In the realm of mathematics, the term “increased by” signifies an operation that adds a specified value to an existing quantity. It represents the process of adding, or incrementing, a given number to another number.
Understanding “Increased by”
The phrase “increased by” is often encountered in mathematical expressions and word problems. For example, the expression “5 increased by 3” would translate to 5 + 3, which equals 8. In this case, the value of 5 is increased by 3 to arrive at the result of 8.
Applications in Everyday Life
The concept of “increased by” has numerous applications in various fields and everyday life situations:
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Finance: Calculating interest on loans or deposits, where the principal amount is increased by the interest amount.
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Commerce: Determining the total cost of goods, which includes the base price increased by applicable taxes.
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Science: Measuring the growth of organisms or the increase in temperature over time.
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Statistics: Calculating the percentage increase in data or population over a specific period.
Examples of “Increased by” in Action
Here are some examples that illustrate the use of “increased by”:
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Temperature increase: The temperature increased by 5 degrees Celsius. (Initial temperature + 5 degrees)
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Population growth: The population increased by 10% from the previous year. (Initial population x 1.10)
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Loan interest: A loan of $10,000 increased by 5% annual interest over 5 years. ($10,000 + (5% x 5) x $10,000)
Additional Considerations
Compounding: In certain scenarios, such as interest calculations, the “increased by” value may be applied multiple times over a period of time, resulting in compounding growth or interest.
Negative values: The phrase “increased by” can also be applied to negative values, indicating a decrease in quantity. In such cases, the negative value would be subtracted from the initial quantity.
Percentage changes: When the “increased by” value is expressed as a percentage, it represents the relative increase compared to the original quantity.
Tables for Reference
| Operation | Expression | Result |
|---|---|---|
| 5 increased by 3 | 5 + 3 | 8 |
| 10% increase on 200 | 200 x 1.10 | 220 |
| Loan of $5,000 increased by 2% monthly interest for 12 months | $5,000 x (1 + 0.02)^12 | $5,243.40 |
| Temperature decreased by 7 degrees Celsius | 25 – 7 | 18 degrees Celsius |
Tips and Tricks
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Identify the initial quantity: Before performing the “increased by” operation, ensure you have identified the starting value or quantity.
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Perform the addition: To calculate the result, simply add the “increased by” value to the initial quantity.
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Use a calculator: If necessary, utilize a calculator to assist with the addition process, especially for large or complex numbers.
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Consider negative values: Be mindful that the “increased by” value can be negative, indicating a decrease in quantity.
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Interpret the result: Once you have obtained the result, interpret it accurately within the context of the problem. For instance, an increased temperature could indicate a rise in heat, while an increased population could suggest growth.
Step-by-Step Approach
To perform the operation of “increased by” step-by-step:
- Label the given quantity as the “initial value” (IV).
- Label the value to be added as the “increase” (I).
- Set up the equation as “IV + I”.
- Perform the addition and obtain the result.
- Express the result appropriately.
Conclusion
The phrase “increased by” is an essential mathematical operation that signifies the addition of a specific value to an existing quantity. It has wide-ranging applications in various domains, including finance, commerce, science, and statistics. By understanding the concept and practical applications of “increased by,” you can effectively solve mathematical problems and make informed decisions in everyday situations.