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Fractions and Decimals - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

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Welcome to quantitative aptitude video

on fractions and decimals from

careerite.com. Placement test, job

interview, bank, MBA and other exams

focus on this topic as basics of a

candidate are put to test by hence they

always have four to five sums related to

it. This video will show some tricks to

quickly find answers to the questions in

the exam. Sums of this topic can be

practiced on career.com which has

practice test as well as thousand plus

aptitude questions. So let's [Music]

[Music]

begin. Most of the sums related to

fractions and decimals are extremely

easy. Most of the students make silly

mistakes and this gives them the wrong

answer. We'll see shortcuts, tips and

tricks while solving the sums directly.

So let's move on to question number

one. What will be fractional form of

0.3523? Now over here it is not just

3523. The 23 is under a bar. Let us

understand what exactly we mean by this

bar. The answer how to find the answer,

how to convert to fraction form is

pretty easy. But let us understand what

exactly this bar means. This bar means

the number is repeating. That means if

there is a bar upon 23 that means 23

keeps on repeating like this 2 3 2 3 2 3

2 3 and so on. So this is written as

0.35 and 23 as repeating. So now let us

see how to convert 05

0.3523 into a normal or a simple

fraction. Okay. Now fraction has two

parts. one is the denominator and one is

the numerator. Okay, let us see what the

denominator would be. Generally, if we

have this, what do we do? We in case of

normal fraction like say 0.525, what do

we write? We write 525 divided by 1,000.

But here you cannot have this. Let us

see what to do over here. Okay, here how

many digits are there after the decimal

point? There are four digits, right? 3 5

2 and three. Okay. Out of that two

digits are not below the line and two

digits are below the line. Correct.

There are only two digits below the

below the bar. So how many digits are

there below the bar? Two. So write two

9ines or write nine two times. Okay. How

many digits are not below the bar? Two.

So write two zeros. Okay. So this is for

the bar. This is for no bar. Okay. So

this is the denominator. Now how to find

the numerator? Right? Write first the

entire fraction or after the decimal

point whatever fraction is there. Let us

write that first. 3 5 2 3 minus what

should we subtract? We should subtract

the number which is not below the line

that is 35. What do we get? we get 3

488 divided by 99 9 0 0. This is the

fraction form of

0.35 23. Understood? Let us take another

small example. Okay, arbitrary example.

Let us say we take

0.46. Okay, bar. What does this mean?

0.466. Okay, now we have to convert this

into normal fraction form. What we'll

write? We'll have the numerator. We'll

have the denominator. What is the

denominator? How many digits are there

below the bar? One. So there will be 1

nine. How many digits are there without

bar? Only one. Okay. There is only one

digit which is which does not have a bar

upon it. So there will be 1 zero. Okay.

What will be the numerator? Write the

fraction. Subtract what? Subtract the

digit which is or the number which is

not below the bar. That is four. What do

we get? 42 upon 90. See how easy it is.

Let us take another example. 0 say 25

and bar. Okay. What it would be? It

actually means 0.25 25 and so on. Okay.

Now what it will be denominator? How

many digits are there below the bar?

Two. So there will be two 9ths. How many

digits are there below without bar?

There are no digits. So no zeros will

come over here. Now 0.25. What will be

the numerator? 25 minus how many digits

are there which do not have bar upon

their head after the decimal point?

There are no such digits. So answer will

be 25 upon 99. See how easy it is. It is

a very very easy trick to convert this

kind of fraction or this kind of number

into its fraction form. Okay, just

remember this trick. Moving to question

number two.

What is value of 5.55 + 5 + 5.5 + 5.555

+ 5.05 +

5.0. Now over here we see that the

maximum number of decimal places is

three. That is there are three digits

after decimal point over here. So write

all the numbers with three decimal

places one below the other. What does

this do? This helps us to avoid any

silly mistakes. Okay. This would be

5.0000 000 0

5.55

550 500 0 add what do we get? 5 15.

Okay. 1 over here 5 6 + 10 is 16. Okay.

