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.
write an expression based on gretchen’s method to find the total number of pieces of fruit?
write an expression based on hayley’s method to find the total number of pieces of fruit?
which property can you apply to hayley’s expression to show that it is equivalent to gretchen’s expression?
what does the fact that the expressions are equivalent mean?