The Distributive Property is one of the number properties. It says that when number is multiplied to an addition of two or more numbers, the result is the same as the sum of the products of the same number and each addend. To define distributive property algebraically, it is expressed in formula form as, a*(b + c) = a*b + a*c. That is, the number is ‘distributed’ to each of the addend and then the addition can be done. Thus, it can also be referred as distributive property of addition.But one must clearly understand that while a*(b + c) = a*b + a*c is true, a/(b + c) is ? (a/b) + (a/c). Hence to stress this point some emphatically refer this property as ‘Distributive Property of Multiplication over Addition’.
Thus in general, the definition of distributive property is when a term is multiplied to the sum of group of terms, then the result is same as the sum of the products of the first term with each of the terms of the sum. It may be noted this property is applicable to subtraction of terms also, because in the general formula any of the three ‘a’. ‘b’ and ‘c’ can also be negative.
The distributive property greatly helps calculations and provides easier methods of solution. For example I need to multiply 51*101. If one tries the actual multiplication he/she has to take a paper and pencil and do the work. But the easiest way is by applying the property we discussed and it may be amazing to note that you can find the answer by mental calculation!. That is,51*101 = 51*(100 + 1) = 51*100 + 51*1 = 5100 + 51 = 5151 which is as fast as a calculator. Please express your views of this topic cbse 10th question papers by commenting on blog.
This property is also a great tool in factorization. In such cases, we use the property the other way round. That is we do, a*b + a*c = a*(b + c). For example let us take a quadratic expressionx2 + 6x + 8. Let us study how the distributive property helps in factoring.
Splitting the middle term, x2 + 6x + 8 = x2 + 4x + 2x + 8
Identifying the common factor x in the first two terms and the common factor 2 in the last two terms and using this property, x2 + 4x + 2x + 8 = x(x + 4) + 2(x + 4)
Again finding a common factor (x + 4) and applying the property once more,
x(x + 4) + 2(x + 4) = (x + 4)(x + 2)
Thus in general, the definition of distributive property is when a term is multiplied to the sum of group of terms, then the result is same as the sum of the products of the first term with each of the terms of the sum. It may be noted this property is applicable to subtraction of terms also, because in the general formula any of the three ‘a’. ‘b’ and ‘c’ can also be negative.
The distributive property greatly helps calculations and provides easier methods of solution. For example I need to multiply 51*101. If one tries the actual multiplication he/she has to take a paper and pencil and do the work. But the easiest way is by applying the property we discussed and it may be amazing to note that you can find the answer by mental calculation!. That is,51*101 = 51*(100 + 1) = 51*100 + 51*1 = 5100 + 51 = 5151 which is as fast as a calculator. Please express your views of this topic cbse 10th question papers by commenting on blog.
This property is also a great tool in factorization. In such cases, we use the property the other way round. That is we do, a*b + a*c = a*(b + c). For example let us take a quadratic expressionx2 + 6x + 8. Let us study how the distributive property helps in factoring.
Splitting the middle term, x2 + 6x + 8 = x2 + 4x + 2x + 8
Identifying the common factor x in the first two terms and the common factor 2 in the last two terms and using this property, x2 + 4x + 2x + 8 = x(x + 4) + 2(x + 4)
Again finding a common factor (x + 4) and applying the property once more,
x(x + 4) + 2(x + 4) = (x + 4)(x + 2)
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