Over here you get

31.655. See how easy it is. Just

remember whenever you are adding decimal

pl decimal numbers or decimals you

should make sure that every all of them

have the same decimal numbers. You

should not do this five plus 0 plus this

five plus this five. Okay. Everyone

should have same number of decimal

places. Right? Moving to next

question. Question number three. What

will be value of this expression? Okay.

Again it is very easy. We have 2.4 into

72 into 4.5 divided by 0.18 into 0.06

into 0.9

* 3. We can write 2.4 4 as 24 upon 10 *

72 as 72 upon 100 * 45 upon 10 divided

by 18 upon 100 * 6 upon 100 * 9 upon 10

* 3 this gets canled over here this gets

canled over here this gets canceled over

here okay now what we can write six

fours are okay 9 8 are right. What we

can have over here is five 3 15s are

three 6 are okay 3 2's are 2 2's are

we'll have 16 into 15 okay 15 into 15 is 225

225

2 and 0 why this zero because this 10

comes over here on the numerator side so

answer is

2400 moving to next

Question. Question number four. What

will be

0.15268 divided by

0.45804? Now this is not normal numbers.

The these have these bars. That means

these are recurring numbers. Okay. And

when we want to divide it is much better

if we have them in the format of a

fraction. So let's convert them in the

format of fraction. What will be a

fraction of this? There would be

numerator. There would be denominator.

Okay. How many numbers are there below

the bar? There are five numbers. So

there will be five nines. How many

numbers are not there below the bar? No

number. So there would be no zero. What

would be the numerator? 1 5 2 6 8 minus.

Since there is no number below the there

are five numbers below the bar, but

there is no number which does not have a

bar above it. So there is no minus.

Okay. So this would become this. And

this fraction would be simply again

similar 9

9 and 4 5 8 0 4. So let us divide what

you'll get. We'll get 152 68 divided by

9999 divided by

45804 divided by

99999. This gets cancelled. you'll get

15268 divided by

45804. Now always remember that there is

no need to actually divide this. Okay,

how to simplify it or how to simply

divide it or how to find the answer?

Very easy. Take a look on at the left

hand side corner. There will always be

mostly three scenarios. Okay, three

scenarios. What is the first one? That

the numerator or the

denominator numerator or the denominator

would be multiple of each other. Right?

Numerator would be 2 * the denominator

or 8 * the denominator something like

that or the denominator will be four

times the numerator something like that.

Okay. Second scenario would be that

numerator and denominator would get

divided or get or simplified by some

common factor like both of them are

divisible by two or both of them are

divisible by say 8 or 20 or something

like that. And the third case is the

rarest case where we actually have to

divide but this is very rare in

competitive exam. The reason being that

you do not have that much time to divide

such big numbers. So let us see which

one of the case we can apply over here.

Let us try with first one. Now over here

how to find out whether it is a multiple

or not. Take a look at the first two

digits of the numerator. It is 1 and 5.

15. Okay. Numerator start numerator

start digits are 15. Denominator start

two digits are 45. We know that 15 into

3 is 45. Right? So let us try to

multiply this by three and let us see

whether we get the answer or not. Okay.

What we'll get over here? We'll get 38

are okay we'll multiply over here 1 52

68 at the bottom okay multiplied by 3 3

8 are 24 3 6 18 + 2 is 20 3 2 6 7 8 3

5's are 15 45 we got the answer so

answer is 1 by 3 okay answer is 1x 3 you

can write 1x 3 like this or you can

write it like

0.333 or that can be expressed as

0.3 bar. Okay, this is the answer. See,

just remember this tip over here that

there are three case scenarios. Either

it is a multiple or it can be divided by

a common factor and reduced so that

division becomes easy or the third one

actually you have to divide. Right? So

try to see which of the following cases

is the cases can be applied over here.

Moving to next

question. Question number five. How much

would be n minus m upon n + m if 2.5 m

is equal to

0.035 n? Very very easy sum. Let us see

how to solve. What have they given? 2.5

m is

0.035 n. So 25 m upon 10 would be equal

to 35 n upon

1,000. What you will get over

here? You'll have 2500.

