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Chapter 5: Problem 74

Estimate each sum. $$\frac{9}{10}+\frac{14}{15}$$

Short Answer

Expert verified
The estimated sum is 2.

Step by step solution

01

Round the Fractions

Round each fraction to the nearest whole number. \( \frac{9}{10} \approx 1 \) and \( \frac{14}{15} \approx 1 \).
02

Add the Estimated Values

Add the rounded numbers together. \( 1 + 1 = 2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rounding Fractions
Rounding fractions is a key skill when working with estimated sums. It involves approximating the fraction's value to the nearest whole number to simplify calculations.
For example, consider the fraction \( \frac{9}{10} \). Since the numerator, 9, is very close to the denominator, 10, the fraction is close to 1. In such cases, we round \( \frac{9}{10} \) to 1.
When rounding, if a fraction is more than halfway to the next whole number (more than \( \frac{1}{2} \)), round up. Otherwise, round down. For \( \frac{14}{15} \), the fraction significantly exceeds \( \frac{1}{2} \), so we also round it to 1. This process makes mental math easier and keeps estimations manageable.
Addition of Fractions
Adding fractions might seem challenging, but it's much simpler with rounded whole numbers. Typically, to add fractions like \( \frac{9}{10} + \frac{14}{15} \), a common denominator is needed, making the process more complex.
By rounding these to the nearest whole numbers, like 1, the equation becomes straightforward: \( 1 + 1 \).
This method simplifies the process, reducing mental strain while allowing us to focus on understanding concepts rather than intricate calculations. It highlights the importance of estimation, streamlining our calculations for quick answers in real-world scenarios.
Estimating Sums
Estimating sums is a practical technique that aids in obtaining approximate results rapidly. It's particularly useful when exact precision isn't crucial, such as in everyday calculations.
For fractional addition, rounding each fraction to the closest whole number provides a quick way to estimate the total. By converting \( \frac{9}{10} \) and \( \frac{14}{15} \) to 1, we easily find the sum is approximately 2.
This rough estimate helps verify more precise calculations or to quickly gauge the magnitude of a potential result, enhancing computational efficiency in both academic and real-life settings.
Whole Numbers in Estimation
Using whole numbers in estimation simplifies the processes of addition, subtraction, or any basic arithmetic operation. This method transforms potentially complex computations into manageable tasks.
By approximating fractions into whole numbers, you can perform calculations mentally, reducing dependency on calculators or paper.
In our example, after rounding \( \frac{9}{10} \) and \( \frac{14}{15} \) to 1, we easily added them to get 2. This not only provides a quick solution but also enhances your mathematical reasoning by honing estimation skills, crucial for solving problems efficiently.

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Most popular questions from this chapter

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