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# Properties of Rational Numbers - Distributivity of Multiplication Over Addition for Rational

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#### notes

Distributive for multiplication over Addition :
To understand this, consider the rational numbers -3/4 , 2/3 and -5/6

-3/4 xx {2/3 + (-5/6)} = -3/4 xx {((4) + (-5))/6}

= -3/4 xx (-1/6) = 3/24 = 1/8

Also -3/4 xx 2/3 = (-3 xx 2 )/(4 xx 3) = -6/12 = -1/2

And -3/4 xx -5/6 = 5/8

Therefore (-3/4 xx 2/3) + (-3/4 xx -5/6) = -1/2 + 5/8 = 1/8

Thus, -3/4 xx {2/3 + -5/6} = (-3/4 xx 2/3) + (-3/4 xx -5/6)

Distributive for multiplication over substraction :

consider the rational numbers  3/8 , -2/5 , 6/7

3/8 xx (-2/5 -  6/7 ) = 3/8 xx (-14 - 30)/35

= 3/8 xx -44/35

= -33/70

Also , 3/8 xx -2/5 - 3/8 xx 6/7

=-6/40 - 18 / 56
= -3/20 - 9/28 = -33/70

Distributive for Divisoin over Addition :

consider the rational numbers  are 3/8 ,-2/5 ,6/7

a ÷ (b + c) = 3/8 ÷ (-2/5 + 6/7) =  3/8 ÷ -16/35

= 3/8 xx 35/-16 = -105/128

a÷b + a÷ c = -1/2

So, a ÷ (b+c) not equal a ÷ b + a ÷ c

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Distributive Property of Rational Number [00:07:22]
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