Question

What are reasons A,B,and C in the proof?

Answer 1

Answer:

Option D is correct.

Explanation:

Commutative Property of Multiplication define that two numbers can be multiplied in any order.

i.e $a\times b =b \times a$

Distributive property of multiplication states that when a number is multiplied by the sum of two numbers i.e, the first number can be distributed to both of those numbers and multiplied by each of them separately.

$a \times (b+c) = a\times b+ a\times c$

Associative property of multiplication states that multiplication allows us to group factors in different ways to get the same product.

Given:

A = $( 4\times 3) + (2 \times 4 )= ( 4\times 3) + (4 \times 2 )$

B = $4 \times ( 3+2)$

C = $4 \times 5$

then;

$( 4\times 3) + (2 \times 4 )$

Using Commutative property of Multiplication we can write $2 \times 4 = 4 \times 2$ then we have;

$( 4\times 3) + (2 \times 4 ) = ( 4\times 3) + (4 \times 2 )$

Using Distributive property of multiplication;

$( 4\times 3) + (4 \times 2 ) = 4 \times ( 3+2)$

by using associative property of multiplication ,

$4 \times (3+2) = 4 \times 5$

Therefore, the reasons  for A , B and C in this proof are;

A.commutative property of multiplication

B. distributive property

C. associative property of multiplication