Gambar Berikut 5/6 × 15 Hasil Dari Perkalian Tersebut Adalah

Hey guys! Today, we're diving into a super common math problem that you'll likely encounter in your studies: multiplying fractions by whole numbers. Specifically, we're going to tackle the question: What is the result of 5/6 multiplied by 15? Don’t worry, it’s not as intimidating as it might seem! We'll break it down step-by-step so you can ace similar problems in the future. This is a crucial skill for anyone studying mathematics, as it lays the foundation for more advanced concepts later on. So grab your pencils, and let's get started!

Understanding the Basics of Fraction Multiplication

Before we jump into the specific problem, let's quickly recap the fundamental principles of multiplying fractions. Multiplying fractions with whole numbers, like our case of 5/6 × 15, might seem tricky at first, but it’s actually quite straightforward once you understand the basic concept. Think of it this way: we’re essentially finding a fraction of a whole number. In our example, we want to find five-sixths (5/6) of 15. The word “of” in math often implies multiplication. So, to multiply a fraction by a whole number, we can follow a simple two-step process. First, we treat the whole number as a fraction by placing it over 1. Any whole number can be expressed as a fraction by writing it as the numerator with a denominator of 1. For example, 15 can be written as 15/1. This doesn't change the value of the number; it just changes how it's represented. This is a crucial step because it allows us to apply the rules of fraction multiplication consistently. Second, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. This is the core rule of fraction multiplication: (a/b) × (c/d) = (a × c) / (b × d). Let's illustrate this with a simple example: If we want to multiply 1/2 by 2/3, we multiply the numerators (1 × 2 = 2) and the denominators (2 × 3 = 6), resulting in 2/6, which can then be simplified to 1/3. This basic understanding is key to tackling more complex problems, and it’s the foundation upon which we’ll build as we solve our original problem of 5/6 × 15. Remember, the key is to break down the problem into manageable steps and apply the rules consistently. With a little practice, you'll find that multiplying fractions becomes second nature.

Step-by-Step Solution: 5/6 × 15

Okay, let's dive into solving our main problem: 5/6 × 15. We'll break it down into easy-to-follow steps so you can see exactly how it's done. Remember, the key is to stay organized and follow the rules of fraction multiplication. Firstly, as we discussed earlier, we need to express the whole number, 15, as a fraction. We do this by simply placing it over 1. So, 15 becomes 15/1. This step is essential because it allows us to treat both numbers in the problem as fractions, making the multiplication process straightforward. Now our problem looks like this: 5/6 × 15/1. Secondly, now that we have two fractions, we can proceed with the multiplication. Remember the rule: multiply the numerators together and multiply the denominators together. The numerator of the first fraction is 5, and the numerator of the second fraction is 15. So, we multiply 5 by 15. What's 5 times 15? It's 75. So, our new numerator is 75. Next, we multiply the denominators. The denominator of the first fraction is 6, and the denominator of the second fraction is 1. So, we multiply 6 by 1. This gives us 6. So, our new denominator is 6. Now we have the fraction 75/6. Thirdly, we have our result as an improper fraction (where the numerator is larger than the denominator). The fraction 75/6 represents the result of our multiplication, but it’s often best to simplify it, if possible, and express it as a mixed number. An improper fraction can be a bit unwieldy, especially when we want to understand the quantity it represents. Converting it to a mixed number, which combines a whole number and a proper fraction, often makes it easier to interpret the value. In this case, we have 75/6. To convert this to a mixed number, we divide the numerator (75) by the denominator (6). So, how many times does 6 go into 75? It goes in 12 times, because 12 multiplied by 6 is 72. This means we have a whole number part of 12. Now, we need to figure out the remainder, which will become the numerator of our fractional part. We subtract the product of 12 and 6 (which is 72) from 75. So, 75 minus 72 gives us a remainder of 3. This remainder becomes the numerator of our new fraction, and we keep the original denominator, which is 6. So, we have 3/6. Therefore, 75/6 can be expressed as the mixed number 12 3/6. But wait, we're not quite done yet! The fraction 3/6 can be further simplified. Both 3 and 6 are divisible by 3. If we divide both the numerator and the denominator by 3, we get 1/2. So, the simplified fraction is 1/2. Therefore, the final answer, in its simplest form, is 12 1/2. So, 5/6 multiplied by 15 equals 12 1/2. Phew! We made it. See, by breaking it down step by step, even what seems like a complicated problem becomes manageable. This methodical approach is key to success in math, so make sure you practice it! And finally, the result of 5/6 multiplied by 15 is 12 1/2. Great job following along! Now you've got the skills to tackle similar problems. Remember, the key is to break down the problem, apply the rules consistently, and simplify your answer whenever possible.

Simplifying Fractions: A Crucial Skill

Simplifying fractions is a super important skill in math, guys. It's like decluttering your room – it makes everything clearer and easier to work with! When we simplify a fraction, we're essentially finding an equivalent fraction that has smaller numbers. Simplifying fractions means expressing them in their simplest form, where the numerator and the denominator have no common factors other than 1. This doesn't change the value of the fraction; it just makes it easier to understand and work with. Think of it like this: 2/4 and 1/2 represent the same amount, but 1/2 is simpler. So, why is simplifying fractions so crucial? Well, first off, it makes calculations easier. Imagine trying to add 75/6 to another fraction versus adding 12 1/2. The smaller the numbers, the less likely you are to make mistakes. Secondly, simplified fractions are easier to compare. It’s much easier to tell that 1/2 is bigger than 1/3 than it is to compare 24/48 and 17/51. And thirdly, simplifying fractions is often required in math problems. Many teachers and tests will ask for answers to be given in simplest form. So, how do we actually simplify fractions? The key is to find the greatest common factor (GCF) of the numerator and the denominator. The GCF is the largest number that divides evenly into both numbers. For example, let’s take the fraction 3/6 from our previous problem. The factors of 3 are 1 and 3. The factors of 6 are 1, 2, 3, and 6. The greatest common factor is 3. Once we've found the GCF, we divide both the numerator and the denominator by it. In our example, we divide both 3 and 6 by 3. 3 divided by 3 is 1, and 6 divided by 3 is 2. So, 3/6 simplifies to 1/2. Let’s try another example. Suppose we have the fraction 12/18. What’s the GCF of 12 and 18? Well, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor is 6. So, we divide both 12 and 18 by 6. 12 divided by 6 is 2, and 18 divided by 6 is 3. So, 12/18 simplifies to 2/3. Practicing this skill is super important. The more you simplify fractions, the faster and more confident you'll become. And remember, always look for the GCF! Once you find it, simplifying the fraction becomes a breeze. Simplifying fractions is an essential skill in mathematics that not only makes calculations easier but also helps in better understanding and comparing fractional values. It ensures that answers are presented in the most concise and understandable form, which is crucial for success in more advanced mathematical topics. So keep practicing, and you'll become a pro at simplifying fractions in no time!

Real-World Applications of Multiplying Fractions

You might be thinking,