Model Adding Mixed Numbers on a Number Line

Property To add mixed numbers on a number line, start at the first mixed number. Then, make a series of jumps to the right representing the second mixed number: first jump by the whole number part, then jump by the fractional part.

Examples To find $1\frac{1}{4} + 2\frac{2}{4}$: Start at $1\frac{1}{4}$. Jump 2 whole units to the right to land on $3\frac{1}{4}$. Then, jump $\frac{2}{4}$ to the right to land on the final answer, $3\frac{3}{4}$. To find $2\frac{3}{5} + 1\frac{4}{5}$: Start at $2\frac{3}{5}$. Jump 1 whole unit to the right to land on $3\frac{3}{5}$. Then, jump $\frac{4}{5}$ to the right to land on $4\frac{2}{5}$.

Explanation Using a number line helps visualize adding mixed numbers as combining lengths. You begin by plotting the first mixed number on the line. Adding the second mixed number is shown by moving to the right, first in large jumps for the whole number and then in smaller increments for the fraction. This method reinforces the concept of addition as "counting on" or moving forward along the number scale.