00:02 Hello, my name is Dorcas Awaye.

00:14 I'll be taking you mathematics today,

00:16 and today's topic is algebraic processes,

00:18 talking about simple equations.

00:20 At the end of today's teaching,

00:24 you should be able to translate word sentences

00:26 into mathematical equations,

00:28 use mathematical equations to represent word sentences,

00:32 solve simple equations and cross-check your answers.

00:36 Translate in word sentences into mathematical equations.

00:41 All algebraic expressions can be very useful

00:43 when you need to solve everyday problems.

00:46 It allows you to use variables

00:47 as representations of numbers where the value may vary.

00:51 For example, you get 500 NARA Pokemon every month,

00:56 and you know that for that month,

00:59 what you do with it is you spend it on sweets,

01:03 transports, and data for your mobile.

01:06 So you can represent these variables

01:08 with alphabet to make an algebraic expression

01:12 or an algebraic equation.

01:14 500 NARA Pokemon every month

01:17 is what you get in total every month.

01:20 So we began to express our words into numbers,

01:26 expressing word problems into algebraic expressions,

01:30 into equations.

01:31 This is how you go about it.

01:33 You go by the word one after the other

01:35 and then you take it easy to interpret them.

01:38 Suppose you get 500 NARA Pokemon every month

01:42 and you want to keep track of the money you spend.

01:44 You know, because you spend money on sweets,

01:47 transports, and data for your mobile,

01:48 it may not be constant every month.

01:51 You may spend more on sweets in January

01:55 than in February.

01:57 You may spend more on transports and data

02:00 than you spend on sweets in another month.

02:03 This is why algebraic expressions, equations,

02:05 or algebra in mathematics are important.

02:08 So you can easily keep track of how you spend.

02:11 So we can create any question from this.

02:14 So you have the money available as 500 NARA

02:17 and you have what sweets,

02:23 sweets you have data and then you spend it on transport.

02:28 So you can easily represent this with Z,

02:34 represent this with D and represent this with S.

02:39 So for your 500 NARA, this is,

02:43 to know how much is left every month,

02:45 say how much money is left or money available at time Z.

02:53 It's equal to the amount you get every month,

02:57 minus the combination of sweets,

03:01 plus data, plus transport.

03:06 So this using our algebraic expressions

03:09 can easily be put simple.

03:12 The entire word here can just be put simple,

03:14 simply like this, with algebraic expressions.

03:19 Use footsteps in solving world problems

03:22 with our algebraic expressions.

03:24 For example, you have three consecutive numbers

03:27 can be represented as X, X plus one, and X plus two.

03:30 That is, the first number is X, second is X plus one

03:34 and the third is X plus two.

03:36 If you have four consecutive numbers,

03:38 then you have X, X plus one, X plus two, X plus three.

03:42 So those are four times.

03:45 When you hear more than, for example,

03:48 maybe five more than, maybe I earn five units more than my brother.

03:58 That is X plus five.

04:00 Because I haven't mentioned how much I earn.

04:02 So how much I earn can be represented with X.

04:05 So if how much my brother earns is X, or X in the era,

04:09 and I say I earn five NARA more than my brother,

04:12 that means I earn X plus five,

04:15 which is also an algebraic expression.

04:18 Because I have not even told you

04:20 how much my brother earn entirely.

04:21 Express is in terms of algebraic expression, which is just X.

04:25 Less than, for example, less than X, that is X minus five.

04:30 Double or twice, for example, has these two times,

04:34 whatever it is, two times X, or two times Y.

04:37 That is two Y or two X, as the case may be.

04:41 How, for example, can have Y divided by two?

04:45 Total costs, for example, maybe cost of pens and rulers.

04:49 The total cost would be expressed in P plus R.

04:54 Every other triangle, length times this breath,

04:57 as L times B parameter of a rectangle,

05:00 2L plus 2B.

05:01 That is how we express words in algebraic terms.

05:06 Let me go with this, let's start with this example.

05:11 A father is X years old.

05:14 His daughter is currently half his age.

05:17 Our horde will be his daughter B in 10 years time.

05:20 If a father is 10 years old, say father is X years old.

05:30 This is his age.

05:32 Just as your age is maybe two years old.

