Addition and Subtraction of Fractions
This lesson covers how to add and subtract fractions with the same and different denominators. It explains finding the least common multiple (LCM) to create equivalent fractions for addition and subtraction. Examples are provided for practice.
- 00:00 “Hello everyone, I'm your Mathematics teacher, Esther Olochi-Ebebeke, and the topic of this lesson is addition and subtraction of fractions. By the end of this lesson you should be able to solve giving problems on additio...”
- 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 2 over 2 over 3. So the same goes with this example, 4, 75, 3, all number, 2 over 5, plus 2, 2 over 2 over 3. You u...”
- 01:39 “of seven and five is 35. So with this, they don't have common denominators, so you can just add this to get us to give you three over, what will it be? It will be three over seven, or will it be three over five. So in th...”
Rational and Non-Rational Numbers
This lesson covers the identification of rational and non-rational numbers. It explains the characteristics of different number sets, including natural numbers, whole numbers, and integers. The lesson also discusses the significance of the number PI in relation to circles.
- 05:41 “All common fractions, whether it's an improper fraction, whether it's a proper fraction, whether it's a mixed fraction, they all fall on that the categories of what rational numbers. Like I said, the proper fraction, the...”
- 06:28 “I have 11 over 20. You could see that 11 smaller compared to 20. I have 17 over 18 at the rest of the others. Now, that is the proper fraction. Now, an improper fraction is the opposite direction, opposite direction in t...”
- 08:00 “the larger volume. So we have percentage. We have fractions. Fractions. Percentage are inside the rational numbers. Take it off. So we have percentage. I said, all percentage are rational numbers. A percentage is a fract...”
Quadratic Equation and Roots
This lesson covers the formation of quadratic equations from given roots. It explains how to find the sum and product of the roots and demonstrates solving for unknown coefficients in a quadratic equation. Examples are provided to illustrate these concepts.
- 07:40 “2 in 4 - 2 times -1/2 -2 + 4 in 4 there's 1 times 3 that gives you 3 there. So this go ahead to put B in a better perspective for you. So you can go ahead and sum up your fraction here to have -2 + 3 I give you 1/4 equal...”
- 20:08 “4 times 3 that gives me minus 12 and I know for the fraction is been done by inverting when you have fraction to have fraction what you do is you invert by much implication and that gives me 64 over 9 minus this leads me...”
- 19:19 “we refer to as reciprocal you invert it okay by inversion I can have minus 2 times 8 over 3 all right so this now leads me to something fantastic that I can do it right away yeah now that we have subset for this sum and...”
Solving Simultaneous Linear Equations
This lesson covers how to solve simultaneous linear equations using substitution and elimination methods. It also explains how to identify linear equations and includes examples for practice.
- 02:43 “So, we're able to solve this very well. You start from equation 2. From equation 2R minus Q over 2 plus 1. In equation 2, I have a fraction. The first step is eliminating your fraction. I'd rather eliminate my fraction h...”
- 13:56 “Don't forget this elimination. To eliminate A. Now P plus R equals 1 over 4. 1. 5P plus 2R equals to 2. Equation 1. I have a fraction here. There are two ways to this. I will solve and I want you to follow what you have...”
- 09:06 “Okay. Just like the first example, I'm having a fraction here. I can solve it with a fraction. The first step is clear your fraction. So where do we have the fraction? I have the fraction in example. That is equation 1....”
Basic Operations on Whole Numbers
This lesson covers addition and subtraction of whole numbers, including how to align numbers by their place values. It also explains multiplication and division by 10, 100, and 1000, and introduces the use of the BODMAS rule for solving mixed operations.
- 01:01:40 “divided by 5 plus 1 over 2, don't forget that this expression in the bracket has been simplified to 70 times of means times, don't forget, of means times times 17 times 17, so now let's simplify it further, 2 goes here 1...”
- 01:02:39 “15 minus 5 times this division must be treated first, so we have 10 over 5, 10 over 5 plus because we have 1 times 35 is 35, so now 15 minus 5, now looking at this place 5 goes here 1, 5 in 10 is 2, so now we have 5 time...”
- 37:25 “Either of this method will work, and you still get your answer. So now, let's continue, because we see more questions. H 0 5 divided by 5, so now I'll keep to one method now, because it's short method, it's short, so I'm...”
