Free Online Math Tutor Free Online Math Tutor Numbers, what are numbers? Very silly question right, you all start learning number from the very first day of school. 1, 2,3, 4... all are numbers. There are many different type of numbers like whole numbers, real numbers, complex numbers, etc. Are you familiar with the properties of numbers. There are three basic property of numbers, Associative property, Distributive property and Commutative property. Today, we will learn about Distributive property and other two properties. The distributive property allows us to multiply a sum by multiplying each addend separately and after this add the products. It helps in developing the mental math and should be taught to children as the method to multiply much quicker in their minds only. In distributive property "the multiplication distributes over the addition" or we can say multiplication of real numbers distributes over the addition of real numbers.

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Lets see it with the help of a derivation or formula: we have a set S and two binary operators and + on S, so, operation is left distributed over addition (+), given some elements a, b and c of S. a * (b + c) = (a * b) + (a * c), and it is right distributive over + if given any elements a,b and c of S, (b+ c) * a = (b* a) + (c * a), here, both the condition are equal. A question must be arising in your mind that here I mentioned that in distributive property multiplication distribute over addition, then what about subtraction? Distributive property also applicable for subtraction let's say we have a equation as: 2 * (3 +(- 2)) = (2* 3) + (2 *(-2)) 2* 1 = 6 + (- 4), 2 = 2, hence, we can say it is applicable in both the cases that is addition and subtraction. Another property of numbers that is associative property say about the grouping. For addition this property is defined as a + (b + c) = (a+ b) + c and for multiplication it says a * (b* c) = (a * b)*c.

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