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Properties of Operations: Tutorial

Activity

Question 1

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.

Part A

Write an expression based on Gretchen's method to find the total number of pieces of fruit.

PEE

B

U X X

Font Sizes

AA-

Which property can you apply to Hayley’s expression to show that it is equivalent to Gretchen’s expression

Answer 1

3x+3y and distributive property

Explanation:

It is given that

Gretchen buys three bags of apples = 3X

Hayley buys three bunches of bananas = 3Y

As it is also mentioned that it first it is multiplied and then it is added

So, the expression for determining the total number of fruit pieces is

3X + 3Y

And, this expression denotes the distributive property in which we multiplied the each variable and then added it