Comparing Fractions with the Same Denominator
Grade 4 Eureka Math students compare fractions with the same denominator by examining only their numerators. Since equal denominators mean the fraction pieces are the same size, the fraction with the larger numerator contains more pieces and is therefore greater. For example, 4/5 > 3/5 because 4 > 3. This rule generalizes to: if a > c, then a/b > c/b. Mastering same-denominator comparison is a prerequisite for ordering fractions and for understanding the number line.
Key Concepts
To compare two fractions with the same denominator, compare their numerators. The fraction with the greater numerator is the greater fraction. If $a c$, then $\frac{a}{b} \frac{c}{b}$.
Common Questions
How do you compare two fractions with the same denominator?
Compare only the numerators. The fraction with the greater numerator is the greater fraction because both fractions have pieces of the same size.
Which is greater: 7/10 or 6/10?
7/10 is greater because 7 > 6 and both fractions have the same denominator.
Why does the denominator not matter when it is the same?
The denominator defines the size of each piece. When denominators are equal, pieces are equal in size, so more pieces always means a greater value.
How do you write a comparison like 4/5 and 3/5 using symbols?
Write 4/5 > 3/5 using the greater-than symbol, or 3/5 < 4/5 using the less-than symbol.
What comes after comparing same-denominator fractions in Grade 4?
Students next compare fractions with different denominators using benchmarks, equivalent fractions, or the least common denominator.