Compare Fractions on a Number Line
Comparing Fractions on a Number Line teaches Grade 3 students to use position on the number line to determine which of two fractions is greater. From Eureka Math Grade 3, the rule: fractions further to the right on the number line are larger. Plot both fractions by partitioning the number line into the appropriate units, then compare their positions. For context-dependent comparison, students must identify the same whole before comparing — comparing 1/3 of a small rectangle to 1/3 of a large one requires recognizing the wholes differ.
Key Concepts
To compare two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, in a real world context, plot them on a number line. The fraction located further to the right is the greater fraction. If $\frac{a}{b}$ is to the right of $\frac{c}{d}$, then $\frac{a}{b} \frac{c}{d}$. If they are at the same point, then $\frac{a}{b} = \frac{c}{d}$.
Common Questions
How do you compare fractions using a number line?
Plot both fractions on the same number line. The fraction positioned further to the right is the greater value.
What does position on the number line tell us about a fraction's size?
A fraction further from zero (further right) is larger in value. A fraction closer to zero is smaller.
How do you plot 3/4 and 2/3 on the same number line to compare them?
Partition the number line into twelfths (LCD of 4 and 3): 3/4 = 9/12 and 2/3 = 8/12. Since 9/12 > 8/12, 3/4 is greater.
Can you compare fractions on a number line if they have different denominators?
Yes, by converting both to equivalent fractions with the same denominator before plotting, or by estimating their positions relative to benchmarks like 1/2.
Why does the whole matter when comparing fractions in context?
1/3 of a large rectangle and 1/3 of a small one represent different amounts. You can only compare fractions if they refer to the same whole.
What Eureka Math grade covers comparing fractions on number lines?
Grade 3, within the Number and Operations—Fractions domain.