Videos uploaded by user “Wrath of Math”

What is a power set? A power set of any set A is the set containing all subsets of the given set A. For example, if we have the set A = {1, 2, 3}. Then the power set of A, denoted P(A), is {{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} where { } is the empty set. We also know that any set with n elements has a total of 2^(n) subsets, so if we have set B with n elements, it has 2^(n) subsets. This means that the cardinality of the power set of B would be 2^(n) also, since the power set contains all subsets of B. Thus, |P(B)| = 2^(n). I hope you find this lesson helpful.
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Views: 26685
Wrath of Math

What is the cardinality of a set? In this video we go over just that, defining cardinality with examples both easy and hard. To find the cardinality of a set, you need only to count the elements in the set. The cardinality of the empty set is 0, the cardinality of the set A = {0, 1, 2} is 3. The cardinality of a set A is written |A|.
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Views: 10911
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What is a subset in math? What is the difference between a proper subset and an improper subset? In this video, we will answer those questions so you know exactly what improper and proper subsets are, as well as how to write about them. In the video I describe writing a subset sign as a C, however it is more accurate to describe it as a capital U on its side, thanks to Greg Adams in the comments for that improved description. I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
An Introduction to Sets: https://www.youtube.com/watch?v=U4wui1mtotg
What is a Union?: https://youtu.be/hJHGyLpa0RQ
What is a Subset?: https://youtu.be/-4KLugkLwHQ
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Views: 17765
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In this math lesson we go over a proof by contradiction that proves there are an infinite amount of primes. It is a very important and interesting result, but it is quite easy to prove! The proof supposes there are finitely many primes then considers the number that is the product of all the primes plus one. From here, using the fundamental theorem of arithmetic, a contradiction follows. Thus, we know that our original assumption is false and there are instead infinitely many primes! Enjoy!
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Views: 2363
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What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go over "What is a Universal Set?" in this video, but I have done a full video on it, look below.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is the Universal Set?: https://www.youtube.com/watch?v=MZbhZMu9NhU
What is Set Subtraction?: https://youtu.be/IL465-AUUVY
An Introduction to Sets: https://www.youtube.com/watch?v=U4wui1mtotg
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Views: 3952
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What is a binomial? A binomial is a two term expression, one of the many types of polynomials. In this video we go over the binomial meaning, giving a definition of binomial as a two term expression. We look at some examples of binomials as well in this video.
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Views: 3533
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Prime numbers are extremely cool, and it turns out they have a slightly less cool cousin called relative primes, relatively prime numbers, mutual primes, mutually prime numbers, coprimes, or coprime numbers. What are relatively prime numbers? We go over that in this math lesson. Relatively prime numbers, mutual primes, or coprimes, are number which have no common factor greater than 1. For example, the factors of 6 are 1, 2, 3, and 6. The factors of 7 are 1 and 7, so the only common factor 6 and 7 have is 1. Therefore, they are relatively prime. 4 and 6 are not relatively prime because their largest common factor is 2. 1 and -1 are the only numbers relatively prime to every number, because they are the only numbers (we are only considering integers) whose largest factor is 1. Additionally, 1 and -1 are the only numbers relatively prime to 0.
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Views: 4856
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How many subsets does a set have? In this video we go over the number of subsets formula for any set. The subsets of a set can be tough to count when you get into larger sets, but it is important to know for things like power sets. So how many subsets in a set with 6 elements? Learn how to figure it out in this video!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Subset?: https://youtu.be/-4KLugkLwHQ
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The roster method is one of several set notations you can use to write a set. It is perhaps the easiest understand, but is only useful for writing out sets when they are finite and small in size, or if they are dictated by an easy to describe pattern (that is finite or infinite). If you are asked to list the elements of the set for any particular set, that is using the roster method. The roster form of a set is simply listing the elements of the set between brackets. Ellipsis are permitted to indicate an ongoing pattern. I hope that after this lesson you can write out a set using the roster method.
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Views: 4748
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The congruent complements theorem is a theorem regarding angles being complementary to the same angle. It is very similar to the congruent supplements theorem but with different angle measures of course. Congruent complementary and supplementary angles are fun topics of discussion, let me know if you'd like more lessons on them. The congruent complements theorem states that if two angles are complementary to the same angle, then they are congruent.
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Views: 1486
Wrath of Math

