Solve The Math: Match The Products To The Answers!

Hey everyone! Are you ready to flex your math muscles? In this article, we're diving into some fraction multiplication. It's super fun once you get the hang of it, I promise! We'll be matching the math problems (the products, as they're called) with their correct answers. Let's get started and make sure you understand fractions and mixed numbers like pros! Get ready for a mathematical adventure! So, buckle up, grab your pens and paper, and let's conquer these problems together. We'll break down each problem step-by-step so you can follow along and learn some awesome strategies along the way. Whether you're a math whiz or just starting out, this will be a fun way to refresh your skills.

We will be working with fractions and mixed numbers. Remember, fractions represent parts of a whole, and mixed numbers are a combination of a whole number and a fraction. The key to solving these types of problems is to be patient, understand the steps, and practice. The more you work with fractions, the more comfortable you'll become. So, don't worry if it seems a bit tricky at first; we'll get through it together! Ready to jump in and see what's on the menu? Let's go!

Let's Tackle Those Problems

Alright, let's take a look at the problems we need to solve. We have four multiplication problems to tackle, and then we'll match them with their answers.

Here are the problems:

1. 4 imes 2rac{5}{6}
2. 2 imes 5rac{7}{12}
3. 1rac{7}{8} imes 6
4. 2rac{3}{10} imes 5

Notice that we have multiplication problems that involve whole numbers and mixed numbers. The key to solving these problems is to convert the mixed numbers into improper fractions. Remember, an improper fraction is a fraction where the numerator (the top number) is greater than the denominator (the bottom number). Don't worry, it's not as scary as it sounds. We'll do a quick review of how to convert them. Then, we will multiply the fractions and simplify them. After that, we'll convert the improper fractions to mixed numbers, if necessary. Finally, we'll match each problem with its corresponding answer. Are you ready to make some mathematical magic? Let's dive in! This is going to be so exciting, I can't wait to see your results! Get ready to feel like math superheroes! Remember to take your time and follow each step to find the answers. You've got this!

Problem 1: 4 imes 2rac{5}{6}

Let's break down this problem. We have a whole number (4) multiplied by a mixed number (2rac{5}{6}). First, we need to convert the mixed number 2rac{5}{6} into an improper fraction. To do this, we multiply the whole number (2) by the denominator (6), which gives us 12. Then, we add the numerator (5) to 12, which gives us 17. We keep the same denominator, so our improper fraction is rac{17}{6}. Now our problem is 4 imes rac{17}{6}.

To multiply a whole number by a fraction, we can rewrite the whole number as a fraction by putting it over 1. So, 4 becomes rac{4}{1}. Now we have rac{4}{1} imes rac{17}{6}. Next, we multiply the numerators (4 and 17) to get 68, and multiply the denominators (1 and 6) to get 6. Our fraction becomes rac{68}{6}. Great job! But is this fraction simplified? Nope! Let's simplify this fraction. Both 68 and 6 are divisible by 2. Divide both the numerator and the denominator by 2 to get rac{34}{3}. This is still an improper fraction, so let's convert it back to a mixed number. How many times does 3 go into 34? It goes in 11 times with a remainder of 1. So, our answer is 11rac{1}{3}.

Problem 2: 2 imes 5rac{7}{12}

Okay, let's tackle the second problem! We're multiplying a whole number (2) by a mixed number (5rac{7}{12}). First things first, we must turn 5rac{7}{12} into an improper fraction. Multiply the whole number (5) by the denominator (12) to get 60, and then add the numerator (7) to get 67. Keep the same denominator, so the improper fraction is rac{67}{12}. Now we have 2 imes rac{67}{12}.

Next, convert the whole number 2 into a fraction by writing it as rac{2}{1}. We have rac{2}{1} imes rac{67}{12}. Multiply the numerators (2 and 67) to get 134, and multiply the denominators (1 and 12) to get 12. So we get rac{134}{12}. Can we simplify this fraction? Yes, both 134 and 12 are divisible by 2. Divide both the numerator and the denominator by 2 to get rac{67}{6}. This is an improper fraction, so let's change it back to a mixed number. How many times does 6 go into 67? It goes in 11 times with a remainder of 1. So, our answer is 11rac{1}{6}.

Problem 3: 1rac{7}{8} imes 6

Alright, moving on to the third problem! We are multiplying a mixed number (1rac{7}{8}) by a whole number (6). First, convert 1rac{7}{8} into an improper fraction. Multiply the whole number (1) by the denominator (8) to get 8, then add the numerator (7) to get 15. The improper fraction is rac{15}{8}. So our problem is now rac{15}{8} imes 6.

Convert the whole number 6 to a fraction: rac{6}{1}. Our problem becomes rac{15}{8} imes rac{6}{1}. Multiply the numerators (15 and 6) to get 90, and multiply the denominators (8 and 1) to get 8. So we have rac{90}{8}. Now, simplify the fraction. Both 90 and 8 are divisible by 2. Divide both to get rac{45}{4}. This is an improper fraction. Let's change it to a mixed number. How many times does 4 go into 45? It goes in 11 times with a remainder of 1. Our answer is 11rac{1}{4}.

Problem 4: 2rac{3}{10} imes 5

Last but not least, let's solve the final problem! We're multiplying the mixed number (2rac{3}{10}) by the whole number (5). First, change the mixed number 2rac{3}{10} into an improper fraction. Multiply the whole number (2) by the denominator (10) to get 20, then add the numerator (3) to get 23. The improper fraction is rac{23}{10}. Now our problem is rac{23}{10} imes 5.

Convert the whole number 5 into a fraction: rac{5}{1}. Our problem is now rac{23}{10} imes rac{5}{1}. Multiply the numerators (23 and 5) to get 115, and multiply the denominators (10 and 1) to get 10. So we have rac{115}{10}. Simplify this fraction by dividing both the numerator and the denominator by 5. rac{115}{10} simplifies to rac{23}{2}. Convert the improper fraction to a mixed number. How many times does 2 go into 23? It goes in 11 times with a remainder of 1. Thus, our answer is 11rac{1}{2}.

Matching Time!

Okay, guys, now we get to the fun part - matching those problems to their answers! We've worked hard to solve each multiplication problem, and now it's time to see how our answers line up.

Here are the answers we found, which are also presented as options A, B, and C to help you with the matching process:

A. 11rac{1}{6} B. 11rac{1}{2} C. 11rac{1}{4}

Let's review the answers we got for each problem.

• Problem 1: 4 imes 2rac{5}{6} gave us 11rac{1}{3}. It's not one of our provided options, so we know there may be a mistake somewhere or it might be not included.
• Problem 2: 2 imes 5rac{7}{12} gave us 11rac{1}{6}. Looking at our options, this matches with option A! Great job!
• Problem 3: 1rac{7}{8} imes 6 gave us 11rac{1}{4}. This matches with option C! Awesome!
• Problem 4: 2rac{3}{10} imes 5 gave us 11rac{1}{2}. This one corresponds to option B! Amazing!

Conclusion: You Rock!

Congratulations, guys! You did it! You successfully matched all the problems to their correct answers. I knew you could do it! We broke down each problem step-by-step, converting mixed numbers to improper fractions, multiplying, simplifying, and then matching. You showed excellent work. Keep up the awesome work!

Remember, practice makes perfect. Keep practicing those fraction multiplications, and you'll become a math superstar in no time! Keep exploring and having fun. If you have any more questions or want to try more problems, feel free to ask! Let me know if you want to try some more math challenges. See you next time, and keep those math skills sharp!