00:00 Hello everyone, I'm your Mathematics teacher, Esther Olochi-Ebebeke, and the topic of this

00:18 lesson is addition and subtraction of fractions. By the end of this lesson you should be able

00:25 to solve giving problems on addition and subtraction of fractions, solve what problems involving

00:31 addition and subtraction of fractions. Two or more fractions can be added or subtracted

00:37 immediately if they both have the same denominator. In which case we had or subtracted the numerators

00:43 and divide by the common denominator. So how do I mean? For example, we have one of the seven

00:54 plus two of the seven. They both have common denominators, so it's very easy. All you need

01:01 to do here is to add the numerators together and divide by the common denominator. So we

01:06 have one plus two, divided by seven equals three over seven. So for example, for this

01:13 second example, we have two over seven plus one over five. In this case, the common denominator

01:21 of the equivalent fraction is SCM of the two original denominators. So from the explanation,

01:27 the above example has the LCM 35. So we have two over seven plus one over five. The LCM

01:39 of seven and five is 35. So with this, they don't have common denominators, so you can just

01:46 add this to get us to give you three over, what will it be? It will be three over seven,

01:50 or will it be three over five. So in this case, what do you do? You look for the equivalent

01:57 fraction. How do you go about that? Two times five, seven times five, giving you ten

02:08 over 35. Then for this other fraction, one times seven, five times seven, giving you seven

02:18 over 35. So both of them now have the same denominators. So from this now, we can now add.

02:27 So we have ten over 35 plus seven over 35, giving you 17 over 35. Can you try this? Five

02:42 over eight plus one, divided by six. You can try that out. The correct answer is 19

02:51 over 24. Now example one, simplify five over six plus three over eight solution. To find

03:03 to do the softest problem, you find a common denominator. Look for the LCM of six and eight,

03:10 which is 24. Then when you do that, you do as I did the other time. So what did I do? Let

03:19 me look at it together. Example one, we have five over six plus three over eight. So the LCM

03:31 of six and eight is 24. I hope you can remember how to solve the LCM. Please don't forget. The

03:37 LCM of six and eight is 24. So we'll have the LCM of six and eight. So how do I make the,

03:46 I want to make the denominator of 24. I want to make five over six. I want this fraction

03:55 to have a denominator of 24, which is the LCM. I also want three over eight to have a denominator

04:01 of 24, which is the LCM. So what do I do? I make this equivalent. I multiply the denominator

04:08 and the denominator by a common number. So to have to have 24 at the denominator of five and six,

04:15 I also multiply six by four to have 24. So it means also that I will multiply the numerator

04:22 by four and the denominator by four, which will give me 20 over 24. So the same thing goes

04:32 for this three over eight. I want eight to have a denominator here to be 24. It means I'm

04:39 going to multiply eight by three, meaning if I multiply it by three to have 24 at the denominator,

04:44 I will also multiply my numerator by three. And that will give me three times three over eight

04:50 times three, giving me nine over 24. Now you can now see that both fractions have 24 as the

04:59 denominator. We did not very simple, very easy for me to add them together. So I have 24, 20 over 24,

05:07 plus nine over 24, giving me 29 over 24. So this is an improper fraction. So I will come back to

05:18 a mixed number. So I will give me one more number, five over 24. So that's the answer to this problem.

05:27 The same thing goes here, simplify one over 10 minus 4 over 15. The same thing goes, use this formula,

05:34 what do we do here? We have the SEM of 10 of 15 is 30. So if you have the SEM of 10 of 50 to be 30,

05:41 it means that you're going to make one over 10 out of the denominator of 30, meaning and what,

05:49 4 over 5, 15, have an denominator of 30. So what we do is you multiply the denominator of the first

05:58 fraction by three, making you give you three over 30. Why do you want to give you eight over 30? So when

06:05 you subtract, you have your answer. This is also the other one, simply SEM of 3, 6 of number 5 over 12,

06:17 minus 3 over 3 over 12. Okay, let's do this because it involves a mixed number. We have

06:24 example 3, 6 over 5 over 12, minus 3 over 3 over 4. So express mixed numbers are improper fraction.