What is that exclamation point next to the number? Why is there an exclamation sign in my math problem? It is called a factorial! What is a factorial? What is the factorial formula for any generic number? What is that factorial of 0? In today's video, we go over all of these questions.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 1559
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The empty set is a very cool and important part of set theory in mathematics. The empty set contains no elements and is denoted { } or with the empty set symbol ∅. As a result of the empty set having no elements is that it is a subset of every set. But why is that? We go over that in this video!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Subset?: https://youtu.be/-4KLugkLwHQ
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What is the congruent supplements theorem? Congruent supplementary angles as I have said before, are always 90 degrees, but that is not quite what this theorem is about. If there are two angles that are both supplementary to one angle, then the former two angles must be congruent, that is what the congruent supplements theorem states. I hope this video helps you fully understand it!
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Views: 1319
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Absolute value takes a negative number and makes it positive, and leaves other numbers unchanged. However, it is not just numbers that can be put between absolute value signs. We can also put operations within absolute value signs, in which case we simply do the operation inside and if it is negative, make it positive. If not, leave it unchanged. This should leave you with little question as to what absolute difference is, knowing that difference implies subtraction. Hopefully after this video, all becomes clear in the realm of absolute difference, the absolute value of subtraction.
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Views: 756
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How do you find the interquartile range of a set of data? What is the interquartile range? In this video we go over an example of finding the interquartile range, or inter-quartile range if you prefer it hyphenated. We define interquartile range as well, if you're into that sort of thing. Hot dog eating contest statistic retrieved from nowhere at all. Let me know if you would like more statistics lessons! Stats for life.
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Views: 642
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Set builder notation is a great way to easily represent sets accurately and without using the roster method. What is set notation? Hopefully you know, as this video is not meant to be an introduction to it, but you may find it helpful in introducing you to set builder notation. In this video we go through a couple methods of representing the even numbers in set builder notation. The odd and even numbers are both easy to represent in this form, and we will cover the odd case in a separate video. The set of even numbers is easy to define, and I hope you agree after this video!
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Views: 1378
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What are similar triangles? In this video we go over properties of similar triangles in Euclidean geometry and what makes similar triangles similar. Similar triangles have many properties, for example their corresponding angles are congruent, the ratios of their corresponding sides are proportional, their corresponding sides are proportional, etc. All congruent triangles are similar, but not all similar triangles are congruent. I hope this video helps!
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Views: 489
Wrath of Math

