Question

use fractions to complete the sentences. the side length of each small tile is \boxed{} units. the area of each small tile is \boxed{} square units. the area of the shaded rectangle is \boxed{} square units. submit work it out

Explanation:

Step1: Determine side length of small tile

The large square has a side length of 1 unit. Looking at the horizontal (or vertical) direction, we can see that the side is divided into 8 equal parts (since there are 8 columns or 8 rows of small tiles). So, the side length of each small tile is the total length (1 unit) divided by the number of tiles along one side. Since there are 8 tiles along one side, the side length of each small tile is $\frac{1}{8}$ units.

Step2: Calculate area of each small tile

The area of a square is side length squared. The side length of each small tile is $\frac{1}{8}$ units, so the area is $(\frac{1}{8})^2=\frac{1}{64}$ square units.

Step3: Calculate area of shaded rectangle

First, we need to find the number of small tiles in the shaded region. Looking at the figure, the shaded rectangle has a width of 6 tiles (since from column 3 to column 8, that's 6 columns) and a height of 5 tiles (from row 1 to row 5, that's 5 rows). So the number of small tiles in the shaded region is $6\times5 = 30$. Since each small tile has an area of $\frac{1}{64}$ square units, the area of the shaded rectangle is $30\times\frac{1}{64}=\frac{30}{64}=\frac{15}{32}$ square units. Alternatively, we can think in terms of the length and width of the shaded rectangle. The length of the shaded rectangle (horizontal) is $\frac{6}{8}=\frac{3}{4}$ units (since 6 out of 8 tiles) and the width (vertical) is $\frac{5}{8}$ units (since 5 out of 8 tiles). Then the area is length times width: $\frac{3}{4}\times\frac{5}{8}=\frac{15}{32}$ square units.

Answer:

The side length of each small tile is $\frac{1}{8}$ units.
The area of each small tile is $\frac{1}{64}$ square units.
The area of the shaded rectangle is $\frac{15}{32}$ square units.