Problem 52 - Prealgebra

Question

A family decides to put tiles in the entryway of their home. The entryway has an area of 6 square meters. If cach tile is 5 centimeters by 5 centimeters, how many tiles will it take to cover the entryway?

Step-by-Step Solution

Answer

The family needs 2400 tiles to cover the entryway.

Step 1: Convert Tile Dimensions to Meters

Each tile measures 5 centimeters by 5 centimeters. To convert this to meters, we use the fact that 1 meter = 100 centimeters. Therefore, each tile measures 0.05 meters by 0.05 meters.

Step 2: Calculate the Area of One Tile

The area of one tile can be found using the formula for the area of a rectangle: \( ext{Area} = ext{length} imes ext{width} \). For one tile, the area in square meters is \( 0.05 imes 0.05 = 0.0025 \) square meters.

Step 3: Calculate the Total Number of Tiles Needed

To find the number of tiles needed, we divide the total entryway area by the area of one tile. So, the number of tiles required is \( rac{6}{0.0025} = 2400 \).

Key Concepts

Unit Conversion

Understanding unit conversion is key when working with measurements. It's all about changing one kind of measurement into another, like turning centimeters into meters.
To convert centimeters to meters, remember that 1 meter equals 100 centimeters. This relationship helps us convert quickly:

• To convert centimeters to meters, divide by 100.
• For example, 5 cm becomes \( 5 \div 100 = 0.05 \) m.

This process ensures measurements are in the same units, simplifying calculations and making them more accurate.

Rectangle Area

The area of a rectangle measures the space within its four sides. To calculate this, you use the simple formula:

• \( \text{Area} = \text{length} \times \text{width} \).

Applying this, if you have a tile that's 0.05 meters by 0.05 meters, its area is:

• \( 0.05 \times 0.05 = 0.0025 \) square meters.

Knowing how to find a rectangle's area is crucial in various practical situations, such as tiling, where you need to know how many tiles cover a given space. Remember, area is most commonly expressed in square units, like square meters.

Tiling Problems

When dealing with tiling problems, the goal is often to determine how many tiles are needed to fill a particular area. Start by knowing two things: the total area you need to tile and the area of one tile.
Here's how to solve it:

• Calculate the area of one tile (as discussed, for a tile 0.05m by 0.05m, it's 0.0025 square meters).
• Determine the total area to cover, like 6 square meters in this exercise.
• Divide the total area by the area of one tile to find how many tiles you need: \( \frac{6}{0.0025} = 2400 \).

This approach is helpful in planning and ensuring you buy the right number of tiles, avoiding shortages or excess.