If you want to know how to find the diameter of a circle, particularly how to measure the diameter of a circle, it is handy to have a few formulas in your backpocket! The diameter of a circle is a segment that has both endpoints on the circle and passes through the center. If we know the length of the circumference of a circle, we can rework the circumference formula to solve for the length of the diameter of the circle. So if you want to know how to calculate diameter by going from circumference to diameter, then watch on! It is time to find diameter of a circle in terms of the circumference!
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Views: 4682
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Have you ever seen that pesky proof some people spread around on social media and the like that 1+1=0? Seems like a pretty ridiculous idea, right? Well it is. But you have seen the proof. In this video I will show you why that proof is bogus, 1+1 does not equal 0. It does, in fact, equal 2. Remember folks, never divide by zero. What's zero divided by zero? It's the end of the world.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 929
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The height of an equilateral triangle is very cool because it can be represented with a handy formula that only requires knowing the length of a side of the triangle! In the case of equilateral triangles, all sides are congruent which is why we get the special relationship that we do. In this video I show you how to find the height of a triangle/how to find the altitude of a triangle if that triangle is equilateral using the handy height formula. With this formula you can quickly get an equally handy area formula for equilateral triangles, and I have a video or two on that as well, including a proof, so check that out too! This is one of many properties of equilateral triangles worth knowing!
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Views: 760
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Math subsets are an important concept to understand. So what is the subset definition in math? What is a subset? We go over that part of set theory in this video as well as some details on the empty set and its subset properties. Enjoy!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
Why is the Empty Set a Subset of Every Set?: https://www.youtube.com/watch?v=nXAOZo_gMaQ
How Many Subsets Does any Given Set Have?: https://www.youtube.com/watch?v=lTs-NGw0FQo
Proper Subsets vs Improper Subsets: https://youtu.be/06PsJYcl2dc
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Views: 1130
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How do Cartesian products work with empty sets? Cartesian products are great and all, but we cannot eagerly dive into working with them without making sure we know how to deal with Cartesian products when empty sets are involved. We go over that in today's math lesson!
Recall that the Cartesian product of two sets, A and B, is the set containing all ordered pairs (a, b) where a is in A and b is in B. Then, by definition, A x B is equal to the empty set if A is the empty set, if B is the empty set, or if both A and B are the empty set. It works just like 0. If the empty set is involved in a Cartesian product, then the product is the empty set because there are no elements in the empty set with which to form any ordered pairs.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 232
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What is set subtraction? In this video we go over that, the set minus set operation, and an example of subtraction in set theory. This is a handy concept to grasp to understand the complement of a set and universal sets, which I also have videos on. Links below.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Set Complement?: https://www.youtube.com/watch?v=vmhssot-DAY
What is the Universal Set?: https://www.youtube.com/watch?v=MZbhZMu9NhU
Union vs Intersection: https://www.youtube.com/watch?v=uZsC5ZKs9tA
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Views: 1146
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What is the area of an equilateral triangle? We know the formula for area of a triangle in general is A = (1/2)bh, but for an equilateral triangle (where all sides are equal), we get a bit of a special formula. Normally, we would need to find the height of a triangle using the Pythagorean theorem in order to find its area, but with equilateral triangle area, we do not have to! So if you want to know how to find the area of an equilateral triangle, watch this video where we go over the new and improved area of a triangle formula for use with equilateral triangles only, but more importantly we prove the area formula! Equilateral triangle height shall not inconvenience us! For an equilateral triangle, the formula for area is A = (b^(2)sqrt(3))/4.
I hope you enjoy this equilateral triangle area formula proof and I hope it deepens your understanding. Let me know if you want to see more geometry proofs, area proofs, triangle proofs, triangle area proofs, etc.
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Views: 1650
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Is zero odd or even? Is zero an even number? Is zero one of the many odd numbers? We already answered all of those questions (link below). But today we tackle it from a different angle. Using an indirect proof. In this video, you will see an example of a contradiction proof. We will prove that 0 is even by contradiction, which means we start by supposing that zero is odd. Pretty cool, huh? Watch the video for the rest of the story!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
Is Zero Even or Odd?: https://www.youtube.com/watch?v=h7ilWSvJrts
Definition of an Even Number: https://www.youtube.com/watch?v=pIIeywr4-Nw
Definition of an Odd Number: https://www.youtube.com/watch?v=GUirt_Tp6EA
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Views: 1371
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What does it mean to find the diagonal of a rectangle? Generally, finding the diagonal of a rectangle means to find the length of the rectangle diagonal. In this video we go over how to do just that. We find the diagonal length of a rectangle, and mention the rectangle diagonal formula for finding the length of any generic rectangle diagonal. As you might expect, it uses the Pythagorean Theorem.
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Views: 1744
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The Lambert quadrilateral is the namesake of Johann Heinrich Lambert. What is a Lambert quadrilateral? It is a quadrilateral, which may be in a non euclidean geometry, with three 90 degree angles. If you need to see more detail, just watch this short video!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Saccheri Quadrilateral?: https://youtu.be/xmdDc5_Zpb8
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Views: 321
Wrath of Math

