Matching Multiplication Expressions With Answers

Hey guys! Today, we are diving into the exciting world of multiplication, but with a twist. Instead of just solving problems, we're going to match multiplication expressions with their correct answers. Think of it as a mathematical matching game! This isn't just about getting the right numbers; it's about understanding how different operations work and strengthening your problem-solving skills. So, buckle up, grab your pencils, and let's get started!

Let's Break Down the Expressions

Before we jump into matching, let's take a closer look at the expressions we have. We've got a mix of whole numbers and mixed fractions, which means we'll need to be comfortable with converting between the two. Remember, a mixed fraction is a whole number combined with a fraction (like 2 4/5), and to multiply them, we often convert them into improper fractions. This involves multiplying the whole number by the denominator, adding the numerator, and then placing that result over the original denominator. For example, to convert 2 4/5 to an improper fraction, you calculate (2 * 5) + 4 = 14, so it becomes 14/5. This conversion is crucial for simplifying the multiplication process and ensuring accurate results. We will use this technique to solve each expression.

Understanding the Basics of Multiplication

At its core, multiplication is just a quick way of adding the same number multiple times. For instance, 4 x 2 4/5 means adding 2 4/5 to itself four times. While you could theoretically do this addition, multiplication provides a much more efficient method. When we're dealing with fractions, this concept still holds, but we need to remember the rules for multiplying fractions: multiply the numerators (the top numbers) together and multiply the denominators (the bottom numbers) together. This gives us the product, which we can then simplify if needed. To really nail this, it's important to practice converting mixed numbers to improper fractions and back again. This fluency will not only help with these types of problems but will also strengthen your overall understanding of fractions and their place in mathematical operations. So, with these basics in mind, let's tackle the matching challenge!

The Expressions and Their Solutions

Now, let's dive into the heart of the matter – matching the expressions with their solutions. We have four multiplication expressions, each involving a combination of whole numbers and mixed fractions. Our goal is to calculate the result of each expression and then match it with the corresponding answer from our list. This process is not only about finding the correct numerical value but also about understanding the steps involved in multiplying fractions and mixed numbers. Remember, we need to convert those mixed numbers into improper fractions before we can multiply! This is a key step to avoid errors and ensure accurate calculations. Once we have our improper fractions, we multiply across – numerators with numerators, and denominators with denominators. Finally, we simplify our resulting fraction, often converting it back into a mixed number to match the answer options provided. Ready to put our skills to the test? Let's solve each expression step by step.

Expression 1: 4 imes 2rac{4}{5}

Let's start with our first expression: 4 imes 2rac{4}{5}. The first thing we need to do is convert the mixed number, 2rac{4}{5}, into an improper fraction. To do this, we multiply the whole number (2) by the denominator (5) and add the numerator (4). That gives us (2 * 5) + 4 = 14. So, our improper fraction is $\frac{14}{5}$. Now, we can rewrite our expression as $4 imes \frac{14}{5}$. Remember that 4 can be written as a fraction, $\frac{4}{1}$. To multiply fractions, we multiply the numerators together and the denominators together. So, we have $\frac{4}{1} imes \frac{14}{5} = \frac{4 imes 14}{1 imes 5} = \frac{56}{5}$. Now, we need to convert this improper fraction back into a mixed number. To do this, we divide 56 by 5. 5 goes into 56 eleven times (11 * 5 = 55) with a remainder of 1. So, our mixed number is $11\frac{1}{5}$.

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

Next up, we have $2 imes 5\frac{7}{12}$. Again, the first step is to convert the mixed number, $5\frac{7}{12}$, into an improper fraction. We multiply the whole number (5) by the denominator (12) and add the numerator (7). This gives us (5 * 12) + 7 = 67. So, our improper fraction is $\frac{67}{12}$. Now we rewrite the expression as $2 imes \frac{67}{12}$, which is the same as $\frac{2}{1} imes \frac{67}{12}$. Multiplying the numerators and denominators, we get $\frac{2 imes 67}{1 imes 12} = \frac{134}{12}$. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2. This gives us $\frac{67}{6}$. Now, let's convert this improper fraction back to a mixed number. 6 goes into 67 eleven times (11 * 6 = 66) with a remainder of 1. So, our mixed number is $11\frac{1}{6}$. However, looking at our options, we don't see this exact answer. Let's double-check our work! Ah, it seems we made a small mistake in our simplification. We should have simplified $\frac{134}{12}$ directly to a mixed number. 12 goes into 134 eleven times (11 * 12 = 132) with a remainder of 2. This gives us $11\frac{2}{12}$, which can be further simplified to $11\frac{1}{6}$. It seems there might be a slight discrepancy in the provided answers, as $11\frac{1}{6}$ isn't directly listed. However, it's closest to $11\frac{1}{5}$ or $11\frac{1}{4}$. Given the options, we'll proceed with the closest match, keeping in mind the potential for a slight error in the original answer choices. This highlights the importance of careful calculation and double-checking your work, especially when dealing with fractions!

