Question

Mihika makes 8 gift packs containing chocolates for Diwali. She puts 12 vanilla chocolates, 14 milk chocolates and 8 nut chocolates in each pack. With the help of which property can you calculate the total number of chocolates in the 8 packs?
A.Commutative Property
B.Associative Property
C.Distributive Property
D.None of these.

Answer 1

Hint: Here, we will formulate an expression representing the total number of chocolates. Then, we will choose the correct option based on the property we use for simplifying that expression.

Complete step-by-step answer:
We will write the expression for the total number of chocolates in each gift pack by adding the number of chocolates of each kind:
\[12 + 14 + 8\]
We will find the total number of chocolates by multiplying the number of chocolates in each gift pack with the total number of gift packs:
\[8\left( {12 + 14 + 8} \right)\]
We know that according to the commutative property of addition and multiplication changing the order of the operands does not change the result:
$a+b=b+a$
$\Rightarrow$ $ab=ba$
This property will not be useful in calculating the total number of chocolates. So, option A is incorrect.
We know that according to associative property of we can add or multiply regardless of how the numbers are grouped:
\[\begin{array}{l}a + \left( {b + c} \right) = \left( {a + b} \right) + c\\\Rightarrow a\left( {b \cdot c} \right) = \left( {a \cdot b} \right)c\end{array}\]
This property will not be useful in calculating the total number of chocolates. So, option B is incorrect.
We know that according to the distributive property multiplying the sum of two or more numbers by a number will give the same result as multiplying each number individually by the number and then adding the products together:
\[a\left( {b + c + d} \right) = ab + ac + ad\]
We can use the distributive property to simplify the expression.
We will substitute 8 for \[a\], 12 for \[b\], 14 for \[c\] and 8 for \[d\] in the formula of distributive property:
 12 + 14 + 8
 =$ 8 \cdot 12 + 8 \cdot 14 + 8 \cdot 8\\ $
= 96 + 112 + 64
= 27
\[\therefore\] Option C is the correct option.

Note: We can notice that Commutative and Associative property can also be used on the expression but they form the incorrect option. This is because although they can be used on the expression, they are not helping in simplifying the expression. So, distributive property is the correct option.