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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. |
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Answer» The property used is distributive propertya * ( B + c ) = ( a * b ) + ( a * c )Explained below ↓Step-by-step explanation:a = -3/4, b = 2/3, c = -5/6Equation 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 = 1/8Equation 2 :( a * b ) + ( a * c ) = ( -3/4 * 2/3 ) + ( -3/4 * -5/6 )= ( -6/12 ) + ( 15/24 ) = -1/2 + 5/8LCM of 2 and 8 is 8= ( -4 + 5 )/8 = 1/8Comparing 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. |
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