Application: Comparing Rational Numbers in Word Problems
Application: Comparing Rational Numbers in Word Problems is a Grade 3 math skill from Eureka Math using number lines to compare fractions in real-world contexts. To compare fractions a/b and c/d, plot both on the same number line. The fraction located farther to the right is greater. If they share the same point, they are equal. This strategy grounds fraction comparison in a visual context and directly connects fraction value to position, helping third graders make sense of comparison problems rather than relying on rules alone.
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 two fractions using a number line?
Plot both fractions on the same number line between 0 and 1. The fraction positioned farther to the right is the greater fraction. If they land on the same point, they are equal.
Why does position on a number line show which fraction is greater?
Numbers increase from left to right on a number line. A fraction farther right represents a larger portion of the whole, just as larger whole numbers sit to the right of smaller ones.
How would you compare 3/4 and 2/3 on a number line?
Mark the number line in fourths (0, 1/4, 2/4, 3/4, 1) and thirds (0, 1/3, 2/3, 1). Plot 3/4 and 2/3. Since 3/4 = 0.75 and 2/3 ≈ 0.667, 3/4 is farther right and therefore greater.
When would a number line comparison show two fractions are equal?
When both fractions land on the exact same point—for example, 1/2 and 2/4 both fall at the midpoint between 0 and 1, showing they are equivalent.
In which textbook is Application: Comparing Rational Numbers in Word Problems taught?
This skill is taught in Eureka Math, Grade 3.