Roots of Quadratic Equations
This lesson covers how to find the sum and product of the roots of a quadratic equation. It also explains how to form a quadratic equation given the roots and states the conditions for equal roots, real roots, and no roots. Additionally, it discusses the relationship between a line and a curve in te
- 15:18 “you can just make it three X over two, and you now go for minus two of five times X, that gives you minus two X over five. And the last one minus two of five times three over two, that gives you minus, okay, six over 10....”
- 13:46 “So for this one, I have X minus two over five, okay, and for this one, I have X equals bigger pardon, X plus one, one number one over two. Equal to zero, equal to zero. One more thing I can do before I bring them togethe...”
- 22:35 “Don't forget, the sum and product of quadratic equation is given as x squared minus r for plus beta, bracket plus x, then plus x, I mean, plus alpha beta. So the coefficient of your x squared must always be one. You know...”
Whole Numbers and Their Properties
This lesson covers whole numbers, including their definition and characteristics. It explains how to express whole numbers and decimal numbers in standard form. The lesson also includes finding prime factors, least common multiples (LCM), and highest common factors (HCF) of numbers.
- 17:03 “it is division. We moved backward. That's out of a 7. So, if you look carefully, so we have, what do I have? I have 7, 7 over how many times do I have? I have 10 ways to power 6. Because of the sign of division, because...”
- 17:50 “and how do I do that? Now, this is 1 over, okay? 1 divided by this. I need to convert this into multiplication. How do I do that? That's the first question. How do I do that? That this one is bit, how do I do that? It be...”
- 18:36 “this is moving up, it becomes a minus. That's negativity. Take notes. It becomes very important. It becomes very important. Now, looking at it again, another example that we have in the part of division. So, you could ha...”
Translating Word Problems into Equations
The lesson teaches how to translate word sentences into mathematical equations. It covers the use of variables to represent numbers and how to express word problems as algebraic expressions. Students will learn to solve simple equations and check their answers.
- 15:18 “So A equals 8 over 3. So A is 8 over 3. The question is to determine the rest. So if A is 8 divided by 3, the rest is A plus 1. The first is A plus 1, which is 8 over 3 plus 1. The second is A plus 2, which is 8 over 3 p...”
- 14:30 “And you may not use inverse operation. Let me teach you this. You can't go like this. Once you have something like this, you want to always find a way to make the one with a variable alone on one of the sides, making it...”
- 17:01 “You can just say 4 X, so you can say X plus X plus X plus X. This is a cost of 4 such as of milk. And 8 such as of noodles, 8 noodles would be since noodles is X plus 20. So you have 8 times of X plus 20. So 4 such as of...”
Simplification of Algebraic Expressions
This lesson covers the definition of algebraic expressions and their components, including terms and coefficients. It explains how to identify like terms, perform arithmetic operations on similar terms, and simplify expressions by inserting or removing brackets.
- 25:31 “is the next one, or division. In the expression, you do multiplication next. So you use the distributive law to multiply the brackets by its coefficient. Remember that 4 times 3x means 4 times 3 times x. 16x plus 2 plus...”
- 22:23 “10 times b is 10b minus 2 times 3 is 6. 6 times c is 6c, 6c. So we have 2a plus 10b minus 6c. So this is the answer to this. I believe you should be able to solve the rest. I'm just going to go through one more example t...”
- 20:52 “Like it says here. Multiply 3 by the second term, like I explained earlier, and you get 3b. At the end of the day, you get 6a plus 3b. More examples. You can solve this on your own. I'll just solve just one of it. Expand...”
Trigonometric Ratios
This lesson covers the identification of sine, cosine, and tangent of an acute angle. It explains how to apply these trigonometric ratios to solve problems involving distances and lengths in right-angled triangles. The relationship between the sides and angles of triangles is also discussed.
- 14:14 “that is given, then your hypotenuse. So, I could read, you could know, the particular one to apply. They are designed to cause all the time. Thank you very much. We've come to the end of the class. My name is Oyase Sunda...”
- 05:55 “over adjacent? Your opposite is what? Your opposite already given to be what? 12. Don't forget. That will give you what? 12. What's your adjacent? 16. So in a simplified fraction. I have three here. Four can go. Successf...”
