7. The ficor of a rectangular room is to be tiled with \( \frac{2}{3} \) foot square tiles along a \( 9 \frac{3}{8} \) foot wall. How many tiles will be needed along the wall?

To determine how many tiles are needed along the wall, we need to follow these steps: 1. **Convert the mixed number to an improper fraction**: The wall length is given as \( 9 \frac{3}{8} \) feet. We can convert this to an improper fraction. 2. **Calculate the area covered by one tile**: Each tile covers \( \frac{2}{3} \) square feet. 3. **Divide the total wall length by the size of one tile**: This will give us the number of tiles needed along the wall. Let's start with step 1: ### Step 1: Convert \( 9 \frac{3}{8} \) to an improper fraction To convert a mixed number to an improper fraction, we use the formula: \[ \text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{Numerator} \div \text{Denominator} \] For \( 9 \frac{3}{8} \): - Whole number = 9 - Numerator = 3 - Denominator = 8 Calculating: \[ 9 \times 8 + 3 = 72 + 3 = 75 \] So, \( 9 \frac{3}{8} = \frac{75}{8} \) feet. ### Step 2: Calculate the number of tiles needed Now, we need to divide the total wall length by the size of one tile: \[ \text{Number of tiles} = \frac{\text{Wall Length}}{\text{Tile Size}} = \frac{\frac{75}{8}}{\frac{2}{3}} \] To divide fractions, we multiply by the reciprocal: \[ \frac{75}{8} \div \frac{2}{3} = \frac{75}{8} \times \frac{3}{2} \] Now, let's perform the multiplication: \[ \frac{75 \times 3}{8 \times 2} = \frac{225}{16} \] ### Step 3: Convert to a mixed number Now, we can convert \( \frac{225}{16} \) to a mixed number to find out how many whole tiles are needed: - Divide 225 by 16: \[ 225 \div 16 = 14 \quad \text{(whole number)} \] - Remainder: \[ 225 - (14 \times 16) = 225 - 224 = 1 \] So, \( \frac{225}{16} = 14 \frac{1}{16} \). Since we cannot use a fraction of a tile, we will need 15 tiles to cover the wall completely. ### Final Answer Thus, the number of tiles needed along the wall is \( \boxed{15} \).