M would be equal to 35 n 5 7s are 5 5

are okay so n upon m would be equal to

500 upon 7 now we got this ratio from

here there are two methods to solve the

sum okay two ways we'll see both of them

okay but what I would prefer is the

first method which I'll show you that I

always prefer it is very easy okay let

us see the first method it is a shortcut

right now first method Do you see this

is n minus n upon n + n. Please take a

look at the ratio and proportion video.

Okay, there this method is given. It is

a property of ratios that is fractions.

Right? So take a look at the ratio and

proportion video and you'll understand

what I'm doing over here. By the if we

have a upon b equal to c upon d then by

component and dividend rule we can have

a + b upon a minus b would be same as c

+ d upon c minus d. I'll do the same

over here. What I have n upon m is 500

upon 7. So n + m upon n minus m would be

500 + 7 is 57. 500 - 7 is 493. So what I

want is exactly opposite. So I get 493

over here. I'll just cross multiply upon

507. Okay. Would be equal to n minus m

upon n + m and you got the answer. Now

let us see what the second method is.

Second method is also easy but it is

little bit lengthy and you might make

mistakes in calculation. Okay. Now I

have n by m is equal to 500 upon 7. What

I want to find? I want to find n minus m

upon n + m. Okay. If I take m common

what I'll get m into n upon m

-1 m into n upon m + 1 okay that would

be this gets cancelled then I'll get 500

by 7 - 1 upon 500 by 7 + 1 that is

nothing but 493 upon 7 divided by 57

upon 7 and I get the same answer as 493

upon upon 57. Okay, I would always

prefer the first method. Whenever you

see such kind of format n + m upon n

minus m or n minus m upon n plus m, try

to use the ratio and proportion trick.

Okay, it would be very easy and

calculation would also become extremely

easy. Moving to next

question. Question number six. Add

17.499, 17.85 and 17.33.

Now here we have again the bars. Let us

convert it into normal fractions. Okay.

What we'll get

17.499 bar. That is nothing but 17 +

0.499 bar. Okay. That would be 17 plus

what would be the denominator? There are

two numbers below the bar. So there will

be two 9ines. There is one number which

does not have a bar. So there will be

one zero. It would be 499 would be

numerator minus there is one number what

is the number four which does not have a

zero which does not have a bar on it. So

answer would be 17 +

495 divided by 990 that is nothing but

17 + this is 1 by 2 that is.5 so 17.5

okay one number is 17.5 second number is

17.85 85. Now let us see the third number.

number.

17.33. What you'll get? 17 +

0.33 3. That would be equal to 17 +

what? Three numbers below the bar. So

three 9ines. No number without bar. So

no zeros. Okay. Numerator would be same.

3 3 minus there is nothing to subtract

as there is no number which does not

have a bar on it. Right? So 1's are 3's

are 17 + 1 by 3. Okay, let us add what

we'll get. 17.5 +

17.85 + 17 + 1 by 3. Right, that would

be 17 + 17 + 17 is 51

+.5 and 85 is 1

35, right? + 1x3 that would be

52.35 plus what is 1x3

0.333 continuously right that would be

52.3 + 3 is 6 y + 3 is 8 3 continuously

that can be written as 52.6 6 83 bar.

Okay. So this is the answer. Moving to next

question. Question number seven. What

will be the value of 1 into.3 into 0.01 into

into

0.003. Now in these sums how to avoid

mistakes? Very easy. Count the number of

decimal places. Here it is 1. Here it is

two. Here there are three. How many

total? That would give us six decimal

places. Okay. six decimal places. Now

consider the numbers only. 1 into 3 into

1 into 3 that would be 9. But this is

not the answer. We need to include these

decimal places. So put a point and put

six decimal places. Okay. 9. First let

us write the number nine. It would come

over here. Now this should be filled by

zero because there is no other number

left. So 0 0

0. Answer is

0 0 0 9. So these are five zeros and

this is the sixth decimal place. Moving

to the next question. Question number

04659. If 1 upon 4.659 is equal to

2146. Now we see over here we have 4659.

Here we are 4659. Just try to bring this

into this format and you'll get the

answer. Very easy, isn't it? See what

we'll do?

