Lesson 7: Model Addition and Subtraction of Mixed Numbers

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.

Property

To subtract mixed numbers on a number line, start at the first number (minuend) and move to the left by the value of the second number (subtrahend).
The final position on the number line represents the difference.

Examples