Oaxaca Cheese Recipe: Calculate Total Cheese Usage
Hey guys! Ever find yourself wondering how much cheese you've actually used in all those delicious dishes you've whipped up? Let's break down a common kitchen scenario and figure out exactly how much Oaxaca cheese was used in total. We're going to tackle a fun math problem that involves adding up fractions – don't worry, it's easier than it sounds! We'll cover everything step-by-step, so you can confidently calculate your cheese consumption (or any other ingredient, for that matter!). So, grab your aprons and let's get started!
Understanding the Problem
So, here's the deal: In the kitchen, 1/2 kg of Oaxaca cheese was used in soups, 4/6 kg was used in quesadillas, and 1/4 kg was used in snacks. The big question is: how much Oaxaca cheese was used in total? This is a classic addition problem involving fractions. To solve this, we need to add these fractions together. But, and this is crucial, we can only add fractions if they have the same denominator (the bottom number). Think of it like trying to add apples and oranges – you need to convert them to a common unit (like “fruit”) before you can add them meaningfully. In our case, we need to find a common denominator for 2, 6, and 4.
Breaking Down the Fractions
Before we dive into finding that common denominator, let's take a closer look at each fraction. We have 1/2 kg used in soups. This means that out of two equal parts, one part was used. Then we have 4/6 kg used in quesadillas. This one is interesting because the fraction 4/6 can be simplified. Simplifying fractions makes our calculations easier. Both 4 and 6 are divisible by 2, so we can divide both the numerator (top number) and the denominator (bottom number) by 2. This gives us 2/3. So, 4/6 is equivalent to 2/3. This means that 4/6 kg is the same amount as 2/3 kg. Last but not least, we have 1/4 kg used in snacks. This means that out of four equal parts, one part was used.
Finding the Least Common Denominator (LCD)
Okay, now for the fun part: finding the Least Common Denominator, or LCD. The LCD is the smallest number that all our denominators (2, 3, and 4) can divide into evenly. There are a couple of ways to find the LCD. One way is to list the multiples of each denominator until you find a common one. Let's try that: Multiples of 2: 2, 4, 6, 8, 10, 12, 14... Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16... Notice that 12 appears in all three lists! So, 12 is a common denominator. And since it's the smallest one, it's the LCD. Another way to find the LCD is to use prime factorization, but for this problem, listing the multiples works just fine. So, our LCD is 12. This means we need to convert each of our fractions (1/2, 2/3, and 1/4) into equivalent fractions with a denominator of 12.
Converting Fractions to a Common Denominator
Now that we've found our LCD (which is 12), we need to convert each fraction to have this new denominator. This involves multiplying both the numerator and the denominator of each fraction by a certain number. The key is that we're multiplying by a form of 1 (like 2/2 or 3/3), so we're not actually changing the value of the fraction, just its appearance. Let's start with 1/2. We need to figure out what to multiply the denominator (2) by to get 12. Well, 2 multiplied by 6 equals 12. So, we multiply both the numerator and the denominator by 6: (1 * 6) / (2 * 6) = 6/12. So, 1/2 is equivalent to 6/12. Next up is 2/3. We need to figure out what to multiply the denominator (3) by to get 12. 3 multiplied by 4 equals 12. So, we multiply both the numerator and the denominator by 4: (2 * 4) / (3 * 4) = 8/12. So, 2/3 is equivalent to 8/12. Finally, we have 1/4. We need to figure out what to multiply the denominator (4) by to get 12. 4 multiplied by 3 equals 12. So, we multiply both the numerator and the denominator by 3: (1 * 3) / (4 * 3) = 3/12. So, 1/4 is equivalent to 3/12. Great! Now we have all our fractions with the same denominator: 6/12, 8/12, and 3/12.
Converting 1/2 to Equivalent Fraction
Let's focus on converting the fraction 1/2 into an equivalent fraction with a denominator of 12. To do this, we need to determine what number we should multiply both the numerator (1) and the denominator (2) by, so that the new denominator becomes 12. We ask ourselves: "What number multiplied by 2 equals 12?" The answer is 6. So, we multiply both the numerator and the denominator of 1/2 by 6. This gives us (1 * 6) / (2 * 6), which simplifies to 6/12. Therefore, 1/2 is equivalent to 6/12.
