Chocolate Torte Math Problem Calculate Remaining Desserts

Let's delve into a delectable math problem that involves a chef, some irresistible chocolate tortes, and a dinner party where guests indulged in these sweet treats. The core question we aim to answer is: if a chef meticulously prepared five chocolate tortes, and the guests consumed a portion of them, precisely how many tortes remain uneaten? This is not just a culinary conundrum; it's a practical application of fractional arithmetic, a fundamental concept in mathematics. To solve this, we need to understand how to subtract mixed numbers and fractions effectively. So, grab your aprons and your thinking caps, as we embark on this mathematical feast!

Understanding the Problem

The scenario presented is straightforward yet requires careful attention to detail. We begin with a chef who has baked a total of 5 chocolate tortes. These tortes are intended for a dinner party, where guests will partake in the delicious desserts. The critical piece of information is that the guests didn't devour all the tortes; instead, they consumed a fraction of them, specifically 2 rac{5}{16} tortes. Our mission, should we choose to accept it, is to determine the number of tortes that are left untouched after the dinner party. This involves subtracting the amount consumed from the initial amount, a classic subtraction problem with a fractional twist.

To fully grasp the problem, let's break it down into its components:

• Initial Amount: The chef starts with 5 whole chocolate tortes. This is our starting point, the total quantity before any consumption occurs.
• Amount Consumed: The guests ate 2 rac{5}{16} tortes. This is a mixed number, representing both a whole number (2) and a fraction rac{5}{16}. It signifies that the guests ate more than two whole tortes but less than three.
• What We Need to Find: We need to calculate the difference between the initial amount (5 tortes) and the amount consumed (2 rac{5}{16} tortes). This difference will tell us how many tortes are remaining.

Converting Mixed Numbers to Improper Fractions

Before we can subtract, we need to convert the mixed number 2 rac{5}{16} into an improper fraction. An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This conversion is necessary because it simplifies the subtraction process. To convert a mixed number to an improper fraction, we follow these steps:

1. Multiply the whole number by the denominator: In our case, we multiply 2 (the whole number) by 16 (the denominator), which gives us 32.
2. Add the numerator to the result: We add 5 (the numerator) to 32, resulting in 37.
3. Place the result over the original denominator: We put 37 over 16, giving us the improper fraction rac{37}{16}.

So, 2 rac{5}{16} is equivalent to rac{37}{16}. Now we have a fraction that we can work with more easily in our subtraction problem.

Converting Whole Numbers to Fractions

To subtract a fraction from a whole number, we need to express the whole number as a fraction with the same denominator as the fraction we are subtracting. In our problem, we are subtracting a fraction with a denominator of 16, so we need to convert the whole number 5 into a fraction with a denominator of 16. To do this, we simply multiply the whole number by the denominator and place the result over the denominator.

In this case, we multiply 5 by 16, which gives us 80. So, we can express 5 as the fraction rac{80}{16}. This means that 5 whole tortes are equivalent to 80 sixteenths of a torte. Now we have both numbers in fractional form with the same denominator, making subtraction straightforward.

Performing the Subtraction

Now that we have converted both the mixed number and the whole number into fractions with a common denominator, we can perform the subtraction. We are subtracting rac{37}{16} (the amount consumed) from rac{80}{16} (the initial amount). To subtract fractions with the same denominator, we simply subtract the numerators and keep the denominator the same.

So, the subtraction looks like this:

rac{80}{16} - rac{37}{16} = rac{80 - 37}{16}

Subtracting the numerators, we get:

$80 - 37 = 43$

Therefore, the result of the subtraction is:

rac{43}{16}

This means that there are rac{43}{16} tortes left. However, this is an improper fraction, so it's best to convert it back into a mixed number to make it easier to understand.

Converting Back to a Mixed Number

To convert the improper fraction rac{43}{16} back into a mixed number, we perform division. We divide the numerator (43) by the denominator (16) and see what we get.

43 divided by 16 is 2 with a remainder of 11. This means that 16 goes into 43 two times fully, with 11 left over. The whole number part of our mixed number is the quotient (2), and the remainder (11) becomes the numerator of the fractional part, with the original denominator (16) staying the same.

So, rac{43}{16} is equivalent to 2 rac{11}{16}. This means that there are 2 whole tortes and rac{11}{16} of a torte remaining.

The Final Answer

After all the calculations, we arrive at the final answer: there are 2 rac{11}{16} tortes left. This is a clear and concise answer that tells us exactly how many tortes the chef has remaining after the dinner party. So, the correct answer is B) 2 rac{11}{16}.

This problem beautifully illustrates how fractions and mixed numbers are used in everyday situations, like calculating leftovers after a delicious meal. By understanding the principles of converting between mixed numbers and improper fractions, and by mastering the art of fraction subtraction, we can confidently tackle similar problems in the future. Bon appétit, and happy calculating!

Original Question: A chef prepared five chocolate tortes for a dinner party. The guests consumed 2 rac{5}{16} tortes. How many tortes are left?

Repaired Question: If a chef makes 5 chocolate tortes and the guests eat 2 rac{5}{16} of the tortes, how many tortes are remaining?

Chocolate Torte Math Problem Calculate Remaining Desserts