0:02 Welcome to quantitative aptitude video
0:04 on fractions and decimals from
0:06 careerite.com. Placement test, job
0:08 interview, bank, MBA and other exams
0:10 focus on this topic as basics of a
0:13 candidate are put to test by hence they
0:15 always have four to five sums related to
0:18 it. This video will show some tricks to
0:20 quickly find answers to the questions in
0:23 the exam. Sums of this topic can be
0:25 practiced on career.com which has
0:27 practice test as well as thousand plus
0:30 aptitude questions. So let's [Music]
0:41 [Music]
0:44 begin. Most of the sums related to
0:47 fractions and decimals are extremely
0:49 easy. Most of the students make silly
0:52 mistakes and this gives them the wrong
0:54 answer. We'll see shortcuts, tips and
0:57 tricks while solving the sums directly.
1:00 So let's move on to question number
1:04 one. What will be fractional form of
1:07 0.3523? Now over here it is not just
1:12 3523. The 23 is under a bar. Let us
1:15 understand what exactly we mean by this
1:17 bar. The answer how to find the answer,
1:18 how to convert to fraction form is
1:21 pretty easy. But let us understand what
1:23 exactly this bar means. This bar means
1:26 the number is repeating. That means if
1:29 there is a bar upon 23 that means 23
1:34 keeps on repeating like this 2 3 2 3 2 3
1:37 2 3 and so on. So this is written as
1:42 0.35 and 23 as repeating. So now let us
1:46 see how to convert 05
1:50 0.3523 into a normal or a simple
1:52 fraction. Okay. Now fraction has two
1:55 parts. one is the denominator and one is
1:58 the numerator. Okay, let us see what the
2:00 denominator would be. Generally, if we
2:04 have this, what do we do? We in case of
2:07 normal fraction like say 0.525, what do
2:11 we write? We write 525 divided by 1,000.
2:14 But here you cannot have this. Let us
2:17 see what to do over here. Okay, here how
2:20 many digits are there after the decimal
2:23 point? There are four digits, right? 3 5
2:26 2 and three. Okay. Out of that two
2:29 digits are not below the line and two
2:32 digits are below the line. Correct.
2:34 There are only two digits below the
2:36 below the bar. So how many digits are
2:39 there below the bar? Two. So write two
2:42 9ines or write nine two times. Okay. How
2:45 many digits are not below the bar? Two.
2:50 So write two zeros. Okay. So this is for
2:55 the bar. This is for no bar. Okay. So
2:58 this is the denominator. Now how to find
3:00 the numerator? Right? Write first the
3:02 entire fraction or after the decimal
3:04 point whatever fraction is there. Let us
3:09 write that first. 3 5 2 3 minus what
3:11 should we subtract? We should subtract
3:14 the number which is not below the line
3:20 that is 35. What do we get? we get 3
3:25 488 divided by 99 9 0 0. This is the
3:26 fraction form of
3:30 0.35 23. Understood? Let us take another
3:32 small example. Okay, arbitrary example.
3:34 Let us say we take
3:37 0.46. Okay, bar. What does this mean?
3:43 0.466. Okay, now we have to convert this
3:45 into normal fraction form. What we'll
3:47 write? We'll have the numerator. We'll
3:49 have the denominator. What is the
3:51 denominator? How many digits are there
3:53 below the bar? One. So there will be 1
3:56 nine. How many digits are there without
3:59 bar? Only one. Okay. There is only one
4:01 digit which is which does not have a bar
4:03 upon it. So there will be 1 zero. Okay.
4:05 What will be the numerator? Write the
4:08 fraction. Subtract what? Subtract the
4:11 digit which is or the number which is
4:13 not below the bar. That is four. What do
4:18 we get? 42 upon 90. See how easy it is.
4:22 Let us take another example. 0 say 25
4:25 and bar. Okay. What it would be? It
4:30 actually means 0.25 25 and so on. Okay.
4:32 Now what it will be denominator? How
4:34 many digits are there below the bar?
4:36 Two. So there will be two 9ths. How many
4:38 digits are there below without bar?
4:40 There are no digits. So no zeros will
4:43 come over here. Now 0.25. What will be
4:47 the numerator? 25 minus how many digits
4:49 are there which do not have bar upon
4:51 their head after the decimal point?
4:53 There are no such digits. So answer will
4:57 be 25 upon 99. See how easy it is. It is
5:00 a very very easy trick to convert this
5:02 kind of fraction or this kind of number
5:06 into its fraction form. Okay, just
5:08 remember this trick. Moving to question
5:10 number two.
5:16 What is value of 5.55 + 5 + 5.5 + 5.555
5:18 + 5.05 +
5:20 5.0. Now over here we see that the
5:23 maximum number of decimal places is
5:24 three. That is there are three digits
5:27 after decimal point over here. So write
5:30 all the numbers with three decimal
5:32 places one below the other. What does
5:34 this do? This helps us to avoid any
5:37 silly mistakes. Okay. This would be
5:41 5.0000 000 0
5:48 5.55
5:55 550 500 0 add what do we get? 5 15.