05:35 Or 3, 5, 12, like that.

05:40 So we don't know the exact value we represented

05:42 it with X years old.

05:44 Our horde will be his daughter.

05:46 Then his daughter is currently at the moment, half is age.

05:50 Remember, his daughter, which is half his age,

05:56 I told you when you were talking about half,

05:57 that is divided by two.

05:58 So his daughter's age, daughter's age now,

06:02 is X divided by two.

06:06 He can also write it as X divided by two, like this.

06:13 Our horde will be his daughter B in 10 years time.

06:17 So in 10 years time, that is when you have plus 10 years,

06:23 that is what it means.

06:24 In 10 years time, our horde will be the daughter B.

06:27 So daughter's age would be is equal to X divided by two plus 10.

06:41 In 10 years time, daughter's age will be this expression.

06:51 So these are your express world problems in algebraic expressions.

06:57 If there was a value given for X, then we

07:04 could find out what the exact age is.

07:07 But as it is now, there's no value.

07:08 We leave it the way it is.

07:10 Second example, a shop owner sells maize at Sunera Parkop.

07:15 She also sells rice Parkop at double the price of the maize.

07:21 If she sold 50 cups of maize and 45 cups of rice,

07:25 what was her income?

07:27 A shop owner sells maize at Sunera Parkop.

07:31 So for one cup of maize, one cup of maize,

07:41 we have Sunera.

07:56 One cup of maize is Sunera.

07:58 She also sells rice Parkop at double the price of the maize.

08:03 So one cup of rice is double the price of maize.

08:08 One cup of rice of one cup is double the price.

08:20 That is two times the price of maize.

08:23 So that is two times the price of maize, which is two times two.

08:28 Because this is Sunera.

08:30 Double the price of maize is the price of rice.

08:34 So if I had not put two here, for example,

08:38 if I had said a cup of maize is say X-Nera or Y-Nera,

08:41 I would have written Y-Nera here.

08:44 And then if she sells a cup of rice as double the price of maize,

08:50 that would be two Y, which is the same thing as two times Y.

08:55 So two times two.

08:58 So she sells a cup of rice at four Nera.

09:04 If she sold 50 cups of maize and 45 cups of rice, what was her income?

09:09 So 50 cups of maize, 50 cups of maize at Sunera of maize is two times 50.

09:23 Because one cup is Sunera.

09:25 So 50 cups of maize would be two times 50, which gives you on red.

09:31 And then she sold 45 cups of rice, 45 cups of rice.

09:43 So 45 times two, 45 now would be 45 times four.

09:48 Because a cup of rice is four Nera, so four multiplied by 45.

09:54 So our income is two times 50 plus four times 45, which is on red.

10:15 Four times 45 would give you 180.

10:21 So our total income is 280 Nera.

10:30 So if these values that we imputed, that is 50 cups.

10:34 And we know the number of cups you bought and then 45 cups.

10:40 Rather, if two Nera was not inclusive in this expression,

10:45 if we did not give information that a shop owner sells maize as--

10:50 let me say a shop owner sells maize as a Q Nera.

10:55 Say maize is equal to Q Nera.

11:02 Or we don't know.

11:04 Say a shop owner sells maize as the rate of Q.

11:09 So we say Q. And rice adds double the price of maize.

11:21 That is two times Q. If she sold 50 cups of maize and 45 cups of rice,

11:29 what was her income?

11:30 So 50 cups of Q, that is 50 of Q, 50 Q plus--

11:44 this is 2Q plus 2Q times 45.

11:52 So we have 50 Q plus 90 Q. Two times 45 is 90.

12:06 So we have 90 Q. So because we have the same terms,

12:10 we can easily add them together, which gives you 140 Q.

12:18 So because the value of Q can vary, just because we had 2 Nera already,

12:25 that was how we could get the value 280.

12:28 So Q, if the price changes to 3 Nera, 4 Nera,

12:31 we can easily use this expression to get how much our income is as price varies.

12:40 So these other examples, I believe, you can solve them.

12:44 I could solve one of them, or let me solve this.

12:56 The sum of three consecutive numbers is 11.

12:59 Remember when we talk about consecutive numbers,

13:02 that is, say, this is example 4.

13:10 I want to start with 4.

