Compare Mixed Numbers with the Same Whole Using a Benchmark
This Grade 4 Eureka Math skill teaches students to compare two mixed numbers that share the same whole number by focusing only on their fractional parts. When both mixed numbers have the same whole, such as 3 1/4 versus 3 5/8, the comparison reduces to comparing the fractions. A benchmark of 1/2 makes this efficient: if one fraction is below 1/2 and the other is above, the comparison is immediate without finding a common denominator. This strategy reduces calculation and develops number sense for fractions.
Key Concepts
To compare two mixed numbers with the same whole number, $W \frac{a}{b}$ and $W \frac{c}{d}$, you only need to compare their fractional parts, $\frac{a}{b}$ and $\frac{c}{d}$. A useful strategy is to use a benchmark fraction like $\frac{1}{2}$. If one fractional part is less than $\frac{1}{2}$ and the other is greater than $\frac{1}{2}$, the mixed number with the fraction greater than $\frac{1}{2}$ is the larger number.
Common Questions
How do you compare mixed numbers with the same whole number part?
Ignore the whole number since it is equal in both. Compare only the fractional parts using a benchmark, common denominator, or number line.
What is the benchmark fraction strategy?
Compare each fraction to 1/2. If one fraction is less than 1/2 and the other is greater than 1/2, the one greater than 1/2 is larger.
How do you compare 3 1/4 and 3 5/8?
Both have whole number 3. Compare 1/4 and 5/8. Since 1/4 is less than 1/2 and 5/8 is greater than 1/2, we know 3 1/4 < 3 5/8.
When should students use a common denominator instead of a benchmark?
When both fractions are on the same side of 1/2, use a common denominator or equivalent fractions to determine which is larger.
Why does having the same whole number simplify the comparison?
Equal whole numbers cancel out, so only the fractional parts determine which mixed number is greater.