6:00 Okay. 1 over here 5 6 + 10 is 16. Okay.
6:04 Over here you get
6:06 31.655. See how easy it is. Just
6:09 remember whenever you are adding decimal
6:12 pl decimal numbers or decimals you
6:14 should make sure that every all of them
6:17 have the same decimal numbers. You
6:20 should not do this five plus 0 plus this
6:22 five plus this five. Okay. Everyone
6:25 should have same number of decimal
6:28 places. Right? Moving to next
6:30 question. Question number three. What
6:34 will be value of this expression? Okay.
6:38 Again it is very easy. We have 2.4 into
6:44 72 into 4.5 divided by 0.18 into 0.06
6:46 into 0.9
6:53 * 3. We can write 2.4 4 as 24 upon 10 *
6:58 72 as 72 upon 100 * 45 upon 10 divided
7:07 by 18 upon 100 * 6 upon 100 * 9 upon 10
7:11 * 3 this gets canled over here this gets
7:14 canled over here this gets canceled over
7:17 here okay now what we can write six
7:22 fours are okay 9 8 are right. What we
7:26 can have over here is five 3 15s are
7:32 three 6 are okay 3 2's are 2 2's are
7:37 we'll have 16 into 15 okay 15 into 15 is 225
7:40 225
7:44 2 and 0 why this zero because this 10
7:47 comes over here on the numerator side so
7:49 answer is
7:51 2400 moving to next
7:54 Question. Question number four. What
7:56 will be
7:59 0.15268 divided by
8:02 0.45804? Now this is not normal numbers.
8:04 The these have these bars. That means
8:08 these are recurring numbers. Okay. And
8:10 when we want to divide it is much better
8:12 if we have them in the format of a
8:14 fraction. So let's convert them in the
8:15 format of fraction. What will be a
8:17 fraction of this? There would be
8:19 numerator. There would be denominator.
8:21 Okay. How many numbers are there below
8:24 the bar? There are five numbers. So
8:26 there will be five nines. How many
8:28 numbers are not there below the bar? No
8:31 number. So there would be no zero. What
8:35 would be the numerator? 1 5 2 6 8 minus.
8:38 Since there is no number below the there
8:39 are five numbers below the bar, but
8:42 there is no number which does not have a
8:44 bar above it. So there is no minus.
8:47 Okay. So this would become this. And
8:50 this fraction would be simply again
8:52 similar 9
8:57 9 and 4 5 8 0 4. So let us divide what
9:03 you'll get. We'll get 152 68 divided by
9:07 9999 divided by
9:10 45804 divided by
9:13 99999. This gets cancelled. you'll get
9:16 15268 divided by
9:20 45804. Now always remember that there is
9:22 no need to actually divide this. Okay,
9:25 how to simplify it or how to simply
9:27 divide it or how to find the answer?
9:28 Very easy. Take a look on at the left
9:30 hand side corner. There will always be
9:33 mostly three scenarios. Okay, three
9:35 scenarios. What is the first one? That
9:37 the numerator or the
9:40 denominator numerator or the denominator
9:42 would be multiple of each other. Right?
9:44 Numerator would be 2 * the denominator
9:46 or 8 * the denominator something like
9:49 that or the denominator will be four
9:50 times the numerator something like that.
9:53 Okay. Second scenario would be that
9:55 numerator and denominator would get
9:58 divided or get or simplified by some
10:01 common factor like both of them are
10:03 divisible by two or both of them are
10:06 divisible by say 8 or 20 or something
10:08 like that. And the third case is the
10:11 rarest case where we actually have to
10:14 divide but this is very rare in
10:16 competitive exam. The reason being that
10:18 you do not have that much time to divide
10:20 such big numbers. So let us see which
10:22 one of the case we can apply over here.
10:24 Let us try with first one. Now over here
10:26 how to find out whether it is a multiple
10:28 or not. Take a look at the first two
10:31 digits of the numerator. It is 1 and 5.
10:33 15. Okay. Numerator start numerator
10:36 start digits are 15. Denominator start
10:39 two digits are 45. We know that 15 into
10:43 3 is 45. Right? So let us try to
10:44 multiply this by three and let us see
10:47 whether we get the answer or not. Okay.
10:49 What we'll get over here? We'll get 38
10:53 are okay we'll multiply over here 1 52
10:55 68 at the bottom okay multiplied by 3 3
11:01 8 are 24 3 6 18 + 2 is 20 3 2 6 7 8 3
11:04 5's are 15 45 we got the answer so
11:09 answer is 1 by 3 okay answer is 1x 3 you
11:12 can write 1x 3 like this or you can
11:13 write it like
11:16 0.333 or that can be expressed as
11:21 0.3 bar. Okay, this is the answer. See,
11:23 just remember this tip over here that
11:24 there are three case scenarios. Either
11:26 it is a multiple or it can be divided by
11:29 a common factor and reduced so that
11:31 division becomes easy or the third one
11:34 actually you have to divide. Right? So
11:36 try to see which of the following cases
11:39 is the cases can be applied over here.
