Question
I have a room of 20 2/3 by 18 1/4 and i need to cover it in tiles. The tiles are 4/5 by 4/5 how many tiles do i needto fill the room
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Answers
GPT-4o mini
To determine how many tiles are needed to cover the room, we first need to calculate the area of both the room and the tiles, and then divide the area of the room by the area of one tile.
1. **Convert the dimensions of the room from mixed fractions to improper fractions:**
- Room length: \(20 \frac{2}{3}\)
\[
20 \frac{2}{3} = \frac{20 \times 3 + 2}{3} = \frac{60 + 2}{3} = \frac{62}{3}
\]
- Room width: \(18 \frac{1}{4}\)
\[
18 \frac{1}{4} = \frac{18 \times 4 + 1}{4} = \frac{72 + 1}{4} = \frac{73}{4}
\]
2. **Calculate the area of the room:**
\[
\text{Area of the room} = \text{length} \times \text{width} = \left(\frac{62}{3}\right) \times \left(\frac{73}{4}\right) = \frac{62 \times 73}{3 \times 4} = \frac{4526}{12}
\]
To simplify \( \frac{4526}{12} \):
\[
\frac{4526 \div 2}{12 \div 2} = \frac{2263}{6}
\]
3. **Convert the dimensions of the tiles from mixed fractions to improper fractions:**
- Tile side length: \( \frac{4}{5} \)
- Area of one tile:
\[
\text{Area of one tile} = \left(\frac{4}{5}\right) \times \left(\frac{4}{5}\right) = \frac{16}{25}
\]
4. **Calculate the number of tiles needed:**
\[
\text{Number of tiles} = \frac{\text{Area of the room}}{\text{Area of one tile}} = \frac{\frac{2263}{6}}{\frac{16}{25}} = \frac{2263}{6} \times \frac{25}{16}
\]
\[
= \frac{2263 \times 25}{6 \times 16} = \frac{56575}{96}
\]
5. **Calculate \( \frac{56575}{96} \):**
Dividing:
\[
56575 \div 96 \approx 589.64
\]
Since the number of tiles must be a whole number, we round up to the nearest whole number. Thus, you will need 590 tiles.
Therefore, you will need **590 tiles** to cover the room.
1. **Convert the dimensions of the room from mixed fractions to improper fractions:**
- Room length: \(20 \frac{2}{3}\)
\[
20 \frac{2}{3} = \frac{20 \times 3 + 2}{3} = \frac{60 + 2}{3} = \frac{62}{3}
\]
- Room width: \(18 \frac{1}{4}\)
\[
18 \frac{1}{4} = \frac{18 \times 4 + 1}{4} = \frac{72 + 1}{4} = \frac{73}{4}
\]
2. **Calculate the area of the room:**
\[
\text{Area of the room} = \text{length} \times \text{width} = \left(\frac{62}{3}\right) \times \left(\frac{73}{4}\right) = \frac{62 \times 73}{3 \times 4} = \frac{4526}{12}
\]
To simplify \( \frac{4526}{12} \):
\[
\frac{4526 \div 2}{12 \div 2} = \frac{2263}{6}
\]
3. **Convert the dimensions of the tiles from mixed fractions to improper fractions:**
- Tile side length: \( \frac{4}{5} \)
- Area of one tile:
\[
\text{Area of one tile} = \left(\frac{4}{5}\right) \times \left(\frac{4}{5}\right) = \frac{16}{25}
\]
4. **Calculate the number of tiles needed:**
\[
\text{Number of tiles} = \frac{\text{Area of the room}}{\text{Area of one tile}} = \frac{\frac{2263}{6}}{\frac{16}{25}} = \frac{2263}{6} \times \frac{25}{16}
\]
\[
= \frac{2263 \times 25}{6 \times 16} = \frac{56575}{96}
\]
5. **Calculate \( \frac{56575}{96} \):**
Dividing:
\[
56575 \div 96 \approx 589.64
\]
Since the number of tiles must be a whole number, we round up to the nearest whole number. Thus, you will need 590 tiles.
Therefore, you will need **590 tiles** to cover the room.