# Distributivity of Multiplication Over Addition for Rational Number:

## 1. 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)

For all rational numbers a, b, and c, a(b + c) = ab + ac.

## 2. Distributive for multiplication over subtraction:

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

For all rational numbers a, b, and c, a(b – c) = ab – ac.

#### Example

Find: 2/5 xx (-3)/7 - 1/14 - 3/7 xx 3/5.

2/5 xx (-3)/7 - 1/14 - 3/7 xx 3/5

= 2/5 xx (-3)/7 - 3/7 xx 3/5 - 1/14    .......(by commutativity)

= 2/5 xx (-3)/7 + ((-3)/7) xx 3/5 - 1/14.

= (-3)/7(2/5 + 3/5) - 1/14                .......(by distributivity)

= (- 3)/7 xx 1 - 1/14

= (- 6 - 1)/14

= -1/2.

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Distributivity of Multiplication over Addition of Rational Numbers [00:07:10]
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