Verify the following 18 × [ 7 + ( – 3 ) ] = [ 18 × 7 ] + [ 18 × ( – 3 ) ]

The product of three integers does not depend upon the grouping of integers. Therefore, the multiplication of integers is associative. Thus, if a , b , and c are three integers, then a × ( b × c ) = ( a × b ) × c = ( a × c ) × b . Then, 18 × [ 7 + ( – 3 ) ] = [ 18 × 7 ] + [ 18 × ( – 3 ) ] 72 = 72 Hence, the associative property verified

Verify the following 18 × [ 7 + ( – 3 ) ] = [ 18 × 7 ] + [ 18 × ( – 3 ) ]

The product of three integers does not depend upon the grouping of integers. Therefore, the multiplication of integers is associative. Thus, if a , b , and c are three integers, then a × ( b × c ) = ( a × b ) × c = ( a × c ) × b . Then, 18 × [ 7 + ( – 3 ) ] = [ 18 × 7 ] + [ 18 × ( – 3 ) ] 72 = 72 Hence, the associative property verified

Verify the following. ( – 21 ) × [ ( – 4 ) + ( – 6 ) ] = [ ( – 21 ) × ( – 4 ) ] + [ ( – 21 ) × ( – 6 ) ]

The product of three integers does not depend upon the grouping of integers. Therefore, the multiplication of integers is associative. Thus, if a , b , and c are three integers, then a × ( b × c ) = ( a × b ) × c = ( a × c ) × b . Then, ( – 21 ) × [ ( – 4 ) + ( – 6 ) ] = [ ( – 21 ) × ( – 4 ) ] + [ ( – 21 ) × ( – 6 ) ] ( - 21 ) × ( - 10 ) = 84 + 126 210 = 210 Hence, the associative property verified

For any integer a , what is - 1 × a equal to?

Given, - 1 × a We can write - 1 × a = - a × 1 And we know that, Multiplicative identity of integers states that, multiplying an integer by 1 does not change the integer. ∴ - a × 1 = - a