Fraction Multiplication: A Step-by-Step Guide

Hey everyone! Today, we're diving into the world of fraction multiplication. Specifically, we're going to break down how to solve the problem: 9 5/12 × 14/21. Don't worry if fractions make you sweat a little; we'll walk through this step-by-step to make it super clear. This is an essential skill in mathematics, popping up everywhere from basic arithmetic to more complex algebra, calculus and beyond! Understanding fraction multiplication is like having a superpower – it unlocks so many other mathematical concepts. Ready to become fraction wizards? Let's get started!

First things first, we'll need to convert the mixed number (9 5/12) into an improper fraction. Remember, a mixed number is a whole number combined with a fraction, while an improper fraction has a numerator (the top number) larger than or equal to its denominator (the bottom number). This conversion is crucial because it allows us to perform the multiplication easily. To convert 9 5/12, we'll multiply the whole number (9) by the denominator of the fraction (12), and then add the numerator (5). So, (9 * 12) + 5 = 108 + 5 = 113. This becomes our new numerator, and we keep the same denominator, which is 12. Therefore, 9 5/12 becomes 113/12. Now our problem looks like this: 113/12 × 14/21. See? We've already made the first big step! Converting to an improper fraction streamlines the entire process. This method ensures that we're dealing with all parts of the number in a way that's mathematically sound. This also makes the subsequent steps less prone to errors. Improper fractions might look a little clunky at first, but trust me, they're our friends in this situation. It's a fundamental trick for handling fractions, so understanding it well is super important. We now have two fractions ready to multiply! But hey, before we multiply, there is an important detail to keep in mind, simplifying fractions before multiplying them makes the math a whole lot easier, plus, it reduces the risk of having to deal with enormous numbers, and that's always a good thing, right?

Simplifying Fractions: A Pre-Multiplication Trick

Alright guys, before we get to the actual multiplication, let's talk about simplifying fractions. Simplifying means reducing a fraction to its lowest terms. This means we'll look for common factors between the numerators and denominators and cancel them out. The cool thing about fraction multiplication is that you can simplify diagonally! Meaning, you can simplify the numerator of one fraction with the denominator of the other, simplifying before you multiply is like giving yourself a head start in the race – it makes the numbers smaller and the calculations simpler. This technique can save you from dealing with giant numbers. This process also decreases the chances of making a mistake. Let's look at our fractions again: 113/12 × 14/21. Can we simplify anything here? Well, 113 is a prime number, meaning it is only divisible by 1 and itself, so it cannot be simplified with 12 or 21. However, let's consider the 14 and the 21. Both of these numbers are divisible by 7! So, let's divide 14 by 7, which gives us 2, and divide 21 by 7, which gives us 3. After simplifying, our problem now looks like this: 113/12 × 2/3. See how much easier that is? By simplifying, you're making the numbers friendlier to work with. Reducing fractions to their simplest form is not just a mathematical convenience; it's a testament to mathematical elegance and a way to avoid unnecessary complexity. This step reduces the risk of making arithmetic errors. Mastering simplification can give you a significant advantage in fraction-related problems. Remember, the goal is always to get to the simplest form possible. This step makes the multiplication process far easier to manage. Now let's move forward and do our multiplication.

Multiplying Fractions: The Final Step

Alright, now that we've simplified our fractions, we're ready for the main event: multiplication! Multiplying fractions is actually super straightforward. All you have to do is multiply the numerators together and multiply the denominators together. So, in our problem 113/12 × 2/3, we multiply 113 by 2 (the numerators) and 12 by 3 (the denominators). 113 multiplied by 2 equals 226, and 12 multiplied by 3 equals 36. This gives us 226/36. We now have the result! But wait, can we simplify this fraction any further? Absolutely! Both 226 and 36 are even numbers, which means they are divisible by 2. So, let's divide both the numerator and the denominator by 2. 226 divided by 2 is 113, and 36 divided by 2 is 18. This gives us 113/18. So the answer is 113/18! We've successfully multiplied the fractions. However, let's take an extra step, because 113/18 is an improper fraction, meaning the numerator is bigger than the denominator. It's often helpful to convert an improper fraction back into a mixed number. This makes it easier to understand the size of the fraction. Let's do that! To convert 113/18 into a mixed number, we need to see how many times 18 goes into 113. 18 goes into 113 six times (6 * 18 = 108) with a remainder of 5. The whole number is 6, the remainder is our new numerator, and the denominator stays the same (18). So, 113/18 simplifies to the mixed number 6 5/18. Voila! We have solved the problem! Congratulations! You’ve successfully navigated the world of fraction multiplication and simplification. Understanding these steps is a great foundation for more complex mathematical concepts.

Review and Recap

Let’s quickly recap what we did, because this is an important part of making sure everything sticks. First, we started with the problem 9 5/12 × 14/21. We converted the mixed number 9 5/12 into the improper fraction 113/12. Then, before we multiplied, we simplified the fractions. We noticed that 14 and 21 could be simplified by dividing both by 7. That led us to the problem 113/12 × 2/3. Next, we multiplied the numerators (113 and 2) to get 226, and multiplied the denominators (12 and 3) to get 36, giving us 226/36. We simplified this fraction by dividing both the numerator and denominator by 2, resulting in 113/18. Finally, because 113/18 is an improper fraction, we converted it to the mixed number 6 5/18. And there you have it! The final answer to the fraction multiplication problem. Always remember that practice makes perfect! So, the more problems you work through, the more comfortable and confident you'll become. By breaking it down into smaller steps, we could solve this problem successfully. Keep practicing, and you'll be a fraction pro in no time! Remember, math is like a muscle – the more you use it, the stronger it gets. So, keep at it, and you'll do great! And that's all there is to it, guys! Fraction multiplication isn't so scary after all, right?