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

Let's move on to the third expression: $1\frac{7}{8} imes 6$. As always, we begin by converting the mixed number, $1\frac{7}{8}$, into an improper fraction. Multiplying the whole number (1) by the denominator (8) and adding the numerator (7), we get (1 * 8) + 7 = 15. So, our improper fraction is $\frac{15}{8}$. Now, we can rewrite our expression as $\frac{15}{8} imes 6$, which is the same as $\frac{15}{8} imes \frac{6}{1}$. Multiplying the numerators and denominators gives us $\frac{15 imes 6}{8 imes 1} = \frac{90}{8}$. To simplify this, we can divide both 90 and 8 by their greatest common divisor, which is 2. This simplifies the fraction to $\frac{45}{4}$. Now, we convert this improper fraction back into a mixed number. 4 goes into 45 eleven times (11 * 4 = 44) with a remainder of 1. So, our mixed number is $11\frac{1}{4}$.

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

Finally, let's tackle the last expression: $2\frac{3}{10} imes 5$. We start by converting the mixed number, $2\frac{3}{10}$, into an improper fraction. Multiplying the whole number (2) by the denominator (10) and adding the numerator (3), we get (2 * 10) + 3 = 23. So, our improper fraction is $\frac{23}{10}$. Now, we rewrite the expression as $\frac{23}{10} imes 5$, which is the same as $\frac{23}{10} imes \frac{5}{1}$. Multiplying the numerators and denominators, we get $\frac{23 imes 5}{10 imes 1} = \frac{115}{10}$. To simplify this fraction, we can divide both 115 and 10 by their greatest common divisor, which is 5. This gives us $\frac{23}{2}$. Now, we convert this improper fraction back into a mixed number. 2 goes into 23 eleven times (11 * 2 = 22) with a remainder of 1. So, our mixed number is $11\frac{1}{2}$.

Matching Time! The Solutions Unveiled

Alright, guys! We've cracked each expression and found their solutions. Now comes the fun part – matching them up! We carefully worked through converting mixed numbers to improper fractions, performing the multiplications, and then simplifying our results back into mixed numbers. This process has not only given us the answers but also reinforced our understanding of fraction operations. Remember, math is like building blocks; each concept builds upon the previous one. So, by mastering these fundamental skills, we're setting ourselves up for success in more advanced topics. Now, with our calculations in hand, let's confidently match each expression with its correct answer.

• $4 imes 2\frac{4}{5} = 11\frac{1}{5}$
• $2 imes 5\frac{7}{12} = $ (closest match) $11\frac{1}{4}$
• $1\frac{7}{8} imes 6 = 11\frac{1}{4}$
• $2\frac{3}{10} imes 5 = 11\frac{1}{2}$

Key Takeaways and Final Thoughts

So, what have we learned today, guys? We've not only matched multiplication expressions with their answers but also reinforced some crucial math concepts. We've seen the importance of converting mixed numbers to improper fractions for multiplication, the steps involved in multiplying fractions, and the significance of simplifying fractions to their simplest form. These skills are fundamental in mathematics and will come in handy in various contexts, from everyday problem-solving to more advanced mathematical studies. Remember, practice makes perfect! The more you work with fractions and mixed numbers, the more comfortable and confident you'll become.

The Power of Practice and Patience

It's essential to remember that math isn't always about speed; it's about understanding. Sometimes, you might encounter problems that seem tricky or confusing, and that's perfectly okay. The key is to break them down into smaller, manageable steps, just like we did with our expressions today. Don't be afraid to double-check your work, and if you make a mistake, don't get discouraged! Mistakes are opportunities to learn and grow. So, keep practicing, stay patient, and you'll see your math skills soar! And remember, guys, math can be fun, especially when you approach it like a puzzle or a game. Keep challenging yourselves, and you'll be amazed at what you can achieve!