4659. We want to shift four decimal

places over here. So, we'll simply write

4.659. And since we are shifting four

decimal places, so 10 - 4 10 -4. Okay,

that would be how much? So 1 upon 4.659

659 multiplied by this 10 - 4 goes up it

becomes 10 to 4. What is this value of

0.214 6 into 10 to 4? You'll get the

answer as 21 4 6. Right? Moving to

question number n

4.142 + 100.8 plus question mark plus

0.053 is equal to 105.153.

Question mark stands for again very easy

we can write question mark is nothing but

but

105.153 minus

4.142 minus

100.8 minus

0.053. Now how to calculate this? Do not

go by decimals or write the decimal

places. Very easy calculation. First

consider the numbers before the decimal

places. What you'll have 105 -4 - 100 -

0. What you'll get this 105 - 4 101 this

is 1. Okay. Now consider the decimal

place numbers be after the decimal

places 153 - 142 - 800. It is not just

8. It is 800 because there has to be

three decimal places everywhere. Okay.

So this is 800 minus

053. How much you'll get at this point?

You'll get 0. this you'll get -

842. How? See this would be 11 -

853. Okay, that would give us - 842. But

-0.842. Okay. Now what do we have? We

have the number 1. We have this. So 1 +

0.842. What we'll get? we'll get 1 -

0.158. This is the answer. Okay. So this

is nothing but question mark. This

should be the question mark. So that

that holds true. Moving to question number

number

10. 19.39 + 10.33 + 7.82 +

3.111 is equal to a 40.66. 66 B 40.65 C

90.856 D

40.566 Now I've included this sum on

purpose over here along with options

because I want to show how we can use

the options to our advantage to solve

the sum quickly. Okay, let us see how to

solve it quickly. Now they have given

this. Now 19 + 10 is 29 + 7 is how much?

29 + 10. 7 + 3 is 10 39. So 90 can never

be the answer because the addition comes

out to be around 40 39 40. Okay. So 90

is not the answer. Now let us see which

one is the answer. Now here we see that

here maximum decimal places are three.

So let's write three decimal places for

everything. 820 330. Here also 660 5 0.

Now we know we have already already

calculated these the addition of numbers

before the decimal point and we have 40

everywhere over here. Let us see what do

we have over here after the decimal

point 399. Then we have 3 0. We have 8 2

0. Then we have 1 1 and 1. 9 + 1 is 10.

Okay. 1. Now which option has zero in

the end? Only these two. This does not

have. So cancel. 9 + 1 is 10. 10 + 3 is

13 + 2 15 + 1 16. And one carried. Which

option has 16 in the end? Only this

option has 16 in the end. So this cancel

and this is the answer. Moving to next

question. What is approximate value of

8459 divided by

11.98US 23.99 divided by 7 upon 140. Now

they want the approximate value. So

while calculating also we can consider

approximate values. We can take this as

8459 can be taken as

8460. 11.98 can be taken as 12. 23.99

can be taken as 24. Okay. And let us calculate

calculate

8460 divided by 12 minus 24 / 7 upon

140. Okay. What we'll get over here 8 4

6 0 divided by 12 would be nothing but

12 7s are 7 12 5 are 60 12 7s are 84 0 5

okay minus 24 upon 7 upon 140 this is

nothing but 20 so we'll get 705 minus 24

into 20 it is 705 - 480 that would be

equal to 225 this This is the

approximate value or approximate answer.

