Math Problems: Step-by-Step Solutions & Explanations

Hey guys! Let's dive into some math problems together. We're going to break down how to solve these fractions step-by-step, making sure it's super clear and easy to understand. Ready to crunch some numbers? Let's go!

Problem 1: Solving 19/46 × 23/38

Alright, first up, we have 19/46 multiplied by 23/38. When multiplying fractions, the cool thing is, it's pretty straightforward. You just multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. But before we get started, let's look at simplifying. Simplifying fractions is your best friend when you want to avoid dealing with huge numbers. It's like tidying up your room before a party – makes everything much neater and easier to manage! So, here is the breakdown.

First, let's see if we can simplify any of the fractions before multiplying. We've got 19/46 and 23/38. Hey, look at that! 19 is a factor of 19 and 38. That means we can simplify 19/38. In fact, 19 goes into 38 exactly twice. So, 19/38 becomes 1/2. Now we have 1/2 * 23/46. Similarly, 23 goes into 46 two times. So the simplified fraction is 1/2. Let's write that out: (19/46) * (23/38). We can simplify before multiplying, which will make our lives easier. Notice that 19 is a factor of both 19 and 38. So 19/19 = 1 and 38/19 = 2. So we can rewrite our equation as (1/2) * (23/23). And 23/23 = 1. Therefore, our result is 1/2. Multiplying the numerators, 1 * 1 = 1. Multiplying the denominators, 2 * 2 = 4. The result of the first fraction is 1/4. We've just turned what could have been a bit of a headache into a breeze! See how much easier that is? Simplify, simplify, simplify! And there you have it – the answer to the first problem is 1/4. Now we go to the next fraction. Make sure that you simplify before you multiply. It's like, a golden rule for fraction multiplication, seriously!

Problem 2: Solving 21/50 × 15/28

Okay, next up, we have 21/50 multiplied by 15/28. Time to put our simplifying skills to the test again! Remember, the goal is to make the numbers as small as possible before we start multiplying, so the calculations are easier. Let's see what we can do here. Let's look at 21/50 and 15/28. We can see that 21 and 28 have a common factor of 7. So, we can simplify 21/28. Also, 15 and 50 are divisible by 5. That means we can simplify 15/50. Dividing 21 by 7 gives us 3 and dividing 28 by 7 gives us 4. So 21/28 becomes 3/4. Dividing 15 by 5 gives us 3 and dividing 50 by 5 gives us 10. So 15/50 becomes 3/10. Now we have 3/10 * 3/4. Multiply those numerators (3 * 3 = 9) and those denominators (10 * 4 = 40). Now, we multiply the simplified fractions: 21/28 can be simplified to 3/4 (dividing both by 7), and 15/50 can be simplified to 3/10 (dividing both by 5). We now have to deal with 3/4 * 3/10. Now, we just multiply across: 3 times 3 equals 9, and 4 times 10 equals 40. Voila! The answer is 9/40! So our final answer is 9/40. Easy peasy!

Problem 3: Solving 2 1/5 × 5/17

Alright, let's finish strong with 2 1/5 multiplied by 5/17. This one includes a mixed number, which means it has a whole number and a fraction combined. Don't worry; we've got this! The first thing we need to do is turn that mixed number into an improper fraction (where the numerator is bigger than the denominator). To do this, we multiply the whole number (2) by the denominator of the fraction (5), and then add the numerator (1). So, 2 * 5 = 10, plus 1 = 11. We keep the same denominator, so our improper fraction is 11/5. Now, we have 11/5 * 5/17. Time to see if we can simplify before we multiply! Hey, look, we have a 5 in the numerator and a 5 in the denominator. That means we can simplify 5/5 to 1/1. Which simplifies the equation to 11/17. Now we multiply the numerators, 11 * 1 = 11, and the denominators, 1 * 17 = 17. The answer is 11/17. Converting the mixed number: 2 1/5 becomes 11/5. Now we have 11/5 * 5/17. Notice that we can simplify here again. The 5 in the numerator and the 5 in the denominator cancel each other out. That leaves us with 11/17, and there are no other common factors, so that's our final answer! The answer to this problem is 11/17. Awesome job! You've successfully navigated these three fraction problems, from mixed numbers to simplifying, multiplying and simplifying again, which means you're a fraction master now. High five!

Final Thoughts and Tips

So there you have it, guys! We've worked through three different fraction multiplication problems. Remember the key takeaways:

• Always simplify before you multiply. This will make your life so much easier and reduce the chance of making a mistake. It's like the golden rule of fraction multiplication!
• When multiplying fractions, multiply the numerators and the denominators separately.
• If you have a mixed number, change it to an improper fraction first.

I hope this explanation was helpful! Keep practicing, and you'll become a fraction whiz in no time. If you have any more questions, feel free to ask! Math can be fun if you break it down into manageable steps. Keep practicing, and you'll get the hang of it! You got this! Go forth and multiply (fractions, that is!). Keep practicing and you will be amazing. Also, understanding the basics of fractions is a cornerstone of math, and mastering these operations will make tackling more complex problems in the future a lot easier. So, keep up the great work, and don't be afraid to ask for help if you need it. Remember that practice is key, and every problem you solve brings you closer to becoming a math superstar. Happy calculating, everyone!