1. Let's analyze the properties used in the given mathematical expressions.
Part (a): [tex]\( 55 \times 49 = 49 \times 55 \)[/tex]
To name the property used in this expression, let’s recall the basic properties of multiplication. Here, the expression shows that the order in which two numbers are multiplied does not affect the product.
This is known as the commutative property of multiplication. The commutative property of multiplication states that for all real numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex], [tex]\( a \times b = b \times a \)[/tex].
So, the property used in [tex]\( 55 \times 49 = 49 \times 55 \)[/tex] is the commutative property of multiplication.
Part (b): [tex]\( 12 + (14 + 19) = (12 + 14) + 19 \)[/tex]
To name the property used in this expression, we need to consider the basic properties of addition. Here, the expression demonstrates that the way in which numbers are grouped (or associated) when adding does not change their sum.
This is known as the associative property of addition. The associative property of addition states that for all real numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], [tex]\( a + (b + c) = (a + b) + c \)[/tex].
So, the property used in [tex]\( 12 + (14 + 19) = (12 + 14) + 19 \)[/tex] is the associative property of addition.
