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Distributivity of Multiplication over Addition



If I ask you to solve (5 X 13), you can easly calculate and say answer is 65
(method 1).

The above problem can also be solved :

(5 X 13) = 5 X ( 10 + 3 )

And further

5 X ( 10 + 3 ) = ( 5 X 10 ) + (5 X 3)

Solve R.H.S and we get

= 50 + 15

= 65 (method 2)

Now the answer in both method 1 and method 2 is same i.e 65.

  • Method 2 is referred to as "Distributivity of Multiplication over Addition"
  • Method 2 is normally used when the multiplication is complex like the following :

    Example 1 = Solve (25 X 52)
    Answer = By using property - Distributivity of Multiplication over Addition, we get
    = 25 X ( 50 + 2)
    = (25 X 50) + (25 X 2)
    = 1250 + 50
    = 1300


    Example 2 = Simply (332 X 48) + (332 X 52) with the help of Property - Distributivity of Multiplication over Addition
    Answer = (332 X 48) + (332 X 52)
    By using property - Distributivity of Multiplication over Addition, we get
    = 332 X ( 48 + 52)
    = 332 X 100
    = 33200

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