Now even if they have not given

approximate value whenever you find such

critical things and in the options if

some number is given directly and there

there is a lot of say there are four

options and there is a lot of difference

between the options like here it is five

and here it is 20 here it is say 45 and

here it is 1. So there is a lot of

difference between the options. So at

such times you can consider approximate

value and get the answer which is and

choose the answer which is nearest to

your answer. Choose the option which is

nearest to your answer. Okay. So this is

nothing but approximation. This is also

a very useful technique to solve sums

quickly. Moving to question number

12. What is value of

945.341 minus

1042.792 +

875.435 plus 31.025 025 and there are

four options given again here we'll see

how options help us. Okay, let us

consider the numbers before the decimal

point. Okay, 945 - 1042 + 875 + 31. Now

here we have 945 here we have 42 1042.

So let us assume approximately this to

be 45. So we'll get 1045. So we'll have

945 - 1045 +

875 + 31 what do we get - 100 + 875 + 31

would give us 86. So which all options

are nearer to 806 this and this. So

cancel the rest of the options. Now let

us check out the numbers which are after

the decimal points. This, this, this and

this. Here first consider only the last

digit. What do you have? One over here.

Then minus. Then we have two over here.

Okay. Then plus. We have five over here.

Okay. And then again five over here. So

+ 5. What do we get? -1 + 10. That would

be equal to 9. Which option has nine at

the end? Only this option has nine at

the end. So this is not the answer. This

is the answer. See how even options help

us. Okay. Moving

on. Question number 13. Which of the

following is largest fraction amongst 5x

8, 3x 7, 2x 9 and 4x 5? Now your

fractions are given. Always remember

there are two ways to solve the

fractions some whenever we have to

compare like find the largest or the

smallest or the middle fraction or

something like that. Okay. Now the first

way we have already learned in ratio and

proportion. Okay. Where we decide how to

find the fraction. We'll see that way

also again over here. But please check

out the video related to ratio and

proportion that would help you solve

fractions very quickly. The trick has

been discussed in detail over there.

Over here also I'll explain what exactly

the trick is. Okay, but do take a look

at the ratio and proportion video. Now

in the second way, okay, here we have to

check that if the denominator is less

than 10. Okay, if it is less than 10,

then we can directly divide. If it is

greater than 10, it becomes difficult to

divide. So if it is 10 or less than 10,

then we can directly divide and find the

answer. So let us go by direct division.

We have 5 by 8 that would be 6. Okay? 6

to something, right? The next one would

be 3 upon 7. 7 0 are 30. 7 4's are 28.

27 2's are 14. Okay? Next one is 2 upon

9. Right? This is 0.20. 21 uh 9 9 2's

are 18 20 again 2 it goes on 4 upon 5

that would be nothing but 0.8 8 we

directly know this is largest. Okay. So

when the denominator is less than 10 it

becomes easier to divide. So directly

divide and get the answer. Now let us

see the second method which we also saw

in ratio and proportion. Okay. What is

the trick? Say there are two fractions a

upon b equal to c upon d. Or there are

two fractions a upon b and c upon d.

Okay. They're not equal but there are

two fractions a upon b and c upon d. Now

just cross multiply what you'll get a d

over here and bc over here. Okay. So if

a d is greater than bc if a is greater

than bc that is left hand side is

greater than right hand side. So the

left hand side fraction should be

greater than right hand fra right hand

side fraction. Which is left hand side

fraction? A by b. So a by b will be

greater than c by d. Say if a d is less

than bc then right hand side is greater

than left hand side. So right hand side

fraction c by d will be greater than the

left hand side fraction. And if a d

equal to bc both the fractions are same.

Now let us solve using this trick. Now

over here we have five fractions and not

two four fractions and not two. So what

to do? Take these two and compare these

two. Take these two and compare these

two. Find the largest among this. Find

the largest among this and then compare

this one and this one. Okay, first let

us take 5x 8 and 3 by 7. Okay, this is a

by b c by dd. 5 7s are 35. 8 3's are 24.

