Lesson 3: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.

Property

A mixed number in the form $W \frac{N}{100}$ is represented visually using area models. This consists of $W$ fully shaded grids (representing the whole number) and one partially shaded grid with $N$ out of 100 squares shaded (representing the fraction part).

Examples

• To represent $1 \frac{25}{100}$, you would shade one entire grid and then shade 25 squares in a second grid.
• To represent $2 \frac{7}{100}$, you would shade two entire grids and then shade 7 squares in a third grid.
• To represent $3 \frac{40}{100}$, you would shade three entire grids and then shade 40 squares (or 4 columns) in a fourth grid.

Explanation

Area models provide a visual way to understand mixed numbers with hundredths. Each whole number is represented by a completely shaded 10x10 grid, which equals one whole. The fractional part is shown by shading the corresponding number of squares in another 10x10 grid. This method helps connect the abstract concept of a mixed number to a concrete visual quantity.

Property

To plot a mixed number, such as $A \frac{bc}{100}$, on a number line, first locate the whole number $A$. The point will be located between $A$ and $A+1$. The fraction part, $\frac{bc}{100}$, determines the precise position past the whole number $A$.

Examples

Property

A mixed number with a fraction in hundredths can be decomposed into ones, tenths, and hundredths. This expanded form directly translates to its decimal representation.

Examples