Hello friends
Today we are going to learn many
simple tricks for simplifications
Trick 1 : For converting decimal
numbers into fractions i.e. Numerator & Denominator
example 1 :
0.2356 (Nothing repeating &
terminating decimal)…called Pure Decimal
0.23565656 = .02356 (0.23
is fixed & then 56 is repeating)…called Mixed decimal
0.33333 (All 3s are repeating)…Called
recurring decimals
All things into one table
& those which seems either
pure or recurring OR neither pure or recurring, they are Mixed Decimals
Q. What makes them so Pure,
Mixed or Recurring?
A. 2,5
Explanation:
1. if
no/(2s&5s multiplication) then its Terminating decimal producer, Meaning if
we divide something with only 2s & 5s multiplication then it becomes pure.
example anything/2 = Pure decimal, 2/2 = 0 is Pure decimal, 3/2 = 1.5 is Pure
decimal, 3.6/2 = 1.8 is Pure decimal, 3/5
= 60% = 0.6 is Pure decimal, 3/(2x5) = 0.3 is Pure decimal, 3/(2x5x5) = 0.06 is
Pure decimal, 3/(2x4x5) = 0.075 is Pure decimal,
2. if
there is no 2s or 5s then that will be recurring decimal. Hope you need explanation
for that take example 1/3 = 0.3, 1/7 = 0.142856, 1/9 = 0.1,
3. Now
last remaining is Mixed Decimals. Obviously such fractions’ denominator always
contents both 2, 5 & others too. Example take example from point 2 above
1/3 = 0.3 , now we try to make Dr as we need. 1/(3x2) = 1/5 = 0.5, Ohhh!!! NO
recurring decimals here Or can I say 0.50 this is not true or,
mathematically correct. Remember this is an exception. Forget that, we are
going too much details here. Still above rules are correct !!! Taking another example 7/(5x3) = 0.46
is Mixed decimal, 5/(2x7) = 0.3571428 is Mixed.
Hope this is done…
Remembering
n/3, n/4, n/5, n/6, n/7, n/8, n/9, n/11 :
Now, we’ll try to remember some
fractions’ values, they are very simple & surely help at last step of your
calculations.
They are n/3, n/4, n/5, n/6, n/7,
n/8, n/9, n/11
Sr.No.
|
Fraction
|
Description Steps
|
1.
|
n/3
|
As we know about 1/3 = 0.333333
2/3 will be (1/3) x 2 = 0.666666
3/3 will be 0.999999 or appx. = 1
|
2.
|
n/4
|
1/4 = 0.25 = 25%
2/4 = .5 = 50%
¾ = .75 = 75%
4/4 = 1 = 100%
|
3.
|
n/5
|
As we know 1/5 = 0.20 = 20 %
What will be 3/5 ?
20% X 3 = 60% = 0.60
2/5 = .40 = 40%
4/5 = 20% X 4 = 80% = 0.80
5/5 = 100%
|
4.
|
n/6
|
1/6 = 1/(3X2)
= 0.50 X 0.333333
or half of 0.33==> Now what is half of 33, it is 16.5 so answer is 0.165
So 1/6 = 0.165
Now Remember 1/6 is $ 16.5 not 0.165 for next steps
For 2/6 = 1/3 = 0.333333 Already Recited
For 3/6 = ½ = 0.5 Already Recited
For 4/6 = 2/3 = 0.666666 Already Recited
For 5/6 = Remember 6-1/6 = 6 – 0.165 = 0.833333
Or $16.5 x 5 = 16X5 + 0.5*5 ==> Now $16 dollars 5 times is 80 & half
cent 5 times means $2.5 so $80+$2.5 = $82.5 ==>
0.825
& 6/6 = 100%
|
5.
|
n/7
|
Remember
14 ones are 14, 14 twos are 28, 14 threes are 57
So 142857
In case of n/7, 142857 always repeats
Now for 1/7 = 0.142857
For 2/7 = 0.285714
Steps to remember this
1.
for example 2/7 ==>
take 2, convert to 20 i.e. multiply by
10==>
2.
20/7 = 2 & forget remainder
3.
start with 2 & complete cycle of 142857
4.
Don’t experiment, there no working trick for
that. I have already tried
For 3/7 ==>
30/7 = 4 è428571
è0.428571
for 4/7 ==>0.571428
5/7 ==>
0.714285
6/7 ==>
0.857142
7/7 = 100%
Remember all decimals are recurring, as 7 is not 2
or 5.
|
6.
|
n/8
|
1/8 = half of $25 = $12.5
3/8 = $12.5 X 3 = 36 + 1.5 = $37.5 ==>
0.375
4/8 = 0.50
2/8 = 0.25
5/8 = 60 + 2.5 = 0.625
6/8 = ¾ = 0.75
7/8 = 84 + 3.5 = 87.5 = 0.875
8/8 = 100%
|
7.
|
n/9
&
n/11
|
Remember 9/11, this is day when World Trade Centre
is Collapsed
For 1/9==>
multiply Nr by 11 & use repeating decimals
1x 11 = 11 So 0.111111
1/9 = 0.111111
2/9 = 0.222222
3/9 = 1/3 = Already Recited
4/9 = 0.444444 Or repeat Nr after 0.
5/9 = 0.555555
.
.
.
8/9 = 0.888888
9/9 = 100%
Same for n/11
Just multiply by 9 with Nr
1/11 ==>
1X9 = 09 Not 9, So 1/11 = 0.090909
2/11 = 0.181818
3/11 = 0.272727
.
.
.
10/11 = .909090
11/11 = 100%
|
Enough for today !!!
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