11:41 Moving to next
11:43 question. Question number five. How much
11:47 would be n minus m upon n + m if 2.5 m
11:49 is equal to
11:52 0.035 n? Very very easy sum. Let us see
11:54 how to solve. What have they given? 2.5
11:56 m is
12:01 0.035 n. So 25 m upon 10 would be equal
12:04 to 35 n upon
12:07 1,000. What you will get over
12:10 here? You'll have 2500.
12:16 M would be equal to 35 n 5 7s are 5 5
12:20 are okay so n upon m would be equal to
12:24 500 upon 7 now we got this ratio from
12:27 here there are two methods to solve the
12:30 sum okay two ways we'll see both of them
12:32 okay but what I would prefer is the
12:33 first method which I'll show you that I
12:36 always prefer it is very easy okay let
12:39 us see the first method it is a shortcut
12:41 right now first method Do you see this
12:43 is n minus n upon n + n. Please take a
12:47 look at the ratio and proportion video.
12:50 Okay, there this method is given. It is
12:52 a property of ratios that is fractions.
12:54 Right? So take a look at the ratio and
12:56 proportion video and you'll understand
12:58 what I'm doing over here. By the if we
13:02 have a upon b equal to c upon d then by
13:05 component and dividend rule we can have
13:08 a + b upon a minus b would be same as c
13:11 + d upon c minus d. I'll do the same
13:15 over here. What I have n upon m is 500
13:19 upon 7. So n + m upon n minus m would be
13:25 500 + 7 is 57. 500 - 7 is 493. So what I
13:27 want is exactly opposite. So I get 493
13:30 over here. I'll just cross multiply upon
13:33 507. Okay. Would be equal to n minus m
13:38 upon n + m and you got the answer. Now
13:40 let us see what the second method is.
13:41 Second method is also easy but it is
13:43 little bit lengthy and you might make
13:46 mistakes in calculation. Okay. Now I
13:50 have n by m is equal to 500 upon 7. What
13:52 I want to find? I want to find n minus m
13:55 upon n + m. Okay. If I take m common
14:00 what I'll get m into n upon m
14:06 -1 m into n upon m + 1 okay that would
14:08 be this gets cancelled then I'll get 500
14:14 by 7 - 1 upon 500 by 7 + 1 that is
14:19 nothing but 493 upon 7 divided by 57
14:24 upon 7 and I get the same answer as 493
14:27 upon upon 57. Okay, I would always
14:29 prefer the first method. Whenever you
14:32 see such kind of format n + m upon n
14:35 minus m or n minus m upon n plus m, try
14:38 to use the ratio and proportion trick.
14:40 Okay, it would be very easy and
14:42 calculation would also become extremely
14:44 easy. Moving to next
14:48 question. Question number six. Add
14:52 17.499, 17.85 and 17.33.
14:55 Now here we have again the bars. Let us
14:58 convert it into normal fractions. Okay.
15:00 What we'll get
15:05 17.499 bar. That is nothing but 17 +
15:09 0.499 bar. Okay. That would be 17 plus
15:11 what would be the denominator? There are
15:13 two numbers below the bar. So there will
15:15 be two 9ines. There is one number which
15:16 does not have a bar. So there will be
15:20 one zero. It would be 499 would be
15:23 numerator minus there is one number what
15:25 is the number four which does not have a
15:27 zero which does not have a bar on it. So
15:31 answer would be 17 +
15:35 495 divided by 990 that is nothing but
15:41 17 + this is 1 by 2 that is.5 so 17.5
15:44 okay one number is 17.5 second number is
15:47 17.85 85. Now let us see the third number.
15:50 number.
15:54 17.33. What you'll get? 17 +
15:58 0.33 3. That would be equal to 17 +
16:01 what? Three numbers below the bar. So
16:04 three 9ines. No number without bar. So
16:07 no zeros. Okay. Numerator would be same.
16:09 3 3 minus there is nothing to subtract
16:11 as there is no number which does not
16:15 have a bar on it. Right? So 1's are 3's
16:19 are 17 + 1 by 3. Okay, let us add what
16:22 we'll get. 17.5 +
16:28 17.85 + 17 + 1 by 3. Right, that would
16:32 be 17 + 17 + 17 is 51
16:36 +.5 and 85 is 1
16:38 1
16:42 35, right? + 1x3 that would be
16:46 52.35 plus what is 1x3
16:49 0.333 continuously right that would be
16:56 52.3 + 3 is 6 y + 3 is 8 3 continuously
17:01 that can be written as 52.6 6 83 bar.
17:04 Okay. So this is the answer. Moving to next
17:05 next
17:08 question. Question number seven. What
17:11 will be the value of 1 into.3 into 0.01 into
17:12 into
17:15 0.003. Now in these sums how to avoid
17:18 mistakes? Very easy. Count the number of
17:21 decimal places. Here it is 1. Here it is
17:23 two. Here there are three. How many
17:26 total? That would give us six decimal
17:30 places. Okay. six decimal places. Now
17:33 consider the numbers only. 1 into 3 into
17:36 1 into 3 that would be 9. But this is
17:39 not the answer. We need to include these
17:42 decimal places. So put a point and put
17:45 six decimal places. Okay. 9. First let
17:47 us write the number nine. It would come
17:50 over here. Now this should be filled by
17:52 zero because there is no other number
17:54 left. So 0 0
17:57 0. Answer is
18:02 0 0 0 9. So these are five zeros and
18:05 this is the sixth decimal place. Moving
18:08 to the next question. Question number
18:18 04659. If 1 upon 4.659 is equal to
18:22 2146. Now we see over here we have 4659.
