Math Problem: Subtracting Lengths - Step-by-Step

Hey everyone! Let's tackle this math problem together. We're going to subtract a mixed number from a whole number, and I'll walk you through it step-by-step. Don't worry, it's easier than it looks! We'll be focusing on the problem: 12m - 5 3/4m. This is a common type of problem you might encounter in math class, especially when dealing with measurements. The key here is understanding how to handle fractions and whole numbers in subtraction. We'll convert the whole number to a fraction with a common denominator, then perform the subtraction. Finally, we'll simplify the result if necessary. We'll break down the process into manageable chunks so you can follow along easily. By the end, you'll be able to confidently solve similar problems. Ready to dive in? Let's go!

To start, we need to understand the basic concept of subtracting lengths. In this case, we have 12 meters and we're taking away 5 and three-quarters meters. Think of it like this: you have a rope that's 12 meters long, and you cut off a piece that's 5 3/4 meters long. How much rope is left? That's what we're trying to figure out. The process involves some simple arithmetic, but the key is to be organized and follow each step carefully. Also, remember that understanding how to work with mixed numbers and fractions is a fundamental skill in mathematics. It's not just about solving this particular problem; it's about building a solid foundation for more complex mathematical concepts later on. We will convert the whole number, 12, into a fraction that has the same denominator as the fraction in the mixed number (which is 4). Then, we will subtract the mixed number from the fraction we got. We'll also cover the process of converting mixed numbers into improper fractions and vice versa, which is a useful skill. This helps you grasp the bigger picture. Are you with me?

Let's get started. First, we need to convert the whole number 12 into a fraction with a denominator of 4. We can rewrite 12 as a fraction by multiplying both the numerator and the denominator by 4: 12 = 12/1. Now multiply both the numerator and denominator by 4: (12 * 4) / (1 * 4) = 48/4. So, 12 is equivalent to 48/4. Next, we look at the mixed number 5 3/4. This means we have 5 whole units plus 3/4 of another unit. To subtract this from our fraction, we can either convert it to an improper fraction or subtract the whole numbers and fractions separately. Let's convert 5 3/4 to an improper fraction. To do this, multiply the whole number (5) by the denominator (4) and add the numerator (3). The result becomes the new numerator, and we keep the same denominator. So, (5 * 4) + 3 = 23. Therefore, 5 3/4 is equivalent to 23/4. Now we have 48/4 - 23/4. Since both fractions have the same denominator, we can simply subtract the numerators and keep the denominator. 48 - 23 = 25. Thus, the result is 25/4. What do we do with the result? We'll simplify this further. Finally, let's simplify the answer, which is currently 25/4. We can convert this improper fraction back into a mixed number by dividing the numerator (25) by the denominator (4). 25 divided by 4 is 6 with a remainder of 1. This means we have 6 whole units and 1/4 of another unit. So, 25/4 is equal to 6 1/4. Therefore, the answer to the problem 12m - 5 3/4m is 6 1/4m. Congratulations, you've solved it! Let me know if you are ready for some practice questions!

Step-by-Step Breakdown of the Math Problem

Okay, let's break down this math problem step-by-step to make it crystal clear. This problem is all about subtracting mixed numbers and whole numbers, and understanding the concept of measurement is crucial. Here's how we'll solve it, broken down into manageable pieces. This approach makes it easier to follow along and understand the logic behind each step. We will transform our whole number into a fraction, subtract the mixed number, and simplify the answer. I will give you the steps involved so that you can see how it works. This structured approach helps ensure accuracy and builds a solid understanding of the concepts. We'll start with the main problem: 12m - 5 3/4m. Let's work through this together. We'll start by making sure we all understand what we are dealing with.

Firstly, we have the whole number '12'. This represents 12 whole meters. Then, we have the mixed number '5 3/4'. This means 5 whole meters and an additional 3/4 of a meter. Our goal is to subtract the mixed number from the whole number. It's like taking away a certain length from a longer length. To begin, convert the whole number (12) into a fraction with a denominator of 4 (because the mixed number has a denominator of 4). To do this, multiply 12 by 4/4 (which is essentially multiplying by 1, so the value doesn't change). 12 * 4/4 = 48/4. Now we can rewrite the problem as: 48/4 - 5 3/4. Next, convert the mixed number 5 3/4 into an improper fraction. To do this, multiply the whole number (5) by the denominator (4) and add the numerator (3). This gives us (5 * 4) + 3 = 23. So, 5 3/4 is equal to 23/4. Now our problem looks like this: 48/4 - 23/4. With the same denominators, you can subtract the numerators: 48 - 23 = 25. Keep the denominator the same (4). This gives us 25/4. Finally, simplify the improper fraction 25/4 to a mixed number. Divide 25 by 4. 4 goes into 25 six times (6 * 4 = 24) with a remainder of 1. So, 25/4 is equal to 6 1/4. Therefore, the final answer is 6 1/4 meters. This means that if you subtract 5 3/4 meters from 12 meters, you are left with 6 1/4 meters. See? It's that easy.

