To calculate the exact result of 235 multiplied by 1.075, we follow the standard multiplication procedure. Multiplication is a fundamental operation in mathematics that involves adding a number a certain number of times, equal to the multiplier. In this case, we are multiplying 235 by 1.075.
Multiplication Process
The multiplication of 235 by 1.075 can be thought of as adding 235 together 1.075 times. However, for practical purposes, we’ll use the distributive property of multiplication over addition to simplify the calculation. We can break down 1.075 into 1 + 0.075 to make the calculation easier.
Distributive Property Application
Using the distributive property, we can rewrite 235 * 1.075 as (235 * 1) + (235 * 0.075). This step simplifies the multiplication process by breaking it down into more manageable parts.
First, calculate 235 * 1, which equals 235. Then, calculate 235 * 0.075. To do this, multiply 235 by 0.075, which gives 17.625. Now, add the two results together: 235 + 17.625 = 252.625.
| Calculation Step | Result |
|---|---|
| 235 * 1 | 235 |
| 235 * 0.075 | 17.625 |
| Total (235 * 1) + (235 * 0.075) | 252.625 |
Verification and Applications
The result of 235 * 1.075 can be verified using a calculator or computational software. This type of calculation is common in various fields such as finance, where it might be used to calculate the total cost of an item after a 7.5% increase, or in science, where it could represent a scaling factor in an experiment.
Financial Application Example
Consider a scenario where a product originally priced at 235 undergoes a price increase of 7.5%. The new price would be calculated as the original price multiplied by 1.075, which, as we've calculated, equals 252.625. This represents the final price after the increase.
In scientific applications, such calculations can be crucial for scaling experiments or understanding the effects of changes in variables. For instance, if 235 represents a baseline measurement and 1.075 is a scaling factor due to an experimental condition, the result of 252.625 would indicate the new measurement after applying the condition.
The importance of precise calculations in these fields cannot be overstated, as small discrepancies can lead to significant errors in final outcomes. Therefore, understanding and accurately performing calculations like 235 * 1.075 are essential skills.
What is the distributive property of multiplication?
+The distributive property of multiplication states that for any numbers a, b, and c, a * (b + c) = (a * b) + (a * c). This property allows us to simplify complex multiplication operations by breaking them down into simpler parts.
Why is precision important in mathematical calculations?
+Precision is crucial in mathematical calculations because small errors can lead to significant discrepancies in final results, especially in applications where calculations are repeated or built upon previous results. In fields like finance, science, and engineering, precise calculations are essential for accuracy and reliability.
