Quants Hacks | Percentage to Fraction Value |

Dear Students,

Quantitative Aptitude is hard in most cases especially in exams like Banks and Insurance. Many Banks exam has a two-tier examination pattern i.e., Prelims and Mains. Most of them have changed their exam patterns and set a sectional timing of 20 minutes on each section. Quantitative aptitude is important for every exam because proper strategy and enough practice can help you score full marks in this section. There may not be assured in the language section and you may be stuck while solving reasoning questions but quants is a scoring subject and assure full marks if the calculation is correct.

So to help you ace the quants and to save your precious time during exam hours Adda247 providing some quant tricks to help aspirants.

Multiplication technique-

Percentage to Fraction value and vice versa plays an important role in Simplification. It makes the calculation easier in the exam. So go through these values and try to understand the logic.

Example1-
75% of 4016
is very easy when we know the fraction value of 75%
Fraction value of 75% is 75/100 i.e. 3/4
3/4*4016=3*1004=3012
Example2-
95% of 25⁵⁄₁₉
if you don’t know fraction value 25⁵⁄₁₉ then it this takes time to solve
break 25⁵⁄₁₉ into (20+ 5⁵⁄₁₉)%
20%=1/5, and 5⁵⁄₁₉ = 1/19
(1/5+1/19)*95=24

A fraction is proper and Improper.

Proper fraction where the numerator is less than the denominator.
Example- 3/4, 17/19.

Improper fraction where the numerator is more than the denominator. We have to make numerator always less than the denominator.
Example- 17/12, 12/7
Note- Always make numerator less than the denominator.
we write 17/12= 1 5/12

Recurring Decimals– recurring decimal is produced by all the denominator which is not divisible by 2 or 5.

In competitive exam percentage to fraction value, up to 20 is asked.
(A) 1/2= 50/100= 50%,
3/2= 3*50%=150%,
5/2= 5*50%=250%

(B) 1/3= 1/3*100=33.33%( Recurring decimal)
2/3= 2*33.33%=66.66%,
4/3= 4* 33.33 but this is not easy we can write it as (1+1/3)*100=100%+33.33=133.33

(C) 1/4= 25%
3/4=3*25%=75%,
5/4 is improper fraction, split it into= (1+1/4)*100=100%+25%=125%
6/4= 3/2*100=150% or if you know table of 25 then directly 6*25=150
7/4= split it (1+3/4)*100=175% or 25*7=175

(D) 1/5= 20%,
2/5=40%,
3/5=60%,
4/5=80%,
6/5= 120%

(E) 1/6=16.66% or 16²⁄₃
2/6=1/3=33.33%,
5/6=5*16.66=83.33% or we can break it into (1-1/6)*100=100%-16²⁄₃=83¹⁄₃
7/6=(1+1/6)=116.66%

Note- 100-16²⁄₃= subtract 17 from the 100 and then subtract 3-2.
all the subtraction in fractions happens as above

(F) 1/7=14.28% or 14²⁄₇,
2/7=28.56 %
3/7= we multiply 3*14 2/7= 3*(14+2/7)%= 42%+6/7%=42.85
4/7=4*(14²⁄₇)=56+8/7=57 1/7
6/7= 1-1/7=100-14²⁄₇=85⁵⁄₇

(G) 1/8= 12.5%,
3/8=37.5%,
5/8= 62.5%,
7/8=(1-1/8)=100%-12.5=87.5%
9/8=(1+1/8)*100=112.5%

(H). 1/9= 11.11%,
2/9=22.22,
4/9= 44.44%,
5/9=55.55%,
6/9=66.66%
[ Note the trend]- same value before and after decimal

(I). 1/10=10%

(J). 1/11=9.09%,
2/11= 18.18%, 3/11=27.27%, 4/11= 36.36 [ Note the trend]- same value before and after decimal

K. 1/12=8.33%, 5/12= 41.66 [ Recurring]

L. 1/13= 7⁹⁄_13%

M. 1/14=7²⁄₁₄, 3/14=21.42%

N. 1/15=6¹⁰⁄₁₅=6²⁄₃=6.66 or divide and multiply by 2 in numerator and denominator=2/30, 4/15=8/30

Note- if denominator has 5 in its unit place make it 10.

O. 1/16=6⁴⁄₁₆=6.25, 3/16=18.75, 5/16= 5*(6.25)=31.25

P. 1/17=5¹⁵⁄₁₇

Q. 1/18=5⁵⁄₉

R. 1/19=5⁵⁄₁₉

S. 1/20= 5%

Now convert a percentage to fraction value-

1. 106²⁄₃= 100%+6²⁄₃
fractional value of 100%=1, and 6²⁄₃%=1/15= 16/15
2. 157¹⁄₇= 100%+ 57¹⁄₇
fractional value of 57¹⁄₇= 4/14= 1+4/14=18/14=9/7
3. 616²⁄₃= 600%+ 16 2/3
600%=6, 16²⁄₃= 1/6= 6+1/6=37/6.

Some Solved Examples-

1. 4%*275=
we write 4% as 4/100=1/25
1/25*275=11

2. 56.25% of 1120=
we write 56.25% as (50%+6.25%)
Fractional value of 50%=1/2 and 6.25%=1/16
Now (50%+6.25%) of 1120=560+1/16*1120=560+70=630

3. 95% of 25 5/19=

Note- a% of b is same as b% of a

we write it as 25⁵⁄₁₉% of 95=
We can write- 25⁵⁄₁₉%= 20%+5⁵⁄₁₉%
the fractional value of 20%=1/5 and 5⁵⁄₁₉=1/19
(1/5+1/19)*95
=19+5=24

4. 81.25% of 128=
81.25= (75%+6.25%)*128=13/16*128=13*8=104

5.206 ¼%*14.4=
we can split this fraction as
(200%+ 6 ¼%)*14.4=28.8+0.9=29.7

6. 91 2/3*1320=
Case 1-we can write (91²⁄₃) as (75%+16 2/3%)
Fractional value of 75=3/4, and 16²⁄₃=1/6
3/4*1320+1/6*1320=990+220=1210
Case2- we can also write as (100%-8¹⁄₃%)=1-1/12=11/12*1320= 1210.

7. 242⁶⁄₇of 714=
we can write 242 6/7 as (200%+42 6/7%)*714=
fractional value of 42⁶⁄₇ is 3/7
the denominator has 1/7 i.e. it is somewhere multiple of 14²⁄₇
=1428+3/7*714=1428+306=1734

8. 12.32% of 1555=
write (1555)%= 1000%+500%+50%+5%
1555% of 32=(1000%+500%+50%+5%) of 32=320+160+16+1.6=497.6

Do it yourself-by Percentage to Fraction

1. 91¹⁄₉*135=
2. 72 ½ of 1280=
3. 343¹⁄₃of 450=
4. 126⁶⁄₉of 54=
5. A is 20% of (B+C+D), C is 20% less than (A+B+D). Find the ratio of A:C