Question

Tell what property allows you to compute \[\dfrac{1}{3} \times \left( {6 \times \dfrac{4}{3}} \right)\] as \[\left( {\dfrac{1}{3} \times 6} \right) \times \dfrac{4}{3}\]

Answer 1

Hint: First we will learn about some basic number properties namely distributive property, associative property, and the commutative property.
Now with the help of the definition of these properties we’ll find which property allows us to compute \[\dfrac{1}{3} \times \left( {6 \times \dfrac{4}{3}} \right)\] as \[\left( {\dfrac{1}{3} \times 6} \right) \times \dfrac{4}{3}\]

Complete step by step Answer:

Given data: The terms\[\dfrac{1}{3} \times \left( {6 \times \dfrac{4}{3}} \right)\]and \[\left( {\dfrac{1}{3} \times 6} \right) \times \dfrac{4}{3}\]
Now, there some properties of basic numbers
Distributive property:
The distributive property helps in making difficult problems easier, we can use this property of multiplication to write an expression by distributing or breaking down a factor as a sum or difference of two numbers.
i.e. \[\left( {a + b} \right) \times c = ac + bc\]or \[\left( {a - b} \right) \times c = ac - bc\]
Associative property:
The associative property states that we can multiply or add regardless of how the numbers are grouped, by grouping we mean which pair we’ll take first to operate.
i.e. \[\left( {a + b} \right) + c = a + \left( {b + c} \right)\] or \[\left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)\]
Commutative property:
 The commutative property states that addition or multiplication of any two numbers can be done in order like if addition or multiplication is the order then if we operate the first number on the second number or we operate the second number on the first number the result will be the same.
Therefore, from the above properties, we can say that the terms \[\dfrac{1}{3} \times \left( {6 \times \dfrac{4}{3}} \right)\] and \[\left( {\dfrac{1}{3} \times 6} \right) \times \dfrac{4}{3}\] are equal as per the associative property or to be the more precise associative property of multiplication.

Note: Some of the students just leave the answer as associative property, there are two types of property namely associative property of multiplication and associative property of addition so be specific.