Solving Fraction Problems Step-by-Step A Penjas Kes Discussion

Hey guys! Today, we're diving into some fraction fun. We've got two problems here that look a bit tricky, but don't worry, we'll break them down step-by-step. Think of it like we're on a mathematical adventure together! We'll explore how to add, subtract, multiply, and divide fractions, and by the end, you'll be feeling like fraction superstars! So, grab your pencils, and let's get started!

Problem 1: Adding and Subtracting Fractions

Okay, our first problem is: What is the result of 4 3/4 - 2/3 + 2 1/2? This looks like a mixed bag of operations, but we can handle it. The key here is to remember the order of operations (which, in this case, doesn’t really matter since we're just adding and subtracting) and how to work with mixed numbers and fractions.

First things first, let's tackle those mixed numbers. We need to convert them into improper fractions. This makes it way easier to do the math. Remember, a mixed number has a whole number part and a fractional part, like our 4 3/4 and 2 1/2. To convert them, we multiply the whole number by the denominator of the fraction, add the numerator, and then put that result over the original denominator.

So, for 4 3/4, we do 4 * 4 = 16, then add 3, which gives us 19. So, 4 3/4 becomes 19/4. For 2 1/2, we do 2 * 2 = 4, add 1, and we get 5. So, 2 1/2 becomes 5/2. Now our problem looks like this: 19/4 - 2/3 + 5/2. Much better, right?

Now, before we can add or subtract fractions, they need to have a common denominator. This means the bottom numbers of the fractions need to be the same. To find the common denominator, we need to find the least common multiple (LCM) of our denominators: 4, 3, and 2. The LCM of 4, 3, and 2 is 12. So, we need to convert each fraction to have a denominator of 12.

To do this, we multiply the numerator and denominator of each fraction by the number that will make the denominator 12. For 19/4, we multiply both top and bottom by 3 (because 4 * 3 = 12), giving us 57/12. For 2/3, we multiply both top and bottom by 4 (because 3 * 4 = 12), giving us 8/12. And for 5/2, we multiply both top and bottom by 6 (because 2 * 6 = 12), giving us 30/12.

Now our problem is: 57/12 - 8/12 + 30/12. We're in the home stretch! Now we can simply add and subtract the numerators (the top numbers) while keeping the denominator the same. So, 57 - 8 + 30 = 79. That means our answer is 79/12. But wait, we're not quite done yet.

79/12 is an improper fraction, meaning the numerator is bigger than the denominator. We should convert it back to a mixed number. To do this, we divide 79 by 12. 12 goes into 79 six times (6 * 12 = 72), with a remainder of 7. So, our mixed number is 6 7/12. Therefore, the final answer to the first problem is 6 7/12. See? We did it! It might seem like a lot of steps, but once you get the hang of it, it becomes second nature. You are doing great, guys! Let's move on to the next problem!

Problem 2: Multiplying and Dividing Fractions

Alright, let's jump into our second problem: What is the result of 3 3/4 × 2 2/5 ÷ 3/2? This time, we're dealing with multiplication and division of fractions. Remember, multiplication and division have the same priority in the order of operations, so we'll just work from left to right.

Just like before, the first thing we need to do is convert those mixed numbers into improper fractions. We already know how to do this! For 3 3/4, we do 3 * 4 = 12, add 3, and we get 15. So, 3 3/4 becomes 15/4. For 2 2/5, we do 2 * 5 = 10, add 2, and we get 12. So, 2 2/5 becomes 12/5. Now our problem looks like this: 15/4 × 12/5 ÷ 3/2. We're making progress!

Now, let's tackle the multiplication first. To multiply fractions, we simply multiply the numerators together and the denominators together. So, 15/4 × 12/5 is (15 * 12) / (4 * 5). 15 * 12 = 180, and 4 * 5 = 20. So, we have 180/20. But before we move on, let's simplify this fraction. Both 180 and 20 are divisible by 20, so we can simplify 180/20 to 9/1, which is just 9. So, 15/4 × 12/5 = 9. Awesome!

Now our problem is even simpler: 9 ÷ 3/2. To divide fractions, we use a little trick: we multiply by the reciprocal of the second fraction. The reciprocal of a fraction is just flipping it over – swapping the numerator and the denominator. So, the reciprocal of 3/2 is 2/3. That means 9 ÷ 3/2 is the same as 9 × 2/3. Remember that whole number 9 can also be written as the fraction 9/1.

Now we multiply: (9/1) × (2/3). Multiply the numerators: 9 * 2 = 18. Multiply the denominators: 1 * 3 = 3. So, we have 18/3. And guess what? We can simplify this fraction too! 18 divided by 3 is 6. So, the final answer to the second problem is 6! You guys are amazing! We've conquered another fraction problem.

Key Takeaways and Practice Makes Perfect

So, there you have it! We've successfully solved two problems involving fractions. The key things to remember are:

• Convert mixed numbers to improper fractions before adding, subtracting, multiplying, or dividing.
• Find a common denominator when adding or subtracting fractions.
• Multiply numerators and denominators when multiplying fractions.
• Multiply by the reciprocal when dividing fractions.
• Simplify your answers whenever possible.

Fractions might seem intimidating at first, but with practice, they become much easier to handle. The more you work with them, the more comfortable you'll become. Try making up your own fraction problems and solving them. You can even challenge your friends or family to see who can solve them the fastest! Remember, math is like a sport – the more you practice, the better you get.

I hope this breakdown was helpful and made fractions a little less scary. Keep practicing, keep learning, and most importantly, keep having fun with math! You guys are doing a fantastic job, and I'm confident you'll become fraction masters in no time. Keep up the great work!

Remember, if you ever get stuck, don't be afraid to ask for help. There are tons of resources available, like your teachers, classmates, online tutorials, and even me! We're all in this together, and we can all learn and grow together. So, keep exploring, keep questioning, and keep challenging yourselves. The world of math is vast and exciting, and I'm thrilled to be on this journey with you. Until next time, happy calculating!