18:25 Here we are 4659. Just try to bring this
18:27 into this format and you'll get the
18:30 answer. Very easy, isn't it? See what
18:31 we'll do?
18:34 4659. We want to shift four decimal
18:37 places over here. So, we'll simply write
18:39 4.659. And since we are shifting four
18:44 decimal places, so 10 - 4 10 -4. Okay,
18:48 that would be how much? So 1 upon 4.659
18:52 659 multiplied by this 10 - 4 goes up it
18:55 becomes 10 to 4. What is this value of
19:00 0.214 6 into 10 to 4? You'll get the
19:04 answer as 21 4 6. Right? Moving to
19:06 question number n
19:08 n
19:12 4.142 + 100.8 plus question mark plus
19:17 0.053 is equal to 105.153.
19:19 Question mark stands for again very easy
19:21 we can write question mark is nothing but
19:23 but
19:25 105.153 minus
19:28 4.142 minus
19:31 100.8 minus
19:33 0.053. Now how to calculate this? Do not
19:35 go by decimals or write the decimal
19:37 places. Very easy calculation. First
19:41 consider the numbers before the decimal
19:45 places. What you'll have 105 -4 - 100 -
19:50 0. What you'll get this 105 - 4 101 this
19:52 is 1. Okay. Now consider the decimal
19:55 place numbers be after the decimal
20:01 places 153 - 142 - 800. It is not just
20:03 8. It is 800 because there has to be
20:05 three decimal places everywhere. Okay.
20:09 So this is 800 minus
20:12 053. How much you'll get at this point?
20:17 You'll get 0. this you'll get -
20:22 842. How? See this would be 11 -
20:27 853. Okay, that would give us - 842. But
20:35 -0.842. Okay. Now what do we have? We
20:41 have the number 1. We have this. So 1 +
20:45 0.842. What we'll get? we'll get 1 -
20:54 0.158. This is the answer. Okay. So this
20:57 is nothing but question mark. This
20:58 should be the question mark. So that
21:01 that holds true. Moving to question number
21:02 number
21:09 10. 19.39 + 10.33 + 7.82 +
21:15 3.111 is equal to a 40.66. 66 B 40.65 C
21:18 90.856 D
21:21 40.566 Now I've included this sum on
21:22 purpose over here along with options
21:25 because I want to show how we can use
21:28 the options to our advantage to solve
21:31 the sum quickly. Okay, let us see how to
21:33 solve it quickly. Now they have given
21:36 this. Now 19 + 10 is 29 + 7 is how much?
21:40 29 + 10. 7 + 3 is 10 39. So 90 can never
21:42 be the answer because the addition comes
21:46 out to be around 40 39 40. Okay. So 90
21:48 is not the answer. Now let us see which
21:50 one is the answer. Now here we see that
21:52 here maximum decimal places are three.
21:54 So let's write three decimal places for
22:00 everything. 820 330. Here also 660 5 0.
22:02 Now we know we have already already
22:05 calculated these the addition of numbers
22:07 before the decimal point and we have 40
22:09 everywhere over here. Let us see what do
22:11 we have over here after the decimal
22:15 point 399. Then we have 3 0. We have 8 2
22:19 0. Then we have 1 1 and 1. 9 + 1 is 10.
22:22 Okay. 1. Now which option has zero in
22:24 the end? Only these two. This does not
22:28 have. So cancel. 9 + 1 is 10. 10 + 3 is
22:33 13 + 2 15 + 1 16. And one carried. Which
22:35 option has 16 in the end? Only this
22:38 option has 16 in the end. So this cancel
22:41 and this is the answer. Moving to next
22:45 question. What is approximate value of
22:47 8459 divided by
22:52 11.98US 23.99 divided by 7 upon 140. Now
22:54 they want the approximate value. So
22:56 while calculating also we can consider
22:59 approximate values. We can take this as
23:01 8459 can be taken as
23:06 8460. 11.98 can be taken as 12. 23.99
23:08 can be taken as 24. Okay. And let us calculate
23:09 calculate
23:16 8460 divided by 12 minus 24 / 7 upon
23:20 140. Okay. What we'll get over here 8 4
23:23 6 0 divided by 12 would be nothing but
23:30 12 7s are 7 12 5 are 60 12 7s are 84 0 5
23:35 okay minus 24 upon 7 upon 140 this is
23:40 nothing but 20 so we'll get 705 minus 24
23:45 into 20 it is 705 - 480 that would be
23:48 equal to 225 this This is the
23:50 approximate value or approximate answer.
