What is the correct explanation to support the comparison of 1/3 and 3/4 on number lines?

• A. A. "One-third is less than three-fourths because three-fourths is bigger than one-third."
• B. B. "One-third is less than three-fourths because it has a smaller value in the numerator."
• C. C. "One-third is less than three-fourths because four is a greater denominator than three."
• D. D. "One-third is less than three-fourths because three-fourths is farther to the right than one-third."

Answer: (D)

The explanation that one-third is less than three-fourths because three-fourths is farther to the right than one-third is correct because it effectively communicates the concept of comparing fractions using a number line. On a number line, the position of a number indicates its value, with numbers further to the right being greater than those to the left.

When you plot both fractions on a number line, one-third (1/3) is located to the left of three-fourths (3/4). This visual representation reinforces the idea that three-fourths has a greater value than one-third, as it is closer to 1 and further from 0.

Understanding fractions in this way helps students see the relationship between the numerators and denominators while grasping the overall concept of magnitude in terms of placement on a number line. Comparing fractions visually is an important skill in developing number sense.