06:39 12 times 6, we give you, only give you 12 times 6, 72, plus 5, 77. So we have 77 over 12,

06:54 minus 3 times 4, 12, 12 plus 3, 15, we have 15 over 4. So with this now, we solve each as I have

07:04 done the one above. So how do we go about solving this? This is 77 over 12. Our SEM is 12. So what do we do?

07:20 This one gives you, that means you're multiplying by 1, 77 over 12. Why this 15 over 4? You multiply

07:28 the denominator by 3 to get to f. It also means that you're multiplying the numerator also by 3.

07:34 Giving you 45 over 12. So for us to solve this problem now, 77 over 12, minus 45 over 12, that will give you

07:57 32 over 12. So 32 over 12 will give you our many own number, will give you

08:07 two on our last 24. So we have 32, 24. We take away half 8 here, 8,

08:24 whatever by 12. So we divide, we have 2 here, 4, 2 here, 6, 2 here, 2, 2 here, 3. So our final answer is

08:39 2 over 2 over 3. So the same goes with this example, 4, 75, 3, all number, 2 over 5, plus 2,

08:48 2 over 2 over 3. You use the same format to also solve this. When you solve this properly, you arrive at

08:54 6 over 1 over 15. Now what problems involving addition and subtraction of numbers of fractions?

09:02 Example 5. A fruit grower uses 1 over 3 of his flan for bananas, 3 over 8 for pineapples,

09:13 1 over 6 for mangoes and the remainder for orange. What fraction of his land is used for orange?

09:22 So that example 5. So we have a fruit grower, 1 over 3 for bananas, 1 over 8 for pineapples,

09:43 then 1 over 6 for mangoes and the remainder for orange. What fraction of his land was used or

10:01 is used for orange? So the entire land, remember the last time we did fraction, I told you the old,

10:13 a fraction is a part of the old and the old, the entire land is a unit which is equals to 1.

10:20 Every other fraction adds up to give 1. So we have bananas, pineapples, mangoes, oranges equals 1.

10:26 When you add up this fraction, you have 1. So now that we have this, we are given for bananas,

10:32 for pineapples, for mangoes, but we are not given the fraction for the fraction of our land that

10:37 was used for oranges. So I have to look for that. So all you need to do is to add up the

10:43 ones that we have given, the fractions of the ones that I have given, then you subtracts it from one,

10:50 then you get the answer for the remainder which is the oranges. So we have to go about that

10:56 very simple. We have 1 over 3, plus 3 over 8, plus 1 over 6. So when you turn this to,

11:09 the LCM of 3, 8 and 6 is 24. Remember when you do, I'm making them have common denominators,

11:18 this will equal, I think, so we have 8 over 24, plus 9 over 24, plus 4 over 24. That will give you 17,

11:30 plus 4, that will give you 21, equals to 21 over 24. Remember the old, the old land is 1.

11:41 The old land is 1, the old land total fraction, let me put it that way, total fraction is 1 over 1.

11:52 Now considering the fact that we want them to have a denominator of 24. So 1 over 1 is equivalent

12:02 to 24 over 24, because when you divide this, you have 1 over 1. Am I right? Okay, so we have the,

12:13 for you to get the fraction that is left, we have the old which is 24 over 24, minus 3 into 1

12:23 over 24, we give you 3 over 24. And this can be simplified towards 3, 1, 3, 8, 1 over 8. That is,

12:35 the fruit grower uses 1 over 8 for oranges. A question for you to solve.

12:47 By how much is the sum of 2 over 4 over 5, and 4 over 1 over 2 less than 8 over 1 over 10? So

12:56 let's solve this. By how much is the sum of this? That means we are supposed to have this together,

13:04 2 over 4 over 5, plus 4 over 1 over 2. So by how much is this less than this? So let's solve this,

13:16 let's change this to improper fraction. So you have 2 times 5 times 10 plus 4, 14, 14 over 5,

13:24 plus 4 times 2, 8, 8 plus 1, 9 over 2. So the LCM of this of 5 and 2 is 10, LCM equals 10.

13:40 So for 14 over 5, I'm going to have to multiply 5 times 2 to get 10. It means I also multiply this by 2,

13:57 28 over 10. Then for 9 over 2, 9 times 5, 2 times 5, 45 over 10.