23:52 Now even if they have not given
23:54 approximate value whenever you find such
23:57 critical things and in the options if
24:00 some number is given directly and there
24:02 there is a lot of say there are four
24:04 options and there is a lot of difference
24:06 between the options like here it is five
24:10 and here it is 20 here it is say 45 and
24:12 here it is 1. So there is a lot of
24:14 difference between the options. So at
24:16 such times you can consider approximate
24:18 value and get the answer which is and
24:20 choose the answer which is nearest to
24:22 your answer. Choose the option which is
24:25 nearest to your answer. Okay. So this is
24:26 nothing but approximation. This is also
24:29 a very useful technique to solve sums
24:31 quickly. Moving to question number
24:34 12. What is value of
24:37 945.341 minus
24:39 1042.792 +
24:42 875.435 plus 31.025 025 and there are
24:44 four options given again here we'll see
24:48 how options help us. Okay, let us
24:50 consider the numbers before the decimal
24:58 point. Okay, 945 - 1042 + 875 + 31. Now
25:01 here we have 945 here we have 42 1042.
25:04 So let us assume approximately this to
25:08 be 45. So we'll get 1045. So we'll have
25:11 945 - 1045 +
25:18 875 + 31 what do we get - 100 + 875 + 31
25:22 would give us 86. So which all options
25:25 are nearer to 806 this and this. So
25:28 cancel the rest of the options. Now let
25:30 us check out the numbers which are after
25:33 the decimal points. This, this, this and
25:35 this. Here first consider only the last
25:38 digit. What do you have? One over here.
25:40 Then minus. Then we have two over here.
25:43 Okay. Then plus. We have five over here.
25:46 Okay. And then again five over here. So
25:50 + 5. What do we get? -1 + 10. That would
25:53 be equal to 9. Which option has nine at
25:55 the end? Only this option has nine at
25:58 the end. So this is not the answer. This
26:00 is the answer. See how even options help
26:03 us. Okay. Moving
26:05 on. Question number 13. Which of the
26:08 following is largest fraction amongst 5x
26:11 8, 3x 7, 2x 9 and 4x 5? Now your
26:13 fractions are given. Always remember
26:15 there are two ways to solve the
26:17 fractions some whenever we have to
26:19 compare like find the largest or the
26:21 smallest or the middle fraction or
26:23 something like that. Okay. Now the first
26:25 way we have already learned in ratio and
26:29 proportion. Okay. Where we decide how to
26:31 find the fraction. We'll see that way
26:33 also again over here. But please check
26:35 out the video related to ratio and
26:37 proportion that would help you solve
26:40 fractions very quickly. The trick has
26:42 been discussed in detail over there.
26:44 Over here also I'll explain what exactly
26:46 the trick is. Okay, but do take a look
26:48 at the ratio and proportion video. Now
26:51 in the second way, okay, here we have to
26:55 check that if the denominator is less
26:58 than 10. Okay, if it is less than 10,
27:00 then we can directly divide. If it is
27:02 greater than 10, it becomes difficult to
27:04 divide. So if it is 10 or less than 10,
27:06 then we can directly divide and find the
27:08 answer. So let us go by direct division.
27:14 We have 5 by 8 that would be 6. Okay? 6
27:17 to something, right? The next one would
27:22 be 3 upon 7. 7 0 are 30. 7 4's are 28.
27:26 27 2's are 14. Okay? Next one is 2 upon
27:32 9. Right? This is 0.20. 21 uh 9 9 2's
27:37 are 18 20 again 2 it goes on 4 upon 5
27:41 that would be nothing but 0.8 8 we
27:45 directly know this is largest. Okay. So
27:47 when the denominator is less than 10 it
27:50 becomes easier to divide. So directly
27:51 divide and get the answer. Now let us
27:54 see the second method which we also saw
27:58 in ratio and proportion. Okay. What is
28:00 the trick? Say there are two fractions a
28:03 upon b equal to c upon d. Or there are
28:05 two fractions a upon b and c upon d.
28:07 Okay. They're not equal but there are
28:10 two fractions a upon b and c upon d. Now
28:14 just cross multiply what you'll get a d
28:18 over here and bc over here. Okay. So if
28:21 a d is greater than bc if a is greater
28:24 than bc that is left hand side is
28:26 greater than right hand side. So the
28:28 left hand side fraction should be
28:29 greater than right hand fra right hand
28:31 side fraction. Which is left hand side
28:34 fraction? A by b. So a by b will be
28:39 greater than c by d. Say if a d is less
28:42 than bc then right hand side is greater
28:43 than left hand side. So right hand side
28:47 fraction c by d will be greater than the
28:49 left hand side fraction. And if a d
28:52 equal to bc both the fractions are same.
28:55 Now let us solve using this trick. Now
28:56 over here we have five fractions and not
28:58 two four fractions and not two. So what
29:01 to do? Take these two and compare these
29:03 two. Take these two and compare these
29:05 two. Find the largest among this. Find
29:08 the largest among this and then compare
29:10 this one and this one. Okay, first let
29:14 us take 5x 8 and 3 by 7. Okay, this is a
29:19 by b c by dd. 5 7s are 35. 8 3's are 24.
