Complete question :
Gretchen and her friend Hayley bought three bags of apples and three bunches of bananas from the fruit vendor. Gretchen and Hayley want to find the total number of pieces of fruit that they bought. Gretchen thinks she should multiply 3 by the number of apples in each bag, x, and add it to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit. Hayley thinks Gretchen should add the number of apples in each bag, x, to the number of bananas in each bunch, y, and then multiply that sum by 3.
Which property can you apply to Hayley’s expression to show that it is equivalent to Gretchen’s expression?
Answer:
The distributive property of multiplication
Explanation:
Number of apples per bag = x
Number of bananas per bunch = y
3 each of bananas and apples were bought
Expression to obtain the total fruits bought :
Gretchen's expression :
3x + 3y
Haley's expression :
3(x + y)
According to the distributive property :
Haley's equation :
3(x + y)
(3 * x) + (3 * y)
3x + 3y
Hence, Gretchen's expression = Haley's expression by the distributive property of multiplication.