Question

Madison and Tyler each wrote an expression that is equivalent to 14.1 (19.8 + 7.6). The expressions they created are shown in the table.

Expressions Madison and Tyler Created
Student
Expression
Madison
14.1 (7.6 + 19.8)
Tyler
14.1 (19.8) + 14.1 (7.6)

Which statement is true?
Madison used the associative property.
Madison used the distributive property.
Tyler used the associative property.
Tyler used the distributive property.

Answer 1

Statements 1 and 4 are true.

• Consider three numbers a,b ,and c.
• The Associative property states that the sum or product of two more than two numbers are the same irrespective of the order of the three numbers

Property : a + b = b + a, a*b = b*a.

• The distributive property states that the multiplication of two or more numbers at a time gives the same result as the addition of the multiplication with each of the numbers.

Property : a(b+c) = a*b + a*c.

• The given expression is 14.1(19.8 + 7.6)
• Madison changed the above expression to 14.1( 7.6 + 19.8) i.e,

c(a+b) = c( b + a) ,Follows associative property.

• Tyler changed the given expression as 14.1*(19.8) + 14.1*(7.6) i.e,

c(a+b) = ac + bc, Follows Distributive proptery.

Hence, Madison used the associative property and Tyler used the distributive property.

Therefore, Statements 1 and 4 are true.