Solve the multiplication problem
in three different ways: by using the common method for writing the standard algorithm, by using the partial-products method for writing the standard algorithm, and by writing the numbers in expanded forms and using properties of arithmetic. For each of the three methods, discuss how the steps in that method are related to the steps in the other methods.
To calculate: The multiplication problem
Answer to Problem 1P
The solution of the problem
Explanation of Solution
Given information:
The expression is
Concept used:
Distributive property is used to simplify the algebraic expression of this kind
The algebraic expression
Calculation:
The multiplication of two numbers
Method I: Common method
Solve the problem by common method, first multiply the number 8 by 6, write the number 8 and carry the number 4now multiply 8 by 9 and then add the carried number 4 and write it as
The solution of the multiplication problem
Method II: Partial product method
The solution of the problem
First multiply the number 8 with 6 and it can be calculated as,
Second multiply the number 8 with 9 tens and it can be calculated as,
Now add all the calculations that is done in above steps as,
The solution of the multiplication problem
Method III: Arithmetic properties
The number
Therefore, the expression
Use the distributive property of multiplication over addition in the expression
The solution of the multiplication problem
It is observed from the calculation that is done by the distributive property
Conclusion:
Thus, the solution of the problem
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