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.
[include_netrun_products_block from-products="product/6-south-carolina-sc-ready-grade-3-math-practice-tests/" product-list-class="bundle-products float-left" product-item-class="float-left" product-item-image-container-class="p-0 float-left" product-item-image-container-size="col-2" product-item-image-container-custom-style="" product-item-container-size="" product-item-add-to-cart-class="btn-accent btn-purchase-ajax" product-item-button-custom-url="{url}/?ajax-add-to-cart={id}" product-item-button-custom-url-if-not-salable="{productUrl} product-item-container-class="" product-item-element-order="image,title,purchase,price" product-item-title-size="" product-item-title-wrapper-size="col-10" product-item-title-tag="h3" product-item-title-class="mt-0" product-item-title-wrapper-class="float-left pr-0" product-item-price-size="" product-item-purchase-size="" product-item-purchase-wrapper-size="" product-item-price-wrapper-class="pr-0 float-left" product-item-price-wrapper-size="col-10" product-item-read-more-text="" product-item-add-to-cart-text="" product-item-add-to-cart-custom-attribute="title='Purchase this book with single click'" product-item-thumbnail-size="290-380" show-details="false" show-excerpt="false" paginate="false" lazy-load="true"]
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 \(1 1/2\).
The Absolute Best Book for 5th Grade Students
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 \(4/5\)?
A Perfect Book for Grade 5 Math Word Problems!
Answers:
1. \(1 1/2\)
2. \(1/4\)
3. \(1\)
4. \(1/2\)
5. \(1 1/4\)
The Best Math Books for Elementary Students
Related to This Article
More math articles
- Relationship Between Sides and Angles in a Triangle
- TASC Testing Accommodation and Support for Disabilities
- FREE 7th Grade PARCC Math Practice Test
- How to Compare Linear Functions: Equations, Tables, and Graphs
- 5th Grade ILEARN Math Worksheets: FREE & Printable
- Billionaire Basics: How to Master Addition and Subtraction of Massive Whole Numbers
- Intelligent Math Puzzle – Challenge 78
- 8th Grade Scantron Math Worksheets: FREE & Printable
- The Ultimate OAE Elementary Education Math (018-019) Course (+FREE Worksheets & Tests)
- How to Use Partial Products to Multiply One-Digit Numbers By Multi-digit Numbers
What people say about "Fractional Forecasts: How to Estimate Sums and Differences Using Benchmarks - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.