14:14 So I have my 28 over 10 plus 45 over 10. That will give me 28 plus 45, 13,

14:30 673 over 10 is also an improper fraction. So that will give me 7 over 10.

14:42 This is just the addition, the sum of 2 over 4 over 5 and 4 over 1 over 2. So the question is,

14:50 by how much is the sum of this less than this? So we have 8 over 1 over 10. So we have 8 to get that,

14:58 we have to subtract your answer from this. So from this, 8 times 10 is 80 plus 1, it's 1, it's 1 over 10,

15:07 minus this 73 over 10. Now that will give you what? It's 1, that will give you 8 over 10.

15:29 You simplify 2, yeah, 4, 2, yeah, 5. I'll give you 4 over 5. So that's the answer.

15:39 So let's move to the next question. A boy plays football for 1 or number 3 before us.

15:51 Place football for 1 by 3 by 4 us. Listen to the radio

16:09 for 3 over 4 us, and spend one on one, spend an own work,

16:18 spend one number, one over 4 us. So how much time does it spend all together, all together,

16:28 doing these things? Very simple. It means that you require to sum, look for the sum or add them together

16:36 to know how much time it spends doing all of those things. So we are supposed to do this,

16:48 one on number 3 over 4 plus 3 over 4 plus one on number 1 over 4. Yeah, this did both this

16:56 and this makes numbers so we convert to improper fraction. So 1 times 4 is 4, 4 plus 3 is 7

17:06 over 4 plus 3 over 4 plus 1 times 1, 1 times 4 is 4 plus 1, 5 over 4. So thank goodness,

17:17 we are at the same denominator. So we don't need to know if I equivalent anything. So what we need

17:22 to do is to adopt the numerators. 7 plus 3 is 10, 10 plus 5 is 15. So 15, divided by 4. That's

17:32 the time spent in all of those things. So this is an improper fraction. So you convert this

17:40 to a mixed number. So 15, divided by 4, we give you how many, we give you

17:48 3 over 1, but that is 12, 3 over 4. So that's our final as a more example. Let's solve this together.

18:03 Simplify 2 on number 1 over 2 plus 1 over 4. We have options. You can do this while I also solve

18:13 this by on end. I also want to take your book and solve this at your own end. So we have 2 on number

18:18 1 over 2 plus 1 over 4. Let's do that quickly.

18:27 So let's convert this.

18:55 So the second one, we have Simplify 4 on number 2 over 5 plus 2, 3 on number 1 over 4.

19:16 So they're both in mixed numbers, so we'll convert to improper fraction.

19:20 4 times 5, 20, 20 plus 2, 22 over 5 plus 3 times 4, 12 plus 1, 13, 13 over 4.

19:36 So the LCM of this of 5 and 4 equals 20. So the LCM of 5 and 4 equals 20. So we have 22 over 5.

19:54 After make the denominator, 20, that means I have to multiply 5 by 4 to have 20.

20:02 Meaning whatever I do to denominator, I have to also do for numerator. So 22 times 4,

20:07 5 times 4. Now give me 88 over 20. Then for 13, 13 over 4, 13 over 4. I also have to make the denominator

20:26 20. It means I have to multiply this by 5. So 13 times 5, we give you what?

20:36 We give you 65 over 20. So now I can now add them together.

20:52 88 over 20 plus 65 over 20. So 88 plus 65 will give you what? 13, 14, 15. So I have 1, 5, 3 over 20.

21:08 This is also an improper fraction. So convert 1, 5, 3 to a mixed denominator will give me about 7

21:18 old number. 7 old number, that's 140. That means 153 minus 14. So we give you what? 13. So 13 over 20.

21:33 Okay, you have this one also. So what is the sum of this? 1, 3, 4, 2, 3, 5, 5, 5, 3, 4.

21:41 So this, you self-attempt this on your own. Okay, this is for you. Simplify the following.

21:48 A, 3 over 7 over 8 plus 2 over 3 over 4. B, 2 over 5 over 6 plus 5 over 7 over 8. Number 2,

21:59 Mr. Op spends 1 over 3 of his n in food and 1 over 4 in clothes. He then saves the rest.

22:05 What fraction does E, A, spend altogether be saved? Thank you for watching. I am Esther Oluqi

22:14 Ibebuki. Till next time.