Fractional Forecasts: How to Estimate Sums and Differences Using Benchmarks
When working with fractions, sometimes an exact calculation isn't necessary. Instead, a close estimate will suffice. Benchmarks, such as \(0\), \(1/2\), and \(1\), can be invaluable tools for quickly estimating the sum or difference of fractions. Let's explore how to use these benchmarks for estimating operations with fractions.
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Estimating Sums and Differences of Fractions Using Benchmarks
Example 1:
Estimate the sum of \(2/3\) and \(3/8\).
Estimation Process Using Benchmarks:
1. \(2/3\) is closer to \(1\) than \(1/2\), so round it to \(1\).
2. \(3/8\) is closer to \(1/2\) than \(0\), so round it to \(1/2\).
3. Estimate the sum: \(1 + 1/2 = 1 1/2\).
Answer:
The estimated sum is \(1 1/2\).
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Example 2:
Estimate the difference between \(5/6\) and \(1/4\).
Estimation Process Using Benchmarks:
1. \(5/6\) is closer to \(1\) than \(1/2\), so round it to \(1\).
2. \(1/4\) is closer to \(0\) than \(1/2\), so round it to \(0\).
3. Estimate the difference: \(1 – 0 = 1\).
Answer:
The estimated difference is \(1\).
Using benchmarks to estimate sums and differences of fractions provides a quick and intuitive approach to understanding the approximate outcome of operations. This method is especially useful when you need a general idea rather than precise calculations. By rounding fractions to the nearest benchmark and then performing the operation, you can get a ballpark figure swiftly. Practice regularly to master this invaluable skill!
Practice Questions:
1. Estimate the sum of \(4/5\) and \(3/7\).
2. What is the estimated difference between \(7/8\) and \(2/3\)?
3. Using benchmarks, estimate the sum of \(1/3\) and \(5/9\).
4. Estimate the difference between \(3/4\) and \(1/6\).
5. What is the estimated sum of \(2/7\) and \(4/5\)?
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Answers:
1. \(1 1/2\)
2. \(1/4\)
3. \(1\)
4. \(1/2\)
5. \(1 1/4\)
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