Question

Find the missing values: \[25\times \left( 15\times \_\_ \right)=\left( \_\_\times 15 \right)\times 10\]?
A) 10, 15
B) 10, 10
C) 15, 25
D) 10, 25

Answer 1

Hint: In the given question, we have been asked to find the missing number and we have given an expression. In order to find the missing value, we need to apply the associative property of multiplication which states that while multiplication the grouping of numbers in any combination does not change the answer i.e. \[a\times \left( b\times c \right)=\left( a\times b \right)\times c\]. Applying this property in the given question will give us the missing numbers. In this way we will get the required answer.

Complete step-by-step solution:
We have given that,
\[25\times \left( 15\times \_\_ \right)=\left( \_\_\times 15 \right)\times 10\]
Using the associative property of multiplication which states that;
In multiplication, grouping of numbers in any way or in any combination does not change the final product i.e. the answer will remain the same.
In mathematical form it will represents as;
\[a\times \left( b\times c \right)=\left( a\times b \right)\times c\]
Applying this property, we get
Here,
In LHS, a = 25, b = 15
In RHS, b = 15, c = 10
So we get the missing terms;
Thus,
\[25\times \left( 15\times \underline{10} \right)=\left( \underline{25}\times 15 \right)\times 10\]
Therefore,
The missing numbers are 10 and 25.

Hence, the option (D) is the correct answer.

Note:In order to solve these types of questions, students must need to know about the associative property of multiplication. The associative property is one of the fundamental properties used in mathematics while solving the expression containing the mathematical operation of multiplication. This property simply states that the way in which the factors are grouped in a multiplication, it will not change the final product.