Max Is Looking To Place A New Tiled Area In The Kitchen. The Spot He's Chosen Is 3 1/2 Yards Wide And 4 3/4 Yards Long. How Many Square Yards Of Tiling Does He Need For This Area?

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Max is embarking on an exciting kitchen renovation project, specifically focusing on adding a new tiled area. To ensure he purchases the correct amount of tiling, accurate measurements are crucial. The chosen spot for the tiling measures 3 1/2 yards in width and 4 3/4 yards in length. The key question Max needs to answer is: how many square yards of tiling are required to cover this particular area? This article will guide you through the process of calculating the necessary tiling, ensuring a smooth and efficient renovation.

Understanding the Problem

Before diving into the calculations, it's essential to understand the core concept: we need to find the area of a rectangular space. The area of a rectangle is calculated by multiplying its width by its length. In Max's case, the width is 3 1/2 yards, and the length is 4 3/4 yards. Both dimensions are given in mixed numbers, which can make the multiplication a bit tricky. The first step is to convert these mixed numbers into improper fractions. This conversion simplifies the multiplication process and reduces the chance of errors. Once we have the dimensions as improper fractions, we can multiply them together to find the area in square yards. This area represents the total amount of tiling Max needs to purchase. It’s always a good idea to add a little extra to account for cuts and breakage, ensuring Max has enough material to complete the job without running short. The final answer will provide Max with the precise quantity of tiling required for his kitchen renovation project, setting the stage for a successful tiling endeavor.

Converting Mixed Numbers to Improper Fractions

To accurately calculate the area, we must first convert the mixed numbers representing the width and length into improper fractions. The width is given as 3 1/2 yards. To convert this, we multiply the whole number (3) by the denominator (2) and then add the numerator (1). This gives us (3 * 2) + 1 = 7. We then place this result over the original denominator, giving us the improper fraction 7/2. Similarly, the length is given as 4 3/4 yards. We convert this by multiplying the whole number (4) by the denominator (4) and adding the numerator (3). This results in (4 * 4) + 3 = 19. Placing this over the original denominator gives us the improper fraction 19/4. Now that we have both dimensions as improper fractions—7/2 yards for the width and 19/4 yards for the length—we can proceed with the multiplication to find the area. This conversion is a crucial step in solving the problem, as it allows for a more straightforward calculation of the area. By working with improper fractions, we avoid the complexities that can arise when multiplying mixed numbers directly, ensuring an accurate result for Max's tiling project. This careful conversion sets the foundation for the next step in determining the total tiling needs.

Calculating the Area

Now that we have converted the mixed numbers to improper fractions, we can proceed with calculating the area of the tiling space. The width is 7/2 yards, and the length is 19/4 yards. To find the area, we multiply these two fractions together. When multiplying fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers) separately. So, we have (7/2) * (19/4) = (7 * 19) / (2 * 4). Multiplying the numerators, 7 * 19 equals 133. Multiplying the denominators, 2 * 4 equals 8. Therefore, the area is 133/8 square yards. This fraction represents the total area Max needs to tile. However, it is an improper fraction, which can be a bit difficult to visualize. To make it more understandable, we will convert this improper fraction back into a mixed number in the next step. This will give Max a clearer sense of how much tiling he needs in terms of whole square yards and a fraction of a square yard. The accurate calculation of the area is a critical step, ensuring that Max purchases the correct amount of tiling for his kitchen renovation project.

Converting the Improper Fraction Back to a Mixed Number

After calculating the area as an improper fraction (133/8 square yards), it is helpful to convert it back into a mixed number. This will provide a more intuitive understanding of the area Max needs to tile. To convert an improper fraction to a mixed number, we divide the numerator by the denominator. In this case, we divide 133 by 8. The quotient becomes the whole number part of the mixed number, and the remainder becomes the numerator of the fractional part, with the original denominator remaining the same. When we divide 133 by 8, we get a quotient of 16 and a remainder of 5. This means that 133/8 can be written as the mixed number 16 5/8. Therefore, the area Max needs to tile is 16 5/8 square yards. This mixed number tells us that Max needs 16 whole square yards of tiling, plus an additional 5/8 of a square yard. This form is much easier to grasp and use when planning the tiling project. Knowing the area in this format allows Max to better estimate the amount of tiling material to purchase, ensuring he has enough to cover the space with a little extra for cuts and potential breakage. The conversion back to a mixed number is a practical step in making the calculated area more usable for the actual renovation.

The Final Answer and Practical Considerations

Based on our calculations, Max needs 16 5/8 square yards of tiling for his kitchen renovation project. This is the area of the space he plans to tile, considering the dimensions of 3 1/2 yards wide and 4 3/4 yards long. However, in a real-world scenario, it's always wise to add a bit of extra material to account for cuts, breakage, and any potential errors during the tiling process. A general rule of thumb is to add 10-15% extra to the calculated area. This ensures that Max won't run out of tiles mid-project and have to make an additional purchase, which can be time-consuming and potentially lead to slight color variations between batches of tiles. For instance, adding 10% to 16 5/8 square yards would mean purchasing approximately 18 square yards of tiling. This buffer provides a safety net and helps ensure a smooth and successful tiling job. In conclusion, while the calculated area is 16 5/8 square yards, Max should plan to purchase closer to 18 square yards of tiling to accommodate the practical aspects of the renovation. This final step of adding a buffer is crucial for a successful outcome, preventing frustration and ensuring a beautifully tiled kitchen area.

Keywords

  • tiling area calculation, kitchen renovation, square yards, mixed numbers, improper fractions