35 greater than 24. So 5 by 8 is

greatest. Okay, this is our first

result. Now let's take 2x 9 and 4x 5. 5

2's are 10. 9 4 are 36. So 36 is greater

than 10. So 4x 5 is greater. This is our

second result. Let's compare 5 by 8 and

4 by 5. 55 are 25. 8 fours are 32. 32

greater than 25. So 4x 5 is largest

amongst them. So see how easy it is. Any

fraction can be compared by this second

method. Even the first method is

applicable to any fraction. But when

number denominator becomes greater than

10, it becomes very difficult to divide.

Right? So when denominator greater than

10, use second method. Denominator less

than 10, then 10 or less than 10, use

the first method. Moving to question number

number

14. The least of the following

0.2.2².2 bar 1 divided by2. Now we have

to find the least number amongst these.

Again this is very easy. First one is 2

right? Second one is 2 squared. So 2

square is 4 and since there is only one

decimal place in the number so square we

will have two decimal places. So we'll have

have

0.04. Okay. Next is 0.2 bar. Now let us

convert it into normal fraction. What

would be the denominator? One digit

below the bar. So 9 would come over here

and numerator would be two. Why? And

there would be no subtraction as there

is no digit which does not have a bar.

Okay. So that would be 9 is

0.2 2 and so on. Okay. Then we have 1

divided by2 1 upon2 that is 10 upon 2

that is 5. Clearly this is the least.

What is the increasing order of the

fractions? 6x 7, 8 by 9, 7 by 8, 9 by

10. Now over here take careful look.

Okay, here denominators are less than

10. So you can simply divide as well as

and write you can simply find the answer

and simply arrange them in the

increasing order. Okay, but let us learn

a new trick over here. Right? Now if you

observe closely you'll see that in all

the four fractions denominator is always

greater than numerator. 7 is greater

than 6. 9 is greater than 8. 8 is

greater than 7. 10 is greater than 9.

Okay. Denominator is greater than

numerator. And also denominator minus

numerator the difference is same. 7 - 6

is 1. 9 - 8 is 1. 8 - 7 is 1. 10 - 9 is

1. Okay. So the difference is same. So

whenever the denominator is greater than

numerator in all fractions and

difference between denominator and

numerator is same. Okay. Then we can say

that smaller the

numerator smaller the fraction and if

greater is the numerator greater is the

fraction. So over here which is the

smallest numerator 6. So 6x 7 fraction

is the smallest. Which is the largest

numerator? 9. So 9x 10 is the greatest.

Now in 8 and 7, 7 is the smaller. So 7

by 8 comes over here. 8 is greater than

7. So 8 by 9 comes over here. This is

the ascending order for the fractions.

See how easy it is. Just remember the

trick. When denominator is greater than

numerator for all the fractions and

denominator minus numerator difference

is same. It is not just the normal

difference. It is denominator minus

numerator difference. Okay. If it is

same exact then smaller the numerator

smaller is the fraction. Greater the

numerator greater is the fraction.

Moving to next

question. What is increasing order of

the fractions? 14 x 17, 10 x 12, 6 x 7,

18 by 22. Again over here we see that

denominator is greater than numerator.

Let us see the difference. 17 - 14 3 12

- 10 2. So the difference is not same.

So now what to do here again what you

can do is either you can divide or you

can use the ratio technique which we

have learned right and find which is the

smallest which is the largest and then

arrange them. Okay? Or let us learn

another new trick. Okay, very easy trick

this is right. This is similar to what

we learned earlier the previous sum but

again this is a little bit different but

very easy. We have learned that we have

seen over here that denominator all the

denominators are greater than numerators

okay respective numerators. Now let us

arrange the numerators from lowest to

largest. There is six then 10 then 14

and 18. Now write the

corresponding denominators also. 6 is 6x

7. 10 is 10 x 12. 14 is for 14 x 7 and

18 is for 18 by 22. Now if you observe

very carefully 6 + 4 is 10, 10 + 4 is

14, 14 + 4 is 18. So numerator is

increasing by a fixed value. Okay? Any

value uh a fixed value that is four over

here. Right? So if numerator is

increasing by fixed value, let us check

if denominator is also increasing or

not. 7 + 5 is 12. 12 + 5 is 17. 17 + 5

is 22. So denominator is also increasing

by a fixed value. Okay. Now if numerator

is increasing by some definite fixed

value and denominator is also increasing

by definite fixed value then smaller the

numerator smaller the fraction. Okay.