What makes a number odd? Is one an odd number? How can you prove a number is odd? Is zero odd or even? We will effectively answer these question in this video, What are the odd numbers? The odd meaning of odd numbers will be explained here, in this video on how to prove a number is odd!
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Views: 420
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The Saccheri quadrilateral is the namesake of Giovanni Gerolamo Saccheri. SO what is this shape? Well, it exists outside and inside of Euclidean geometry. I love non euclidean geometries. Anyways, a Saccheri quadrilateral is a quadrilateral with two congruent sides that are both perpendicular to the base! Watch the video for more details and illustrations.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Lambert Quadrilateral?: https://youtu.be/QhLW9OlMIls
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Views: 1015
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Why do triangles have 180 degrees? In Euclidean geometry, such is life, the sum of angles in a triangle is 180 degrees. Pick a triangle, any triangle, and its three angle measure will add up to 180. But why should this be so? Well, in this video I have a great geometry proof for you. We will dive headfirst into the wonderful world of triangles and mathematical proof to show why triangles do indeed have an angle sum of 180 degrees. Strap up, and let's get to mathing!
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Views: 5423
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The height of an equilateral triangle is very cool because it can be represented with a handy formula that only requires knowing the length of a side of the triangle! In the case of equilateral triangles, all sides are congruent which is why we get the special relationship that we do. In this video I show you a geometric proof for the equilateral triangle height formula/ With this formula you can quickly get an equally handy area formula for equilateral triangles, and I have a video or two on that as well, including a proof, so check that out too! This is one of many properties of equilateral triangles worth knowing! Let me know if you would like to see more mathematical proofs, or more geometry proofs in general.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 1638
Wrath of Math

What is a negative reciprocal? The negative reciprocal of a fraction is found by flipping the numerator and denominator and then multiplying by negative one. Note that any number can be made to look like a fraction by putting it over one. For example, the negative reciprocal of 4 is -(1/4). Also note that if two lines are perpendicular then the slope of one is the negative reciprocal of the other.
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down in the comments!
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Views: 1655
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How do you prove that rectangle diagonals bisect each other? In today's video we will be going over the simple geometry proof that the diagonals of a rectangle bisect each other. We will prove this using the AAS triangle congruence postulate.
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Views: 1496
Wrath of Math

What is the intersection of sets? This is another video on set theory in which we discuss the intersection of a set and another set, using the classic example of A intersect B. We do not quite go over a formal definition of intersection of a set in this video, but we come very close! Be sure to let me know if you want to know more about set operators and set operations!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
Union vs Intersection: https://youtu.be/uZsC5ZKs9tA
What is a Union?: https://www.youtube.com/watch?v=hJHGyLpa0RQ
An Introduction to Sets: https://www.youtube.com/watch?v=U4wui1mtotg
Proper Subsets vs Improper Subsets: https://www.youtube.com/watch?v=06PsJYcl2dc
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Views: 765
Wrath of Math

What is the meaning of quotient in math? The quotient of a number and another number is the quantity resulting from the division of the two numbers. So what does find the quotient mean? it means divide! Watch the video for more on the quotient definition and what is the quotient in division.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 10170
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What is a spanning subgraph? We go over this special type of subgraph in today's math lesson! Recall that a graph is an ordered pair G = ( V(G), E(G) ) with vertex set V and edge set E. Another graph, H = ( V(H), E(H) ) is a subgraph of G if and only if V(H) is a subset of V(G) and E(H) is a subset of E(G). Basically, this means H is a subgraph of G if everything in H is also in G. Then, H is a spanning subgraph of G if and only if V(H) = V(G). In other words, H is a spanning subgraph of G if H is a subgraph of G, and H has the same vertex set as G. The graph H 'spans' the vertex set of G and has some or all of the edges in G. Also, remember that H has no edges not in G. So one last time, H is a spanning subgraph of G if and only if H is a subgraph of G, and the vertex set of H is equal to the vertex set of G.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 173
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How do you find the GCF and the LCM of any two numbers? GCF and LCM stand for greatest common factor and least common multiple, respectively. So do you want to know how to find the greatest common factor and how to find the least common multiple? It is quite easy, and very cool. The method I show in this video involves prime factors and factor trees, if you do not understand it from watching this video, let me know and I would be happy to make a video on it. So, enjoy this video on GCF and LCM.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is a Greatest Common Factor?: https://youtu.be/p4lWELbAP7U
What is a Least Common Multiple?: https://youtu.be/dWfJVwFhj_g
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Views: 141
Wrath of Math

What are irregular polygons? Regular polygons are convex shapes that have congruent angles and congruent sides, that is they are both equiangular and equilateral. An irregular polygon is any polygon that does not have those characteristics. For example, every rectangle that is not a square is an irregular polygon because it is not equilateral.
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Views: 248
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What is the symmetric difference of 2 sets? In this video we go over the symmetric difference of sets, explaining it in a couple ways including what is probably the briefest way. The symmetric difference of two sets A and B is (A union B)-(A intersect B). If you need to know what the definition of intersection is or what the definition of union is, I have links to that below! Hope it helps!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
What is Set Subtraction?: https://www.youtube.com/watch?v=IL465-AUUVY
Union vs Intersection: https://www.youtube.com/watch?v=uZsC5ZKs9tA
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Views: 694
Wrath of Math

What is the distributive property? What does distributive property mean? We go over that in this video through an explanation of the multiplication properties necessary for using the distributive property and examples on how to do distributive property problems that involve fractions. I also have a proof of distributive property video, so you can check that out if you fancy! Using the distributive property is an important part of doing lots of problems, so let's get to it! Let me know if you would like to see anymore distributive property examples with fractions!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Views: 2222
Wrath of Math

What does divisible mean? If a is divisible by b, what does that tell us about a? How can we represent a as a multiple of b? How can we represent b as a factor of a? We go over these questions in this video. We are not talking about tests of divisibility, though you can certainly use this definition of divisible meaning to do a traditional sort of test with no funky tricks.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Wrath of Math

What is the order and size of a graph? We'll go over them both in this math lesson! A graph is an ordered pair with a vertex set and an edge set. The order of a graph is the cardinality of its vertex set, which is the number of vertices in the graph. The size of a graph is the cardinality of its edge set, which is the number of edges in the graph. So the order is the number of vertices, and the size is the number of edges. Simple as that!
If we have a graph G = (V, E), then the order of G is the cardinality of V, |V|, and the size of G is the cardinality of E, |E|.
Ask yourself some questions about order and size. Can the order and size ever be equal? Can the size be greater than the order?
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Wrath of Math

How do we change the denominator of a fraction? How do we change it to the exact number we want it to be without changing the value of the fraction? We go over all of this in today’s math lesson on fractions and changing denominators!
There are three important things we need to remember to change fraction denominators. First, remember that anything times 1 is itself. Secondly, remember that a fraction with equal numerator and denominator is equal to 1. Third, remember how to multiply fractions. All we have to do to multiply fractions is multiply across the numerator and multiply across the denominator. All of these topics are covered in the video lesson.
With all of that in mind, we can change a fraction’s denominator, without changing the value of the fraction, by multiplying by different representations of 1. For example, we can change 2/3 to 4/6 by multiplying 2/3 by 2/2. Since 2/2 is equal to 1, we are not changing the fraction’s value because we are simply multiplying by 1.
If you want to change a fraction’s denominator to a specific number, which you probably do in order to add or subtract fractions or do a number of other things, we can do that as well! Suppose we have the fraction 6/7, and we want to change the denominator to 21. All we have to do is divide our new denominator (21) by our old denominator (7), so we have 21/7, which is equal to 3. This tells us we just have to multiply 6/7 by 3/3 to change the denominator to 21. If we multiply 6/7 by 3/3, we get 18/21, which we know is equal to 6/7 since we just multiplied it by 1. So we successfully changed the denominator without changing the value! As always, this information is covered in greater detail in the video, and includes different examples.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
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Wrath of Math

What is a star graph in graph theory? We go over star graphs in today's lesson! Star graphs are special types of trees. Any graph with n vertices, where 1 vertex has degree n - 1 and any other vertex has degree 1, is a star graph. The star graph of order n is isomorphic to the complete bipartite graph that has one partite set with cardinality 1 and one partite set with cardinality n - 1.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Soundcloud: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
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Views: 163
Wrath of Math

What is a set in math? What are elements? What is cardinality? What are subsets? In this video we will answer all of those questions. We will pinpoint the definition of sets in math, talk about elements, explain what cardinality is, and what a subset is. I hope you find this video helpful, and be sure to ask any questions down in the comments!
Related Videos:
Proper Subsets vs Improper Subsets: https://youtu.be/06PsJYcl2dc
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Wrath of Math

Do you want to know how to convert Fahrenheit to Celsius? It is a fairly easy temperature conversion. In this video we will go over the degrees Fahrenheit to Celsius conversion formula and we will go over a Fahrenheit to Celsius example. By the end of this video, I hope you will be able to convert Fahrenheit to Celsius!
The Fahrenheit to Celsius formula is C = (F - 32)/1.8
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Wrath of Math

An even number squared is even, and in this video we will prove just that! It is a very easy mathematical proof, so I will also give it to you here in the description. We are proving if n is even, then n squared is also even. So we know n = 2k for some integer k. Then, (2k)^2 = 4k^2 = 2(2k^2). Thus, by definition of an even number, n squared is even. There ya go, try proving the analogous fact about odd numbers squared!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Wrath of Math

Calculating a 15% tip made easy! It is always a pain waiting for the bill at a restaurant after a nice meal and then having to fumble around with calculations and maybe having to find a pen and paper to figure out how much of a tip you should leave your waiter/waitress. In this math lesson I will show you how to make calculating the standard 15% tip amount a breeze that can be done in your head with ease, and your tipping at restaurants should become a much easier process, and of course you can adjust the number you get based on the exceptional or not so exceptional service you receive.
The process is simple, just take 10% of your bill, which can be done easily by moving the decimal point one place value to the left. Then take half of this amount and add it back to the original 10% amount. Voila! You have a 15% tip.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Wrath of Math

What are adjacent vertices? Graphs are made up of vertices and edges. Each edge joins a pair of vertices. When two vertices are joined by an edge, we say those vertices are "adjacent". Adjacent vertices are vertices that are joined by an edge, non-adjacent vertices are vertices not joined by an edge. A vertex that is adjacent to no vertices is called an "isolated vertex". A vertex adjacent to one vertex is called a "leaf" or "end vertex". The number of vertices a vertex V is adjacent to is the "degree" of the vertex V.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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What are vertex-induced subgraphs? We go over them in today's math lesson! Recall that a graph H is a subgraph of a graph G if and only if every vertex in H is also in G, and every edge in H is also in G. In other words, the vertex set and edge set of H are subsets of the vertex set and edge set of G, respectively. Then, H is a vertex-induced subgraph of G if and only if every pair of vertices in H, that is joined by an edge in G, is also joined by an edge in H. So two vertices in H are adjacent if and only if they are adjacent in G, this is what makes a subgraph a vertex-induced subgraph. We can think of it as taking some vertices from G, and all edges joining any of those vertices.
Suppose G = ( { a, b, c, d, e }, { ab, ac, de, da, ce, db } ). We can denote the subgraph of G induced by the vertex set A as G[A]. Let A = { a, c, d }. Then G[A] = ( { a, c, d }, { ac, da } ). The graph G[A] is a vertex-induced subgraph of G, and it is induced by the vertex set A. So G[A] has all vertices in A, and has all edges from G that join any vertices in A.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Soundcloud: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
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Follow Wrath of Math on...
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Views: 106
Wrath of Math

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© 2019 College Girl Secret Romance With Boy Friend In Hostel

As a child, there was a portrait in our family home in Paris that I always loved. Today, it’s known as Maya with Doll – but to me it was just a portrait of my mother, albeit a remarkable one. “Your grandfather was a painter,” she would say, whenever the subject of the canvas, one of many that hung around the house, came up in discussion. It was only when I began school, and whispers about my heritage started to follow me, that I realised what an understatement that was. My grandfather was far more than a painter. He was the defining figure of 20th-century art – and, as I would learn later from years of academic study, a true genius. It was a revelation that would shape the course of my life in many ways. When Picasso died – in 1973, the year before I was born – he left behind 45,000 works, not to mention personal objects and correspondence.