Compare Fractions Using Whole Number Benchmarks
This Grade 4 Eureka Math skill teaches students to compare fractions by using a whole number benchmark such as 1 or 2. Students determine whether each fraction is less than, equal to, or greater than the benchmark, then compare distances from it. For example, to compare 5/4 and 6/5 using benchmark 1: 5/4 = 1 + 1/4 and 6/5 = 1 + 1/5. Since 1/4 > 1/5, then 5/4 > 6/5. This reasoning strategy, from Chapter 23 of Eureka Math Grade 4, avoids the need for common denominators in many comparison problems.
Key Concepts
To compare fractions using a whole number benchmark ($n$, like 1 or 2), first determine if each fraction is less than, equal to, or greater than $n$. If both fractions are on the same side of the benchmark (e.g., both are greater than $n$), compare their distances from $n$.
Common Questions
How do you use a benchmark to compare fractions?
Choose a whole number benchmark (like 1). Determine if each fraction is greater than, equal to, or less than the benchmark. If both are greater, the fraction farther from the benchmark (larger excess) is greater.
How do you compare 5/4 and 6/5 using the benchmark 1?
Both are greater than 1: 5/4 = 1 + 1/4, and 6/5 = 1 + 1/5. Compare the excesses: 1/4 vs. 1/5. Since 1/4 > 1/5 (same numerator, smaller denominator is larger), then 5/4 > 6/5.
What if one fraction is less than the benchmark and one is greater?
The fraction greater than the benchmark is automatically larger. For example, if one fraction is less than 1 and the other is greater than 1, the latter is bigger without further comparison.
Why is the benchmark strategy useful for comparing fractions?
It avoids finding common denominators by using a known reference point. Once you know where each fraction sits relative to a benchmark, comparison becomes simple reasoning.
Can you use 2 as a benchmark?
Yes. For fractions near 2, determine how each relates to 2 (greater, equal, or less) and compare their distances from 2 to determine which is larger or smaller.