To calculate 2200 x 1.075, we follow the standard procedure of multiplication. First, we understand that multiplying by 1.075 is the same as multiplying by 1 and then adding 75% of the original number, due to 0.075 being 75% of 1, or 7.5% of the whole.
Multiplication Process
We start by multiplying 2200 by 1, which equals 2200. Then, to find 75% of 2200, we multiply 2200 by 0.075. So, 2200 * 0.075 = 165. This means 75% of 2200 is 165.
Adding the Results
Now, we add the two results together: 2200 (which is 100% of 2200) and 165 (which is 7.5% of 2200). So, 2200 + 165 = 2365.
| Calculation Step | Result |
|---|---|
| Multiplying 2200 by 1 | 2200 |
| 75% of 2200 (2200 * 0.075) | 165 |
| Adding the results (2200 + 165) | 2365 |
In essence, multiplying 2200 by 1.075 directly or breaking it down into simpler steps yields the same result: 2365. This method can be applied to similar multiplication problems involving decimals, making calculations easier and more intuitive.
Real-World Application
In real-world scenarios, such as finance, engineering, or science, being able to perform calculations quickly and accurately is crucial. Understanding how to break down complex calculations into simpler steps can significantly enhance one’s ability to solve problems efficiently.
Example in Finance
Consider a scenario where an investment grows by 7.5% in a year. If you start with 2200, calculating the new total after one year involves multiplying the initial amount by 1.075, which, as we've calculated, results in 2365. This demonstrates how the calculation can be applied in financial contexts to determine growth or interest.
Moreover, this calculation can be used in various fields where percentages and growth rates are crucial, such as in understanding population growth, chemical reactions, or mechanical engineering applications.
What is the significance of understanding decimal multiplication in real-world applications?
+Understanding decimal multiplication, such as calculating 2200 x 1.075, is significant because it allows for the accurate assessment of growth, interest, and changes in quantities across various fields, including finance, science, and engineering. It enables individuals to make informed decisions based on precise calculations.
How can the method of breaking down decimal multiplication be applied to other calculations?
+This method can be applied by recognizing that any decimal multiplication can be broken down into simpler multiplication and addition steps. For example, multiplying by 1.25 involves multiplying by 1 (which is the whole number part) and then adding 25% of the original number, which is equivalent to multiplying by 0.25 and then adding the results.