Greater the numerator greater the

fraction. So here smaller numerator is 6

by 7. Greatest numerator is 18 by 22.

Again 14 and 10. 10 is smaller than 14.

So 14 by 17. So this is the increasing

order of the fractions. Please remember

it is not compulsory that if this is

increasing by say + 3, this has to

increase by only one that is +4. Okay.

Numerator might increase by say + 17 and

denominator might increase by say

plus,000 also. There's no issue at all.

Some any number is fine over here. It

might also be +4 and +4. Okay? So it

just has to be some fixed value from one

fraction to other. Okay. Now moving to

next question. 4x 7 of 2x3 of 5x 6 of 5x

8 of 108 is again very easy of means

multiplication right. So we are just

multiplying this. Let us see what do we

get. 1,8 that would be equal to 4 2's

are 8. Okay. So we'll have 5 5 are 25

over here. Right? Now 7 7 1's are 7 30 7

4 are 20 28 1 144 okay into 1 44 3 into

6 6 2's are 12 24 4 are 8 are answer is

200. Moving to question number 18. If a

fraction's denominator is decreased by

80%. And numerator is increased by 300%,

the fraction becomes 2x9. What is the

fraction? Let us assume the fraction B.

A upon B. What is the numerator? A. What

is the denominator? B. Numerator is

increased by 300%. So numerator becomes

A + 300% of A. That would be equal to a

+ 300 upon 100 into a that would a + 3 a

that is 4 a. This is the new numerator.

Denominator is decreased by 80%. Okay.

So new denominator becomes 100 minus

80%. That is nothing but 20% of the

original. Okay. There is an 80% decrease

in the denominator. So the new

denominator will be 20% of the original

denominator. that is nothing but B. So

we'll have 0.2B as the new denominator

and the numerator is increased by 300%.

So whatever value is there there is a

300% increase in the value. So it would

be a plus 300% increase that is 4 a. And

they said that the new fraction becomes

2x 9. What is the new fraction?

Numerator that is 4 a divided by

denominator that is 2 b. What it would

be 2 upon 9. Okay, this would be 2 upon

9 would be equal

to 20. A upon d, right? This becomes 10.

So, a upon b would be equal to 1 upon

90. This is the answer. This is the

fraction. Question number

19. In three fractions when the largest

fraction is divided by smallest fraction

the result 5x4 is greater than the

middle fraction by 1x2. If sum of the

three fractions is 2 3x2 what will be

the difference between largest and

smallest fraction. Again very easy. Let

us see what have they given. Let the

largest fraction be a. Okay. This be the

largest fraction. Let the middle

fraction be b and let the smallest one

be c. Okay. What have they given when

the largest is divided by smallest? The

answer is 5x4. Okay. So what do we get?

A is 5x4 * of C. Okay. Also the result

which is there 5x4. Okay. The result 5x4

is greater than middle fraction by 1x2.

So 5x4 is nothing but middle fraction

plus 1 by 2. So middle fraction greater

than middle fraction by 1x2 is nothing

but this result. So what is the middle

fraction over here? 5x 4 minus 1x2 it

would be equal to B. That would be equal

to say LCM would be four. So 5 - 2 is 3

upon 4. This is the value of B. Also

they have given that the addition of all

the three numbers all the three

fractions is 2 3x 12. So a + b + c is 2

3x 12 that is 12 2 are 24 + 3 is 27 by

12. What is the value of a? We can

express everything in the form of c. A

value of a is 5x 4 c. Value of b is 3x 4

+ c equal to 27 upon 12. When you solve

all this what you'll get? You'll get

value of c as 2 upon 3. Now put in the

value of c and find the value of a. A is

5 by 4 C. Okay, that would be 5 upon 4

into 2 upon 3 2's are that is 5 upon 6.