Similar Shapes
This lesson covers the identification of similar shapes such as triangles, rectangles, squares, cubes, and cuboids. It explains the criteria for similarity, including proportional sides and equal angles. The lesson also includes methods for enlarging figures using scale factors and calculating lengt
- 11:57 “smaller one, what longest side of the smaller one, that's 9. Because of this point, decimal place, you multiply by 10. So, when you multiply, because of the decimal place, to take it off, you are going to be having 2.5,...”
- 23:43 “triangle, BAC, that's remember from the scalar, from the scalar that we meant comparison, now you will see why the scalar of 2 can also be checked, so that gives me 384, the bigger one, over 96, now if you look at 96, so...”
- 24:32 “smaller one, square, the bigger one is multiplied 4 times the smaller one, but in this proportion, this 4 can say 2 is to power 2, multiplied by water by 96 centimeter square, remember what's okay, as scalar factor is gi...”
Linear Inequalities in One Variable
This lesson covers linear inequalities in one variable. It includes identifying, solving, and representing solutions of linear inequalities on a number line. Word problems involving linear inequalities are also addressed.
- 22:13 “us 20 divided by x, okay, now bring them together, this is 25 divided by 2x, remember, because we said it's twice, bring them together, bring them together, the two ways is not less than, it's not less, it's not less tha...”
- 23:49 “okay, 25, plus what, plus 40, okay, less than what, 5 times x, now give us what, 5x, so that will give us 25 plus 40, that gives us what, 65, 65, less than 5x, find your inverse 2, that's the multiplicative inverse, down...”
Factorization of Algebraic Expressions
This lesson covers the factorization of simple algebraic expressions and quadratic expressions. It includes methods for identifying factors and solving related word problems.
- 22:49 “There are twice as many boys as there are girls. Now, every word problem gives you an insight to what you want to do. But technique, that means in that school, there are boys and there are girls. But there are twice as m...”
- 25:15 “From the extra. Now, what are the number of boys? We have it as two, two X plus what's the number of girls? We have it as what? X. Equal to 360. So, I have two X plus X. Remember? That gives me word, three X equal to 360...”
- 12:30 “So that we will have, what we have, 2x squared, good. 2x squared is common to the 3 of them. That gives us an example to be able to factorize them out. Now, the question is, how do you now rewrite them? How? How do you w...”
Gravitational Force and Fields
The lesson covers the concept of gravitational fields and the laws of gravitational force as proposed by Isaac Newton. It explains the relationship between masses and the distance between them in determining gravitational force.
- 25:13 “now let's get 0.2 times 0.2 give us 0.0.04, now 2.8 points 1 for divided by 0.04 now give us, now give us our fourth is equal to 7.003.5 times 10 raise to the power minus 9,”
- 23:31 “this as F is equal to 6.67 times 10 to the power minus 11 times, this time this we give us 42, 1, 2 we give us 1, 2 over 0.2 or square, now from this side I can take care of this as 1, 2, 2 or this one we are taking off,...”
Solving Linear and Quadratic Equations
This lesson covers the methods for solving simultaneous linear and quadratic equations using substitution. It explains the definitions of linear and quadratic equations and demonstrates how to manipulate these equations to find solutions.
- 15:30 “X minus two is equals to zero. From here, our S is equals to five or S is equals to two. Since you've gotten the value of X, substitute the value of X into equation three. When X is equals to five, substitute it into equ...”
- 13:57 “Divide through by two. Now the coefficient of S square is one, our constant is 10. Then we have 10. The two numbers that we multiply together that we give you 10 is minus five and minus two. And if you hide minus five an...”
Whole Numbers and Prime Factorization
This lesson covers the expression of whole numbers and decimal numbers in standard form. It includes finding prime factors of numbers up to 200, determining the least common multiple (LCM), and finding the highest common factor (HCF). Additionally, it addresses perfect squares and square roots using
- 25:55 “so split them into 2, I have 3 times 5 times 7, for the first part, and the second part, I have 3 times 5 times 7, now splitting them into 2, 3 times 5, that's 15, 15 times 7, that is 1, 0, 5, multiply by 3 times 5, 15,...”
- 08:57 “get two, now using the division method, division method method B, also for clarification, let's see the division method now, in the division method, that's method B, it will give you, we have it as right out the division...”