Evaluate 5793405 x 99999
579334706595
Evaluate 5793405 x 99999 Using Simplification
This explanation will guide you through calculating the product of 5793405 and 99999 efficiently, using a common mathematical shortcut.
Understanding the Simplification Strategy
Directly multiplying large numbers like 5793405 by 99999 can be challenging and prone to errors. A simpler method is to rewrite 99999 as a number that is easier to work with, specifically by relating it to 100000. We can express 99999 as the difference between 100000 and 1:
$$99999 = 100000 - 1$$
Substituting this into the original multiplication problem gives us:
$$5793405 \times 99999 = 5793405 \times (100000 - 1)$$
Applying the Distributive Property
To solve this, we use the distributive property of multiplication over subtraction. The property states that for any three numbers a, b, and c, the expression $a \times (b - c)$ is equal to $(a \times b) - (a \times c)$. Applying this to our problem:
$$5793405 \times (100000 - 1) = (5793405 \times 100000) - (5793405 \times 1)$$
Step-by-Step Calculation
-
Step 1: Multiply 5793405 by 100000
Multiplying a number by 100000 is straightforward; you simply add five zeros to the end of the number.
$$5793405 \times 100000 = 579340500000$$
-
Step 2: Multiply 5793405 by 1
Multiplying any number by 1 results in the number itself.
$$5793405 \times 1 = 5793405$$
-
Step 3: Subtract the results from Step 1 and Step 2
Finally, subtract the result of the second multiplication from the result of the first multiplication.
$$579340500000 - 5793405$$
To perform this subtraction accurately, we can align the numbers vertically:
579340500000
- 5793405
----------------
579334706595
The result of this subtraction is 579334706595.
Final Answer
By using the simplification $99999 = 100000 - 1$ and applying the distributive property, we find the product:
$$5793405 \times 99999 = 579334706595$$
This method helps in breaking down a complex multiplication into simpler steps.
Important Questions from Problem Solving
A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it?
(Earth’s circumference is roughly 40000 km. The height of human beings is between 1 & 2m)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
- Arrange the problem-solving strategy.
(A) Generate many possible solutions
(B) Determine how to implement the solution and evaluate the success of the solution
(C) Make a decision
(D) Evaluate each solution
(E) Define the problem
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Many a times confusion and frustration lead them to commit suicide. Being a responsible doctor and senior officer in the health department you will give priority to initiate drive for....
