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    Pre-Algebra 7 – Associative & Distributive Properties of Multiplication

    Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture we saw that addition and multiplication are both commutative operations. The order of numbers which are added or multiplied can be rearranged without affecting the result. As we saw, addition also has an “associative” property. According to the Associative Property of Addition three or more numbers which are added can be grouped in any way without affecting the result. Does this also apply to multiplication? Let’s start with our stack of 24 boxes and group them in different ways before multiplying. For instance if we group the two and the three we get four groups of…

  • Properties of Integrals and Evaluating Definite Integrals
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    Properties of Integrals and Evaluating Definite Integrals

    Professor Dave here, let’s take some integrals. Hopefully we now understand the relationship between differentiation and integration. These are inverse operations, in the sense that integration requires taking the antiderivative of a function. For basic functions, this is easy to do, but it gets extremely complicated as the functions get more complex, and we will have to learn a number of different strategies to tackle the tougher ones. But that will come later. For now, let’s just go over a few properties of integrals, and then try some simple examples. As we said, it will be a good idea to quickly highlight some important properties of definite integrals. First, if…

  • Pre-Algebra 5 – Commutative & Associative Properties of Addition
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    Pre-Algebra 5 – Commutative & Associative Properties of Addition

    Hello. I’m Professor Von Schmohawk and welcome to Why U. In the first lecture, we explored the origins of the first number systems. We also saw how the people on my primitive island of Cocoloco first learned about the decimal number system. Once the Cocoloconians discovered decimal numbers we could do much more than count coconuts. We could do arithmetic calculations with coconuts! The first arithmetic operations we invented were addition and subtraction which came in very handy when dealing with coconuts. For instance, if you have three coconuts and then your neighbor gives you five more you will have eight coconuts. Interestingly, if you start out with five coconuts…

  • The Distributive Property for Arithmetic
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    The Distributive Property for Arithmetic

    It’s Professor Dave; let’s introduce the distributive property. As we learn math, we will see that there are certain properties of numbers that are very important. We already learned about the commutative property and the associative property, and we saw how addition and multiplication abide by these properties, while subtraction and division do not. Now let’s learn another property, the distributive property. To see how this works, let’s look at some more apples. Say we have five piles of seven apples. Five piles times seven apples per pile gives us thirty-five apples. What if we split each pile up into a group of three and a group of four? There…

  • Distributive Property
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    Distributive Property

    Distributive Property, a la Shmoop. King Moneylust values gold and jewels above all else. [King Moneylust sat on a throne] One day, the king’s first steward brought him 5 gold bars and 1 precious diamond. [Steward drops 5 gold bars and a diamond for the King] His second steward entered the court, also bringing the king 5 gold bars and 1 precious diamond. Moneylust’s third steward, never one to be a trailblazer, followed suit. [Third steward drops gold bars and diamond on the floor] In he came with 5 gold bars and 1 precious diamond. Because Moneylust is a busy guy and hardly has time to sit around and count…

  • Pre-Algebra 6 – Commutative Property of Multiplication
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    Pre-Algebra 6 – Commutative Property of Multiplication

    Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture, we saw how the people on my primitive island of Cocoloco discovered addition and subtraction. Once we had invented addition and subtraction the Cocoloconians could calculate very complicated coconut transactions with great precision. But we soon found out that with only addition and subtraction some calculations could take a very long time. For instance, once a year, everyone on Cocoloco must donate three coconuts for the annual feast of Mombozo. So if all 87 inhabitants of Cocoloco each donate three coconuts then how many coconuts will we have for the feast? Before we discovered multiplication, we…