29:22 35 greater than 24. So 5 by 8 is
29:24 greatest. Okay, this is our first
29:29 result. Now let's take 2x 9 and 4x 5. 5
29:34 2's are 10. 9 4 are 36. So 36 is greater
29:38 than 10. So 4x 5 is greater. This is our
29:42 second result. Let's compare 5 by 8 and
29:47 4 by 5. 55 are 25. 8 fours are 32. 32
29:51 greater than 25. So 4x 5 is largest
29:54 amongst them. So see how easy it is. Any
29:56 fraction can be compared by this second
29:58 method. Even the first method is
30:00 applicable to any fraction. But when
30:02 number denominator becomes greater than
30:04 10, it becomes very difficult to divide.
30:08 Right? So when denominator greater than
30:10 10, use second method. Denominator less
30:13 than 10, then 10 or less than 10, use
30:15 the first method. Moving to question number
30:16 number
30:21 14. The least of the following
30:24 0.2.2².2 bar 1 divided by2. Now we have
30:26 to find the least number amongst these.
30:29 Again this is very easy. First one is 2
30:33 right? Second one is 2 squared. So 2
30:37 square is 4 and since there is only one
30:40 decimal place in the number so square we
30:42 will have two decimal places. So we'll have
30:43 have
30:48 0.04. Okay. Next is 0.2 bar. Now let us
30:50 convert it into normal fraction. What
30:52 would be the denominator? One digit
30:55 below the bar. So 9 would come over here
30:58 and numerator would be two. Why? And
30:59 there would be no subtraction as there
31:01 is no digit which does not have a bar.
31:05 Okay. So that would be 9 is
31:09 0.2 2 and so on. Okay. Then we have 1
31:14 divided by2 1 upon2 that is 10 upon 2
31:18 that is 5. Clearly this is the least.
31:25 What is the increasing order of the
31:30 fractions? 6x 7, 8 by 9, 7 by 8, 9 by
31:33 10. Now over here take careful look.
31:36 Okay, here denominators are less than
31:39 10. So you can simply divide as well as
31:41 and write you can simply find the answer
31:43 and simply arrange them in the
31:46 increasing order. Okay, but let us learn
31:50 a new trick over here. Right? Now if you
31:52 observe closely you'll see that in all
31:55 the four fractions denominator is always
31:57 greater than numerator. 7 is greater
31:59 than 6. 9 is greater than 8. 8 is
32:02 greater than 7. 10 is greater than 9.
32:04 Okay. Denominator is greater than
32:07 numerator. And also denominator minus
32:12 numerator the difference is same. 7 - 6
32:17 is 1. 9 - 8 is 1. 8 - 7 is 1. 10 - 9 is
32:20 1. Okay. So the difference is same. So
32:24 whenever the denominator is greater than
32:26 numerator in all fractions and
32:28 difference between denominator and
32:32 numerator is same. Okay. Then we can say
32:35 that smaller the
32:40 numerator smaller the fraction and if
32:44 greater is the numerator greater is the
32:47 fraction. So over here which is the
32:50 smallest numerator 6. So 6x 7 fraction
32:52 is the smallest. Which is the largest
32:55 numerator? 9. So 9x 10 is the greatest.
32:58 Now in 8 and 7, 7 is the smaller. So 7
33:01 by 8 comes over here. 8 is greater than
33:04 7. So 8 by 9 comes over here. This is
33:08 the ascending order for the fractions.
33:10 See how easy it is. Just remember the
33:12 trick. When denominator is greater than
33:15 numerator for all the fractions and
33:17 denominator minus numerator difference
33:19 is same. It is not just the normal
33:21 difference. It is denominator minus
33:23 numerator difference. Okay. If it is
33:26 same exact then smaller the numerator
33:28 smaller is the fraction. Greater the
33:30 numerator greater is the fraction.
33:33 Moving to next
33:35 question. What is increasing order of
33:38 the fractions? 14 x 17, 10 x 12, 6 x 7,
33:42 18 by 22. Again over here we see that
33:44 denominator is greater than numerator.
33:47 Let us see the difference. 17 - 14 3 12
33:50 - 10 2. So the difference is not same.
33:53 So now what to do here again what you
33:54 can do is either you can divide or you
33:56 can use the ratio technique which we
33:58 have learned right and find which is the
34:00 smallest which is the largest and then
34:03 arrange them. Okay? Or let us learn
34:07 another new trick. Okay, very easy trick
34:09 this is right. This is similar to what
34:11 we learned earlier the previous sum but
34:13 again this is a little bit different but
34:15 very easy. We have learned that we have
34:17 seen over here that denominator all the
34:19 denominators are greater than numerators
34:21 okay respective numerators. Now let us
34:25 arrange the numerators from lowest to
34:28 largest. There is six then 10 then 14
34:30 and 18. Now write the
34:33 corresponding denominators also. 6 is 6x
34:37 7. 10 is 10 x 12. 14 is for 14 x 7 and
34:42 18 is for 18 by 22. Now if you observe
34:47 very carefully 6 + 4 is 10, 10 + 4 is
34:52 14, 14 + 4 is 18. So numerator is
34:55 increasing by a fixed value. Okay? Any
34:58 value uh a fixed value that is four over
35:01 here. Right? So if numerator is
35:02 increasing by fixed value, let us check
35:04 if denominator is also increasing or
35:11 not. 7 + 5 is 12. 12 + 5 is 17. 17 + 5
35:15 is 22. So denominator is also increasing
35:19 by a fixed value. Okay. Now if numerator
35:21 is increasing by some definite fixed
35:24 value and denominator is also increasing
35:27 by definite fixed value then smaller the
35:32 numerator smaller the fraction. Okay.
