# i am not understanding what is distributive property

Let us consider two whole numbers 4 and 5. The product of 4 and 5 is 20.

Now, if we break 5 as (2 + 3), then we can write 4 × 5 as 4 × (2 + 3) = 20

Observe that (4 × 2) + (4 × 3) = 8 + 12 = 20

Thus, 4 × (2 + 3) = (4 × 2) + (4 × 3)

This is called the distributive property of whole numbers for multiplication over addition. We can generalize this property as follows.

Suppose we have three whole numbers a, b, and c. It does not matter whether we add b and c first, and then multiply the product with a or whether we multiply a with b and a with c and then add the two products”.

This can be written as

a × (b + c) = a × b + a × c

This property also holds for multiplication over subtraction i.e.,

a × (b c) = a × b a × c

This property can be very useful in multiplying bigger numbers. Suppose we have to multiply 19 and 45. It would take us a long time to do this if we follow the usual approach.

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if a,b,care any whole number ,then a * (b+c) = a*b+a*c

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if a,b,care any whole number ,then a * (b+c) = a*b+a*c

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ifa,b,care any whole number ,thena * (b+c) = a*b+a*c

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if a,b,care any whole number thena *[b+c}=a*b+a*c

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a*(b+c)=(a*b)+(a*c)

This is distributivity of multiplication over addition.

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