left(\frac{53}{99} \times \frac{90}{53}\right) \times \frac{11}{4}$
$=\frac{7}{8} \times \frac{12}{70}-\frac{3}{2}+\frac{10}{11} \times \frac{11}{4}$
$=\frac{3}{20}-\frac{3}{2}+\frac{5}{2}$
$=\frac{3-30+50}{20}$
$=\frac{23}{20}$

$\Rightarrow$ Using BODMAS concept
$
\begin{aligned}
&=\frac{2}{5}-\left[1 \frac{1}{3}+\left(1 \frac{1}{4}-2 \frac{1}{3}\right)\right] \div 2 \frac{2}{3} \times \frac{3}{5}+\frac{2}{5} \\
&=\frac{2}{5}-\left[\frac{4}{3}+\left(\frac{5}{4}-\frac{7}{3}\right)\right] \div \frac{8}{3} \times \frac{3}{5}+\frac{2}{5} \\
&=\frac{2}{5}-\left[\frac{4}{3}-\frac{13}{12}\right] \div \frac{8}{3} \times \frac{3}{5}+\frac{2}{5} \\
&=\frac{2}{5}-\left[\frac{4}{3}-\frac{13}{12}\right] \div \frac{8}{3} \times \frac{3}{5}+\frac{2}{5} \\
&=\frac{2}{5}-\frac{3}{12} \times \frac{3}{8} \times \frac{3}{5}+\frac{2}{5} \\
&=\frac{2}{5}-\frac{9}{160}+\frac{2}{5}=\frac{119}{160}
\end{aligned}
$