Converting the Whole Number to a Fraction

Let's get into the nitty-gritty of converting that whole number into a fraction. This is a crucial step in solving this type of problem, so let's make sure we understand it. The whole number in our problem is '12'. To subtract our mixed number, 5 3/4, we need to convert this whole number into a fraction with the same denominator as the fraction in the mixed number, which is 4. This ensures that we can easily subtract the fractions. Now, why do we do this? Because, when subtracting fractions, it's essential that they have the same denominator. This allows us to directly subtract the numerators while keeping the same unit. This process may sound complicated, but it's really pretty straightforward once you get the hang of it. We're going to transform 12 into an equivalent fraction. Here's how: Write 12 as a fraction over 1: 12/1. To get a denominator of 4, we multiply both the numerator and the denominator by 4: (12 * 4) / (1 * 4). Now, 12 times 4 equals 48. And 1 times 4 equals 4. So, 12/1 becomes 48/4. Thus, 12 is equivalent to 48/4. What we've done here is simply rewriting the whole number 12 in a form that makes it easier to subtract from the mixed number. Doing this correctly ensures we can accurately perform the subtraction. This step is a fundamental technique when dealing with fractions and whole numbers. Understanding this conversion process is not just about this particular problem but will help you with a wide range of math problems. We’re essentially making sure everything is in the same ‘language’ (same denominator) before we subtract. By now, you should be able to transform a whole number into a fraction with any denominator, so you can solve this type of problem on your own.

Subtracting the Mixed Number

Alright, let's move on to the actual subtraction part. Now that we've converted the whole number to a fraction with a common denominator, we can finally subtract the mixed number. This is where all our preparation pays off! We've transformed 12 into 48/4, and we're subtracting 5 3/4 from it. Remember, 5 3/4 can be written as 23/4. Now we have 48/4 - 23/4. The beauty of having a common denominator is that you only need to subtract the numerators. Keep the denominator (4) the same. So, 48 - 23 equals 25. Therefore, the result of the subtraction is 25/4. What we are doing is essentially subtracting like units. Imagine you have 48 slices and you are taking away 23 of those slices. This simple step is at the heart of our calculation, and understanding this makes the rest of the problem easy. Subtracting fractions with the same denominator is a fundamental skill in mathematics, so pay close attention. It is a critical component of many mathematical operations. Because the denominators are the same, we can easily see how much 'space' is left after we subtract. We're directly comparing the 'slices' (or in our case, fourths of a meter) to find the difference. This step is about applying what we learned about fractions to get the solution. Remember, the denominator indicates the size of the 'slices' (the size of the fractional parts), and the numerator tells us how many of those slices we have. To reiterate, the subtraction is performed by subtracting the numerators (48 - 23 = 25) while keeping the denominator unchanged (4). This gives us 25/4. Now, the next step involves simplifying this result.

Simplifying the Answer

We're in the home stretch, folks! Our answer currently is 25/4, which is an improper fraction. To finish this problem and make the answer easier to understand, we need to simplify it. Simplifying involves converting the improper fraction back into a mixed number. This is a common practice to express answers in a more intuitive and manageable format, especially when dealing with real-world measurements. Converting an improper fraction into a mixed number allows us to easily grasp how many whole units and fractional parts are in our result. This is about making sure the answer is as clear as possible. With the improper fraction 25/4, it's easy to convert this to a mixed number through the following steps. Firstly, we divide the numerator (25) by the denominator (4). 25 divided by 4 equals 6 with a remainder of 1. The whole number part of our mixed number is the quotient (6). The remainder (1) becomes the numerator of the fractional part, and we keep the same denominator (4). This means that 25/4 is equivalent to 6 1/4. We started with 12 meters, subtracted 5 3/4 meters, and we now know the result is 6 1/4 meters. The simplification process does not change the value of the number; it just changes how it's represented. This step makes the answer easier to interpret and gives you a more intuitive sense of the measurement. With a little practice, simplifying fractions like these becomes second nature. And there you have it! You've successfully solved the problem and simplified the answer. Now you know how to subtract mixed numbers from whole numbers, including how to handle the fractions involved. You're well on your way to mastering these kinds of math problems. Keep practicing, and you'll find it gets easier every time. Excellent work, everyone!