Converting 4/6 to Equivalent Fraction
Now, let's convert the fraction 4/6 into an equivalent fraction with a denominator of 12. Again, we need to find a number to multiply both the numerator and the denominator by. However, before we do that, remember that we simplified 4/6 to 2/3 earlier. It's generally easier to work with simplified fractions. So, we'll work with 2/3 instead. We ask ourselves: "What number multiplied by 3 equals 12?" The answer is 4. So, we multiply both the numerator and the denominator of 2/3 by 4. This gives us (2 * 4) / (3 * 4), which simplifies to 8/12. Therefore, 4/6 (which is the same as 2/3) is equivalent to 8/12.
Converting 1/4 to Equivalent Fraction
Lastly, let's convert the fraction 1/4 into an equivalent fraction with a denominator of 12. We need to find a number that, when multiplied by 4, gives us 12. That number is 3. So, we multiply both the numerator and the denominator of 1/4 by 3. This gives us (1 * 3) / (4 * 3), which simplifies to 3/12. Therefore, 1/4 is equivalent to 3/12.
Adding the Fractions
Now for the moment we've been waiting for: adding the fractions! We have 6/12 (from the soups), 8/12 (from the quesadillas), and 3/12 (from the snacks). Since they all have the same denominator, we can simply add the numerators and keep the denominator the same. So, we add 6 + 8 + 3, which equals 17. Our new fraction is 17/12. This fraction represents the total amount of Oaxaca cheese used. But wait, 17/12 is an improper fraction because the numerator is larger than the denominator. This means it represents more than one whole kilogram. We can convert this improper fraction to a mixed number, which is a whole number and a fraction combined.
Adding 6/12 + 8/12 + 3/12
Let's add the fractions 6/12, 8/12, and 3/12 together. Remember, when adding fractions with the same denominator, we only need to add the numerators. The denominator stays the same. So, we have 6 + 8 + 3, which equals 17. This gives us a new fraction of 17/12. This means we have seventeen twelfths. Now, let's think about what this fraction means in terms of kilograms of cheese.
Converting Improper Fraction to Mixed Number
To convert the improper fraction 17/12 to a mixed number, we need to figure out how many whole times 12 goes into 17. In other words, we need to divide 17 by 12. 12 goes into 17 one time (1 x 12 = 12). So, we have a whole number of 1. Now, we need to find the remainder. We subtract 12 from 17, which gives us 5. This remainder becomes the numerator of our fractional part, and the denominator stays the same (12). So, the fractional part is 5/12. Therefore, the improper fraction 17/12 is equivalent to the mixed number 1 5/12. This means that a total of 1 and 5/12 kilograms of Oaxaca cheese was used.
Dividing 17 by 12
To convert the improper fraction 17/12 into a mixed number, the first step is to divide the numerator (17) by the denominator (12). When we divide 17 by 12, we find that 12 goes into 17 one time. This "1" becomes the whole number part of our mixed number. But we're not done yet! We need to figure out the remainder, which will help us determine the fractional part of the mixed number.
Determining the Remainder
After dividing 17 by 12 and finding that it goes in one whole time, we need to calculate the remainder. This remainder represents the amount "left over" after we've taken out the whole number. To find the remainder, we subtract the product of the whole number (1) and the denominator (12) from the original numerator (17). So, we calculate 17 - (1 * 12), which is 17 - 12. This gives us a remainder of 5. This remainder of 5 will be the numerator of the fractional part of our mixed number.
Writing the Mixed Number
Now that we have the whole number (1) and the remainder (5), we can write the mixed number. The whole number is simply written as is. The remainder becomes the numerator of the fractional part, and the denominator stays the same as the original improper fraction (12). So, the fractional part is 5/12. Combining the whole number and the fractional part, we get the mixed number 1 5/12. This means that 17/12 is equivalent to 1 and 5/12.
Final Answer
So, after all that math, we've arrived at our final answer! A total of 1 5/12 kilograms of Oaxaca cheese was used in the kitchen for soups, quesadillas, and snacks. That's a lot of cheese! But hey, who can resist a cheesy dish? This exercise shows how fractions are used in everyday life, even in the kitchen. Understanding how to add and convert fractions can help you with all sorts of things, from cooking to measuring ingredients for a recipe. So, the next time you're in the kitchen, remember this problem and you'll be a fraction-calculating pro!
Expressing the Total Amount
The final answer is 1 5/12 kilograms. This mixed number tells us that a little over one kilogram of Oaxaca cheese was used in total. The "1" represents one whole kilogram, and the "5/12" represents an additional five-twelfths of a kilogram. This is a precise way to express the total amount of cheese used, combining both a whole unit and a fractional part. So, next time someone asks how much cheese you used, you can confidently say, "One and five-twelfths kilograms!"