35:35 Greater the numerator greater the
35:38 fraction. So here smaller numerator is 6
35:42 by 7. Greatest numerator is 18 by 22.
35:46 Again 14 and 10. 10 is smaller than 14.
35:49 So 14 by 17. So this is the increasing
35:52 order of the fractions. Please remember
35:54 it is not compulsory that if this is
35:56 increasing by say + 3, this has to
35:59 increase by only one that is +4. Okay.
36:02 Numerator might increase by say + 17 and
36:04 denominator might increase by say
36:07 plus,000 also. There's no issue at all.
36:09 Some any number is fine over here. It
36:14 might also be +4 and +4. Okay? So it
36:16 just has to be some fixed value from one
36:19 fraction to other. Okay. Now moving to
36:24 next question. 4x 7 of 2x3 of 5x 6 of 5x
36:28 8 of 108 is again very easy of means
36:32 multiplication right. So we are just
36:34 multiplying this. Let us see what do we
36:38 get. 1,8 that would be equal to 4 2's
36:42 are 8. Okay. So we'll have 5 5 are 25
36:47 over here. Right? Now 7 7 1's are 7 30 7
36:53 4 are 20 28 1 144 okay into 1 44 3 into
37:00 6 6 2's are 12 24 4 are 8 are answer is
37:04 200. Moving to question number 18. If a
37:06 fraction's denominator is decreased by
37:10 80%. And numerator is increased by 300%,
37:12 the fraction becomes 2x9. What is the
37:15 fraction? Let us assume the fraction B.
37:18 A upon B. What is the numerator? A. What
37:22 is the denominator? B. Numerator is
37:25 increased by 300%. So numerator becomes
37:31 A + 300% of A. That would be equal to a
37:36 + 300 upon 100 into a that would a + 3 a
37:39 that is 4 a. This is the new numerator.
37:42 Denominator is decreased by 80%. Okay.
37:46 So new denominator becomes 100 minus
37:50 80%. That is nothing but 20% of the
37:53 original. Okay. There is an 80% decrease
37:54 in the denominator. So the new
37:57 denominator will be 20% of the original
37:59 denominator. that is nothing but B. So
38:02 we'll have 0.2B as the new denominator
38:05 and the numerator is increased by 300%.
38:07 So whatever value is there there is a
38:10 300% increase in the value. So it would
38:13 be a plus 300% increase that is 4 a. And
38:16 they said that the new fraction becomes
38:19 2x 9. What is the new fraction?
38:22 Numerator that is 4 a divided by
38:25 denominator that is 2 b. What it would
38:28 be 2 upon 9. Okay, this would be 2 upon
38:30 9 would be equal
38:37 to 20. A upon d, right? This becomes 10.
38:40 So, a upon b would be equal to 1 upon
38:43 90. This is the answer. This is the
38:47 fraction. Question number
38:50 19. In three fractions when the largest
38:53 fraction is divided by smallest fraction
38:56 the result 5x4 is greater than the
38:59 middle fraction by 1x2. If sum of the
39:02 three fractions is 2 3x2 what will be
39:03 the difference between largest and
39:05 smallest fraction. Again very easy. Let
39:07 us see what have they given. Let the
39:10 largest fraction be a. Okay. This be the
39:13 largest fraction. Let the middle
39:16 fraction be b and let the smallest one
39:18 be c. Okay. What have they given when
39:21 the largest is divided by smallest? The
39:24 answer is 5x4. Okay. So what do we get?
39:30 A is 5x4 * of C. Okay. Also the result
39:33 which is there 5x4. Okay. The result 5x4
39:37 is greater than middle fraction by 1x2.
39:40 So 5x4 is nothing but middle fraction
39:43 plus 1 by 2. So middle fraction greater
39:46 than middle fraction by 1x2 is nothing
39:48 but this result. So what is the middle
39:52 fraction over here? 5x 4 minus 1x2 it
39:54 would be equal to B. That would be equal
39:59 to say LCM would be four. So 5 - 2 is 3
40:02 upon 4. This is the value of B. Also
40:05 they have given that the addition of all
40:06 the three numbers all the three
40:11 fractions is 2 3x 12. So a + b + c is 2
40:15 3x 12 that is 12 2 are 24 + 3 is 27 by
40:17 12. What is the value of a? We can
40:20 express everything in the form of c. A
40:24 value of a is 5x 4 c. Value of b is 3x 4
40:28 + c equal to 27 upon 12. When you solve
40:30 all this what you'll get? You'll get
40:34 value of c as 2 upon 3. Now put in the
40:38 value of c and find the value of a. A is
40:42 5 by 4 C. Okay, that would be 5 upon 4
40:48 into 2 upon 3 2's are that is 5 upon 6.
