Rule for Comparing Fractions with the Same Numerator
Rule for Comparing Fractions with the Same Numerator teaches Grade 3 students a counterintuitive but important pattern: when numerators are equal, the fraction with the larger denominator is actually smaller. From Eureka Math Grade 3, the reasoning: a larger denominator means the whole was divided into more pieces, so each piece is smaller. 1/5 < 1/3 because fifths are smaller than thirds. Formally, for equal numerator n: n/c < n/b when c > b. This rule helps students compare fractions quickly without drawing models.
Key Concepts
When comparing two fractions with the same numerator ($n$) and different denominators ($b$ and $c$), the fraction with the smaller denominator is the larger fraction. If $b < c$, then: $$\frac{n}{b} \frac{n}{c}$$.
Common Questions
When two fractions have the same numerator, which is larger?
The fraction with the smaller denominator is larger. Fewer, bigger pieces means each piece is larger.
Which is greater: 1/3 or 1/5?
1/3 > 1/5. Thirds are bigger pieces than fifths — splitting into fewer parts makes each part larger.
Which is greater: 3/8 or 3/5?
3/5 > 3/8. The same number of pieces (3), but each fifth is larger than each eighth.
Why does a larger denominator mean smaller pieces?
The denominator tells you how many equal parts the whole is cut into. More cuts means each piece is smaller.
How does this rule save time compared to drawing fraction models?
Once you recognize the same-numerator rule, you can compare immediately: bigger denominator = smaller fraction, no drawing needed.
What Eureka Math grade teaches the same-numerator comparison rule?
Grade 3, within the Number and Operations—Fractions domain.