Question

Verify the property of multiplication a*(b+c)= (a*b)+(a*c) for the rational numbers a= -3/4 b= 2/3 c= -5/6. Also name the property used.

Answer 1

Answer:

The property used is distributive property

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

Explained below ↓

Step-by-step explanation:

a = -3/4, b = 2/3, c = -5/6

Equation 1 :

a * ( b + c ) = -3/4 ( 2/3 + {-5/6} ),

LCM of 3 and 6 is 6

= -3/4 ( {4-5}/6 ) = -3/4 ( -1/6

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

Equation 2 :

( a * b ) + ( a * c ) = ( -3/4 * 2/3 ) + ( -3/4 * -5/6 )

= ( -6/12 ) + ( 15/24 ) = -1/2 + 5/8

LCM of 2 and 8 is 8

= ( -4 + 5 )/8 = 1/8

Comparing Equation 1 and Equation 2,

= 1/8 = 1/8

∴ We can conclude that a * ( b + c ) = ( a * b ) + ( a * c )

This property is called distributive property of multiplication.

Hope this helps.