We want what do we want to find? We want

a minus C 5 by 6 - 2 by 3. What you'll

get? The answer comes out to be 1 upon

6. This is the difference between

largest and smallest fraction. Moving to

the next question.

Express 2x3 of 1x4 of rupees 25.20 as a

fraction of 1 1x2 of rupees 36. Now pay

close attention to what exactly they

have asked. Actually the sum is very

easy. You can solve it once you

understand what they have asked. You can

solve it with your eyes closed. It is

very very easy. But we first need to

understand what are they asked. They are

saying that express 2x3 of 1x4 of means

multiplication of 1x4 of rupees 25.20 of

25.20 as a fraction of do we know the

fraction over here? No, we know fraction

over here 2x3 of again fraction over

here 1x4. We do not know fraction over

here. So let that fraction be say m.

Okay. Fraction of 1 1 by 2 of rupees 36.

Express it means equal to. So we have to

make sure that this side is something is

equal to some fraction of 1 1x2 of 36.

Okay. So that we have to find what

exactly is the fraction that will make

these two sides equal. Let us assume the

fraction is m. So what we will have over

here 2 2's are so 1 by 6 into

25 20 would be equal to m into 2 1's are

2 + 1 33 3 upon 2 into 36 2 into 18. So

m would be equal to what?

25.20 divided by 6 into

3 into 18. Okay. So let us see is it

divisible by 3 3 8 are

242 3 4 are 12 okay this is divisible by

3 let us see whether it is divisible by

6 6 1's are 6 24 6 4 are 24 1.4 that is

1.40 40 divided by 18. Okay, that is

nothing but what we'll have we we can

divide it 7 upon 9 that is 7 upon 90.

This is the answer. So the fraction is 7

upon 90 8 - 8 into 2 1x 5 - 1 2x 7

divided by 2 - 1 upon 6 - 1x 6 is equal

to this is extremely easy. You might see

it as a complicated sum but it is

actually not. Just solve it step by

step. There is no trick. It is very

simple. What you'll have 8 - 8 * 5 2's

are 10 + 1 11 upon 5 - 7 1 are 7 + 2 is

9 9 by 7 / 2 - 1 / 6 6 are 36. Take the

LCM and calculate this. 6 6 are the LCM

if it is 6 you'll have 6 6 are 36 - 1 35

what you'll get over here 8 - 8 * LCM is

35 11 7S are 77 95 are 45 divided by 2 -

6 upon 35 what you'll get 8 - 8

* 32 upon 35 upon 35 into 2 LCM is 35 35

35 2 are 70 - 6 is 64. This 35 gets

cancelled. 32 into 2. Okay. So you'll

have over here 8 - 8 into 1 upon 2 this

is 4. Answer is 4. Moving to question number

number

22 8 1x 6 + 5 1x 8 + 4 2x3 equal to. Now

let us see a very simple tip to solve

such kind of sums. You can convert it

into normal fraction and also solve it.

But let us see another way. Just take 8

+ 5 + 4. That would be 13 + 4 is 17.

Okay. Then we'll have 1x 6 + 1x 8 and 2

by 3. Okay. What is LCM? It is 24. For 8

and 6 it is 24. It is divisible uh 24 is

divisible by 3 also. 6 4 are. So 8 3's

are plus 3 into 8 16 what you'll get? 20

23 upon 24 answer is 1723 by 24. See how

easy it is. Fractions simple and decimal

fractions as well as the decimal numbers

or the decimal sums are very very easy.

Just pay close attention. You'll be able

to solve. There are take the help of

options also. There is nothing much to

it. Just pay close attention. They are

easy and you can score in them. Okay?

Just make sure you're calculating

properly. Also with practice your

calculation will increase. It will

become faster and more and more

accurate. Okay. Please practice this

topic as it will help in calculations of

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YouTube Transcript:Fractions and Decimals - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

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Fractions and Decimals - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams