Simplification – basics, definition, formula, questions

‘BODMAS’ RULE :

The rule depicts correct sequence in which the operations are to be executed, so as to find our the value of a given expression.

BBracket
OOf
DDivision
MMultiplication
AAddition
SSubtraction
BODMAS CALCULATION METHOD
\text{Find the value of } 12 \div 2 \times 10+12(12-1) \\\frac{12}{2} \times 10+12(12-1) \\6 \times 10+12(12-1) \\60+12(12-1) \\60+12(11) \\60+132 \\192=\text { Ans }

IMPORTANT FORMULA

(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b) \\\left(a^{3}+b^{3}\right)=(a+b)\left(a^{2}-a b+b^{2}\right) \\\left(a^{3}-b^{3}\right)=(a-b)\left(a^{2}+a b+b^{2}\right) \\\left(a^{2}-b^{2}\right)=(a+b)(a-b) \\(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b) \\(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(a b+b c+c a) \\a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) \\(a+b)^{2}=\left(a^{2}+b^{2}+2 a b\right) \\(a-b)^{2}=\left(a^{2}+b^{2}-2 a b^{2}\right) \\(a+b)^{2}+(a-b)^{2}=2\left(a^{2}+b^{2}\right) \\(a+b)^{2}-(a-b)^{2}=4 a b \\
QUESTION 01
\text{find the value of }\left(\frac{1,00,500 \times 1,00,500-90,000 \times 90,000}{10,500}\right) \\\frac{(1,00,500)^{2}-(90,000)^{2}}{(1,00,500-90,000)} \\\frac{a^{2}-b^{2}}{a-b} \\(a+b)(a-b)=\left(a^{2}-b^{2}\right) \\\frac{a^{2}-b^{2}}{a-b}=a+b \\a=1,00,500 \\b=90,000 \\=1,00,500+90,000 \\=1,90,500 \\
QUESTION 02
\text{find the value of }\frac{628 \times 628 \times 628+888 \times 888 \times 888}{628 \times 628-628 \times 888+888 \times 888} \\a=628 \\b=888 \\\frac{a^{3}+b^{3}}{a^{2}-a b+b^{2}} \\\left(a^{3}+b^{3}\right)=(a+b)\left(a^{2}-a b+b^{2}\right) \\\frac{a^{3}+b^{3}}{a^{2}-a b+b^{2}}=(a+b) \\=628+888 \\=1,516 \\
QUESTION 03
\text{find the value of }\frac{10 \times 10 \times 10+12 \times 12 \times 12+13 \times 13 \times 13-3(10 \times 12 \times 13)}{10 \times 10+12 \times 12+13 \times 13-10 \times 12-12 \times 13-13 \times 10} \\ a=10 \\b=12 \\c=13 \\\frac{a^{3}+b^{3}+c^{3}-3(a b c)}{a^{2}+b^{2}+c^{2}-a b-b c-c a} \\a^{3}+b^{3}+c^{3}-3(a b c)=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) \\\frac{a^{3}+b^{3}+c^{3}-3(a b c)}{a^{2}+b^{2}+c^{2}-a b-b c-c a} =(a+b+c) \\=10+12+13 \\=35 \\
QUESTION 04
\text{find the value of }110 \times 110+115 \times 115 -2 \times 110 \times 115 \\a =110 \\b =115 \\a^{2}+b^{2}-2 a b =(a-b)^{2} \\=(110-115)^{2} \\=(-5)^{2} \\=25 \\
QUESTION 05
\text{find the value of }512 \times 512 \times 512-510 \times 510 \times 510 -3 \times 512 \times 510(512 -510) \\a =512 \\b =510 \\a^{3}-b^{3}-3 a b(a-b) =(a-b)^{3} \\=(512-510)^{3} \\=(2)^{3} \\=8 \\
QUESTION 06
\text{find the value of }2 \times(988 \times 988+984 \times 984) -(988+984)^{2} \\a =988 \\b =984 \\2\left(a^{2}+b^{2}\right)-(a+b)^{2} =(a-b)^{2} \\=(988-984)^{2} \\=(4)^{2} \\=16 \\

ROOT FORMULA

SQUARESQUARE ROOTSQUARESQUARE ROOT
1^{2}=1 \\ 2^{2}=4 \\ 3^{2}=9 \\ 4^{2}=16 \\ 5^{2}=25 \\ 6^{2}=36 \\ 7^{2}=49 \\ 8^{2}=64 \\ 9^{2}=81 \\ 10^{2}=100 \\ 11^{2}=121 \\ 12^{2}=144 \\ 13^{2}=169 \\ 14^{2}=196 \\ 15^{2}=225 \\ \sqrt{1}=1 \\ \sqrt{4}=2 \\ \sqrt{9}=3 \\ \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \\ \sqrt{49}=7 \\ \sqrt{64}=8 \\ \sqrt{81}=9 \\ \sqrt{100}=10 \\ \sqrt{121}=11 \\ \sqrt{144}=12 \\ \sqrt{169}=13 \\ \sqrt{196}=14 \\ \sqrt{225}=15 \\ 16^{2}=256 \\ 17^{2}=289 \\ 18^{2}=324 \\ 19^{2}=361 \\ 20^{2}=400 \\ 21^{2}=441 \\ 22^{2}=484 \\ 23^{2}=529 \\ 24^{2}=576 \\ 25^{2}=625 \\ 26^{2}=676 \\ 27^{2}=729 \\ 28^{2}=784 \\ 29^{2}=841 \\ 30^{2}=900 \\ \sqrt{256}=16 \\ \sqrt{289}=17 \\ \sqrt{324}=18 \\ \sqrt{361}=19 \\ \sqrt{400}=20 \\ \sqrt{441}=21 \\ \sqrt{484}=22 \\ \sqrt{529}=23 \\ \sqrt{576}=24 \\ \sqrt{625}=25 \\ \sqrt{676}=26 \\ \sqrt{729}=27 \\ \sqrt{784}=28 \\ \sqrt{841}=29 \\ \sqrt{900}=30 \\
QUESTION 07
\text{find the value of }\sqrt{383+\sqrt{302-\sqrt{164+\sqrt{28-\sqrt{9}}}}} \\\sqrt{383+\sqrt{302-\sqrt{164+\sqrt{28-3}}}} \\\sqrt{383+\sqrt{302-\sqrt{164+\sqrt{25}}}} \\\sqrt{383+\sqrt{302-\sqrt{164+5}}} \\\sqrt{383+\sqrt{302-\sqrt{169}}} \\\sqrt{383+\sqrt{302-13}} \\\sqrt{383+289} \\\sqrt{400} \\20 \\
QUESTION 08
\text{find the value of }\sqrt{48}-3 \sqrt{108}+2 \sqrt{27}+\sqrt{192} \\\sqrt{4^{2} \times 3}-3 \sqrt{6^{2} \times 3}+2 \sqrt{3^{2} \times 3}+\sqrt{8^{2} \times 3} \\4 \sqrt{3}-3 \times 6 \sqrt{3}+2 \times 3 \sqrt{3}+8 \sqrt{3} \\4 \sqrt{3}-18 \sqrt{3}+6 \sqrt{3}+8 \sqrt{3} \\-14 \sqrt{3}+14 \sqrt{3} \\0 \\

CUBE METHOD

\begin{equation}
\begin{array}{l|l|l|l|l}
1^{3}=1 & 11^{3}=1331 & 21^{3}=9261 & 31^{3}=29791 & 41^{3}=68921 \\
2^{3}=8 & 12^{3}=1728 & 22^{3}=10648 & 32^{3}=32768 & 42^{3}=74088 \\
3^{3}=27 & 13^{3}=2197 & 23^{3}=12167 & 33^{3}=35937 & 43^{3}=79507 \\
4^{3}=64 & 14^{3}=2744 & 24^{3}=13824 & 34^{3}=39304 & 44^{3}=85184 \\
5^{3}=125 & 15^{3}=3375 & 25^{3}=15625 & 35^{3}=42875 & 45^{3}=91125 \\
6^{3}=216 & 16^{3}=4096 & 26^{3}=17576 & 36^{3}=46656 & 46^{3}=97336 \\
7^{3}=343 & 17^{3}=4913 & 27^{3}=19683 & 37^{3}=50653 & 47^{3}=103823 \\
8^{3}=512 & 18^{3}=5832 & 28^{3}=21952 & 38^{3}=54872 & 48^{3}=110592 \\
9^{3}=729 & 19^{3}=6859 & 29^{3}=24389 & 39^{3}=59319 & 49^{3}=117649 \\
10^{3}=1000 & 20^{3}=8000 & 30^{3}=27000 & 40^{3}=64000 & 50^{3}=125000 \\
\end{array}
\end{equation}
QUESTION 09
\text{find the value of }\sqrt[3]{-121+\sqrt[3]{-61+\sqrt[3]{-26+\sqrt[3]-1}}} \\ \sqrt[3]{-121+\sqrt[3]{-61+\sqrt[3]{-26-1}}} \\ \sqrt[3]{-121+\sqrt[3]-61+\sqrt[3]{-27}} \\ \sqrt[3]{-121+\sqrt[3]{-61-3}} \\ \sqrt[3]{-121+\sqrt[3]{-64}} \\ \sqrt[3]{-121-4} \\\sqrt[3]{-125} \\ -5 \\

MISSING NUMBER

QUESTION 10
\text{find the value of }(?-10) \div 15 \times 10=100 \\\frac{x-10}{15} \times 10=100 \\\frac{x-10}{15}=\frac{100}{10} \\\frac{x-10}{15}=10 \\x-10=10 \times 15 \\x-10=150 \\x=150-10 \\x=140 \\
QUESTION 11
\text{find the value of }\frac{113 \times 4-x \times 2}{13 \times 9-5 \times 7}=5 \\\frac{452-2 x}{117-35}=5 \\\frac{452-2 x}{82}=5452-2 x=5 \times 82 \\452-2 x=410 \\452-410=2 x \\42=2 x \\x=\frac{42}{2} \\x=21 \\

FRACTION

BASIC METHOD
\text{find the value of } \\ 1+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2} \\ \text{find the value of } \\ \frac{1}{2}+2 \frac{1}{2}=\frac{3}{2}+\frac{5}{2}=\frac{8}{2} \\=4 \\ \text{find the value of } \\\frac{1 \frac{1}{2}}{1 \frac{1}{2}}=\frac{\frac{3}{2}}{\frac{3}{2}}=\frac{3}{2} \times \frac{2}{3} \\=0 \\
QUESTION 12
\text{find the value of }\frac{13 \frac{4}{7} \times 13 \frac{4}{7}+8 \frac{3}{7} \times 8 \frac{3}{7} }{13 \frac{4}{7}-8 \frac{3}{7}} \\a=13 \frac{4}{7} \\b=8 \frac{3}{7} \\a^{2}+b^{2}=(a+b)(a-b) \\=(a+b) \\=13 \frac{4}{7}+8 \frac{3}{7} \\=\frac{95+59}{7} \\=\frac{154}{7} \\=22 \\
QUESTION 13
\text{find the value of }1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+2 / 3}}}}} \\ \text{down to up }\uparrow \\ =\frac{5}{3} \\=\frac{8}{5} \\=\frac{13}{8} \\=\frac{21}{13} \\\text{ans}=\frac{34}{21} \\
QUESTION 14
\text{find the value of }1 \frac{3}{4}-1 \frac{1}{5}+1 \frac{5}{8} \\= \frac{7}{4}-\frac{6}{5}+\frac{13}{8} \\\text { LCM }= 4 \times 5 \times 2=40 \\= \frac{70-48+65}{40} \\= \frac{87}{40} \\= 2 \frac{7}{40} \\
simplification - basics, definition, formula, questions
LCM

9 MULTIPLE TRICK

9=10 \\99=100 \\999=1000 \\9999=10000 \\99999=100000 \\
QUESTION 15
\text{find the value of } \\ 458 \times 9= \\=4580-458 \\=3825 \\8987 \times 99= \\=89870008987 \\=889713 \\ 1,01,001 \times 999= \\=101,001,000-1,01,001 \\=100,899,999 \\568,721 \times 9999= \\=5687210000-568721 \\=56866412890 \\
QUESTION 16
\text{find the value of }999 \frac{995}{999} \times 999 \\=\frac{998,996}{999} \times 999 \\=9,98,996 \\

STATEMENT METHOD

QUESTION 17

Along a yard 300 metres long, 31trees are planted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees?

31 trees have 30 gaps between them

=\frac{300}{30}\text{m} \\

=10 metres

QUESTION 18

A tank is \frac{2}{4} full. If 16 litres of water is added to the tank, it becomes \frac{6}{8} full. The capacity of the tank is

\frac{6}{8}x-\frac{2}{4}=16 \\ 6x-4x=16\times8 \\ 2x=128 \\ x=\frac{128}{2} \\

x=64

QUANTITATIVE APTITUDE STUDY MATERIAL

Ration and proportional

Simplification

Percentage

Number series

L.C.M and H.C.F

Simple Interest

Compound Interest

Related search:

simplification

simplification aptitude

simplification formula

simplification question and answer pdf

simplification video class

simplification for tnpsc

simplification for ssc

simplification for rrb

simplification for bank exam

simplification for upsc

simplification for mba

simplification for rbi

simplification for cbi

simplification formula for abtitude

simplification for competitive exam

simplification for bank exam

simplification for rrb group d

simplification formula and tricks

SHARE

Leave a Comment

Your email address will not be published.

%d bloggers like this: