• Articles

    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…

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

    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…

  • Pre-Algebra 6 – Commutative Property of Multiplication
    Articles,  Blog

    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…

  • A clever application of the distributive property to solve a multi-step equation | Khan Academy
    Articles,  Blog

    A clever application of the distributive property to solve a multi-step equation | Khan Academy

    We have the equation 3/4x plus 2 is equal to 3/8x minus 4. Now, we could just, right from the get go, solve this the way we solved everything else, group the x terms, maybe on the left-hand side, group the constant terms on the right-hand side. But adding and subtracting fractions are messy. So what I’m going to do, right from the start of this video, is to multiply both sides of this equation by some number so I can get rid of the fractions. And the best number to do it by– what number is the smallest number that if I multiply both of these fractions by it,…