13:11 First, let's do 4.

13:13 Now, sum of three consecutive numbers is 11.

13:15 So three consecutive numbers.

13:17 The first one is A. The second one is A plus 1.

13:21 It can be Y. It can be C O. And the third one is A plus 2.

13:25 When you hear consecutive numbers, just put it like this.

13:28 So if the sum of all of these gives 11, this is how you express it.

13:32 The sum of these three gives 11.

13:34 So A plus 1 plus A plus 2 all gives you 11.

13:44 And the first of the three numbers is A, as it is C in A, determine the rest.

13:52 These are the rest, but what is the value?

13:54 That is what we want to get now.

13:56 Because we can get the value.

13:58 See, let's see if we can get the value.

14:00 So we have A plus A plus 1 plus A plus 2 equals 11.

14:08 Remember, like I taught you earlier, you're going to bring like times together.

14:11 So A plus A plus A plus 1 plus 2 equals 11.

14:19 So A in three places is 3A plus 3 equals 11.

14:27 So how do you solve it?

14:29 Using the inverse operation.

14:30 And you may not use inverse operation.

14:32 Let me teach you this.

14:33 You can't go like this.

14:34 Once you have something like this, you want to always find a way to make the one with

14:38 a variable alone on one of the sides, making it the subject of the formula.

14:45 So you can say 3A plus 3, the inverse of 3 is minus 3, and then you have 11 minus 3.

14:58 So you have 3A plus 0 equals 8.

15:05 So 3A equals 8.

15:09 We are not looking for 3A.

15:10 We are looking for A.

15:12 So A would be 8 divided by 3.

15:18 So A equals 8 over 3.

15:23 So A is 8 over 3.

15:25 The question is to determine the rest.

15:27 So if A is 8 divided by 3, the rest is A plus 1.

15:32 The first is A plus 1, which is 8 over 3 plus 1.

15:38 The second is A plus 2, which is 8 over 3 plus 2.

15:47 So moving on to this example.

15:51 It's small such as of milk cost X-Nyron, milk, X-Nyron, and it's small such as of noodles

16:13 cost 20 more.

16:15 So noodles is X plus 20.

16:25 What are the cost of 4 such as of milk and 8 such as of noodles?

16:32 So for 4 such as of milk, 4 such as of milk, that's 4, say 4 milk, 4 milk such as X and 4

16:51 places, X in 4 places, which is the same as 4 X.

17:01 You can just say 4 X, so you can say X plus X plus X plus X.

17:05 This is a cost of 4 such as of milk.

17:07 And 8 such as of noodles, 8 noodles would be since noodles is X plus 20.

17:18 So you have 8 times of X plus 20.

17:27 So 4 such as of milk is 4 X, 8 such as of noodles is the same thing as, now we can now,

17:37 we want to expand this.

17:38 Just the way I taught you to expand in the previous lesson 8 into bracket X plus 20.

17:48 Using the distributive law, you use this to multiply this and then use the same to multiply

17:53 this as well.

17:54 So you have 8 times X plus 8 times 20.

18:04 So you have 8 X plus 160.

18:10 So this is the cost of 8 such as of noodles of noodles.

18:20 We've come to the end of the examples.

18:25 You have your exercise, a pencil costs X, Nara, a ruler costs 10, Nara less than a pencil.

18:32 Remember the tips, you can just go back to the tips to know what to use for each of them.

18:37 A pencil costs 5 Nara more than a ruler.

18:39 The price of a small exercise book is twice the price of a ruler, calculate the cost

18:43 of 3 pencils, 2 rulers and 4 exercise books.

18:46 So you have like 3 variables in this word problem.

18:51 From the tips I gave you, you should be able to decipher which of the expressions to use.

19:00 The second is the sum of 4 consecutive numbers which is 16.

19:04 Find the numbers.

19:05 We did an example that has to do with 3 consecutive numbers.

19:08 So I believe you should be able to solve this.

19:11 The length of a rectangle is 3 cm more than its breadth, calculate the perimeter of the

19:17 rectangle.

19:18 From the tips, I believe you should be able to solve this and it should be easy.

19:25 We've come to the end of today's class.

19:27 Thank you so much for watching.

19:29 My name is Dorkas Aoye, till next time.