Solving 5/10 × 12 Understanding Mixed Fraction Multiplication
Hey guys! Let's dive into solving the math problem 5/10 × 12, breaking it down step-by-step so everyone can follow along. This is a fantastic example of how we handle fractions and whole numbers in multiplication, especially when we want to express our final answer as a mixed fraction. So, grab your pencils, and let's get started!
Understanding the Problem
When we see a problem like 5/10 × 12, the first thing to recognize is that we're multiplying a fraction by a whole number. To tackle this, we need to remember a fundamental concept: any whole number can be written as a fraction by placing it over a denominator of 1. So, 12 can be rewritten as 12/1. This might seem like a small step, but it's crucial because it allows us to treat both numbers in the problem as fractions, making the multiplication process much smoother.
Now, our problem looks like this: 5/10 × 12/1. This setup is much easier to work with directly. When multiplying fractions, we simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. This method gives us a clear path to the solution and helps avoid confusion. Multiplying fractions in this way ensures we accurately combine the quantities represented by each fraction. Understanding this basic principle is key to mastering fraction multiplication and will help in more complex problems later on. So, with our fractions aligned, we’re ready to perform the multiplication.
Multiplying Numerators and Denominators
Okay, let's get into the nitty-gritty of multiplying these fractions. As we discussed, we multiply the numerators together and the denominators together. So, we have: Numerators: 5 × 12 Denominators: 10 × 1
When we calculate these, we get: 5 × 12 = 60 10 × 1 = 10
So, our new fraction is 60/10. This fraction represents the result of our multiplication, but it’s not in its simplest form yet. We've successfully multiplied the fractions, but to truly solve the problem, we need to simplify this fraction and, if possible, convert it into a mixed fraction. Simplifying fractions is a critical skill in mathematics because it helps us express numbers in their most understandable form. A simplified fraction is easier to visualize and compare with other numbers, which is why it’s always a good practice to simplify your results. So, next, we'll look at how to simplify 60/10.
Simplifying the Fraction
Alright, we've arrived at the fraction 60/10. The next step is to simplify this fraction. Simplifying a fraction means reducing it to its lowest terms. To do this, we need to find the greatest common divisor (GCD) of both the numerator and the denominator and then divide both numbers by this GCD. In simpler terms, we're looking for the largest number that divides evenly into both 60 and 10.
In this case, both 60 and 10 are divisible by 10. So, 10 is our GCD. Now, we divide both the numerator and the denominator by 10: 60 ÷ 10 = 6 10 ÷ 10 = 1
This gives us the simplified fraction 6/1. While this is a simplified fraction, it's also an improper fraction because the numerator is greater than the denominator. In many cases, especially when dealing with real-world applications, it’s more useful to express improper fractions as mixed fractions. So, let’s take a look at how we can convert 6/1 into a mixed fraction, making it easier to understand in practical terms.
Converting to a Mixed Fraction
So, we've simplified our fraction to 6/1. Now, let’s convert this improper fraction into a mixed fraction. An improper fraction is one where the numerator is greater than or equal to the denominator, and a mixed fraction is a whole number combined with a proper fraction. In our case, 6/1 is quite straightforward to convert.
To convert an improper fraction to a mixed fraction, we divide the numerator by the denominator. The quotient becomes the whole number part of the mixed fraction, and the remainder becomes the numerator of the fractional part. The denominator stays the same. So, let's divide 6 by 1: 6 ÷ 1 = 6 with a remainder of 0.
This tells us that 6/1 is equivalent to the whole number 6. There’s no fractional part in this case because the remainder is 0. Therefore, 6/1 simplifies to 6. This is a clean, simple whole number, which is often the most practical way to express this particular fraction. Understanding how to convert between improper and mixed fractions is super useful because it allows us to express numbers in the most convenient form for the situation, whether it's for cooking, measuring, or solving more complex math problems.
Final Answer: 6
So, guys, we've journeyed through the problem 5/10 × 12 step by step, and we've arrived at our final answer: 6. We started by understanding the problem, then we multiplied the fractions, simplified the result, and finally converted the improper fraction to a whole number. Each step is crucial in ensuring we not only get the correct answer but also understand the process behind it. Remember, math isn't just about getting the right answer; it's about understanding why that answer is correct. This understanding will help you tackle more complex problems with confidence.
If you found this breakdown helpful, keep practicing, and don't hesitate to break down problems into smaller, manageable steps. You've got this!
