Lesson 1: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models.

Property

To model operations with a whole number and a fraction using a tape diagram, represent the whole number with complete bars.
For addition ($W + \frac{a}{b}$), add a partially shaded bar.
For subtraction ($W - \frac{a}{b}$), partition the final whole bar into fractional units to remove the required amount, which shows that $W - \frac{a}{b} = (W-1) + \frac{b-a}{b}$.

Examples

Property

To subtract a fraction from a whole number $W$, decompose the whole number into $(W-1)$ and $1$.
Then, convert $1$ into a fraction with a common denominator to subtract.

To add a fraction to a whole number, combine them to form a mixed number: $W + \frac{a}{b} = W\frac{a}{b}$.

Examples