Rule for Comparing Fractions with Same Numerators
Rule for Comparing Fractions with Same Numerators is a Grade 3 math skill from Eureka Math establishing a counterintuitive but reliable rule: when two fractions have the same numerator, the fraction with the smaller denominator is larger. Formally, if b < c, then a/b > a/c. This happens because a smaller denominator means each part is larger—the whole is cut into fewer pieces. For example, 1/3 > 1/5 because thirds are bigger than fifths. This rule is one of two core fraction comparison strategies taught in Grade 3 alongside comparing same-denominator fractions.
Key Concepts
When comparing two fractions with the same numerator, the fraction with the smaller denominator is the larger fraction. If $b < c$, then $\frac{a}{b} \frac{a}{c}$.
Common Questions
When two fractions have the same numerator, which is larger?
The fraction with the smaller denominator is larger. For example, 3/4 > 3/8 because fourths are larger than eighths.
Why is the fraction with a smaller denominator larger when numerators are equal?
A smaller denominator means the whole is divided into fewer, larger parts. Taking the same number of larger parts gives a bigger total than taking the same count of smaller parts.
What is the rule for comparing fractions with same numerators?
If two fractions have the same numerator a, and denominators b and c where b < c, then a/b > a/c. Smaller denominator means larger fraction.
How do you compare 2/3 and 2/7 using this rule?
Both have numerator 2. Since 3 < 7, the fraction 2/3 is greater than 2/7. Thirds are bigger parts than sevenths.
In which textbook is the Rule for Comparing Fractions with Same Numerators taught?
This skill is taught in Eureka Math, Grade 3.