40:50 We want what do we want to find? We want
40:56 a minus C 5 by 6 - 2 by 3. What you'll
40:59 get? The answer comes out to be 1 upon
41:00 6. This is the difference between
41:03 largest and smallest fraction. Moving to
41:06 the next question.
41:11 Express 2x3 of 1x4 of rupees 25.20 as a
41:16 fraction of 1 1x2 of rupees 36. Now pay
41:18 close attention to what exactly they
41:20 have asked. Actually the sum is very
41:22 easy. You can solve it once you
41:23 understand what they have asked. You can
41:25 solve it with your eyes closed. It is
41:28 very very easy. But we first need to
41:29 understand what are they asked. They are
41:33 saying that express 2x3 of 1x4 of means
41:38 multiplication of 1x4 of rupees 25.20 of
41:41 25.20 as a fraction of do we know the
41:44 fraction over here? No, we know fraction
41:46 over here 2x3 of again fraction over
41:49 here 1x4. We do not know fraction over
41:52 here. So let that fraction be say m.
41:59 Okay. Fraction of 1 1 by 2 of rupees 36.
42:02 Express it means equal to. So we have to
42:07 make sure that this side is something is
42:11 equal to some fraction of 1 1x2 of 36.
42:12 Okay. So that we have to find what
42:14 exactly is the fraction that will make
42:17 these two sides equal. Let us assume the
42:19 fraction is m. So what we will have over
42:23 here 2 2's are so 1 by 6 into
42:27 25 20 would be equal to m into 2 1's are
42:34 2 + 1 33 3 upon 2 into 36 2 into 18. So
42:38 m would be equal to what?
42:42 25.20 divided by 6 into
42:47 3 into 18. Okay. So let us see is it
42:52 divisible by 3 3 8 are
42:55 242 3 4 are 12 okay this is divisible by
42:58 3 let us see whether it is divisible by
43:04 6 6 1's are 6 24 6 4 are 24 1.4 that is
43:08 1.40 40 divided by 18. Okay, that is
43:11 nothing but what we'll have we we can
43:17 divide it 7 upon 9 that is 7 upon 90.
43:20 This is the answer. So the fraction is 7
43:25 upon 90 8 - 8 into 2 1x 5 - 1 2x 7
43:30 divided by 2 - 1 upon 6 - 1x 6 is equal
43:33 to this is extremely easy. You might see
43:35 it as a complicated sum but it is
43:36 actually not. Just solve it step by
43:39 step. There is no trick. It is very
43:43 simple. What you'll have 8 - 8 * 5 2's
43:49 are 10 + 1 11 upon 5 - 7 1 are 7 + 2 is
43:55 9 9 by 7 / 2 - 1 / 6 6 are 36. Take the
43:58 LCM and calculate this. 6 6 are the LCM
44:03 if it is 6 you'll have 6 6 are 36 - 1 35
44:08 what you'll get over here 8 - 8 * LCM is
44:14 35 11 7S are 77 95 are 45 divided by 2 -
44:19 6 upon 35 what you'll get 8 - 8
44:26 * 32 upon 35 upon 35 into 2 LCM is 35 35
44:30 35 2 are 70 - 6 is 64. This 35 gets
44:34 cancelled. 32 into 2. Okay. So you'll
44:38 have over here 8 - 8 into 1 upon 2 this
44:41 is 4. Answer is 4. Moving to question number
44:43 number
44:49 22 8 1x 6 + 5 1x 8 + 4 2x3 equal to. Now
44:52 let us see a very simple tip to solve
44:53 such kind of sums. You can convert it
44:56 into normal fraction and also solve it.
44:58 But let us see another way. Just take 8
45:03 + 5 + 4. That would be 13 + 4 is 17.
45:06 Okay. Then we'll have 1x 6 + 1x 8 and 2
45:11 by 3. Okay. What is LCM? It is 24. For 8
45:14 and 6 it is 24. It is divisible uh 24 is
45:18 divisible by 3 also. 6 4 are. So 8 3's
45:21 are plus 3 into 8 16 what you'll get? 20
45:27 23 upon 24 answer is 1723 by 24. See how
45:30 easy it is. Fractions simple and decimal
45:33 fractions as well as the decimal numbers
45:36 or the decimal sums are very very easy.
45:38 Just pay close attention. You'll be able
45:40 to solve. There are take the help of
45:43 options also. There is nothing much to
45:45 it. Just pay close attention. They are
45:47 easy and you can score in them. Okay?
45:49 Just make sure you're calculating
45:51 properly. Also with practice your
45:53 calculation will increase. It will
45:55 become faster and more and more
45:58 accurate. Okay. Please practice this
46:00 topic as it will help in calculations of
46:03 other topics too. Do share the video
46:05 with friends and give it a like if you
46:06 liked it. Leave your comments and
46:09 suggestions for us. You can even request
46:11 a video on topic of your choice. Also
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46:15 and stay updated about upcoming tutorials.
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