Multiply Mixed Numbers: 1 4/7 X 2 3/5

Dec 8, 2025 by Andrew McMorgan 38 views

Multiply Mixed Numbers: $1 rac{4}{7} imes 2 rac{3}{5}$

Hey guys, ever get stumped on multiplying mixed numbers? It's a super common math problem, and today we're going to break down exactly how to solve $1 rac{4}{7} imes 2 rac{3}{5}$ . Don't sweat it, by the end of this, you'll be a pro at tackling these kinds of calculations. We'll walk through it step-by-step, explaining each part so it makes perfect sense. You'll see that with a little practice, multiplying mixed numbers becomes a piece of cake. So, let's dive in and conquer this math challenge together!

Step 1: Convert Mixed Numbers to Improper Fractions

First things first, to multiply mixed numbers, we need to convert them into improper fractions. This is a crucial step, guys, because our standard multiplication rules work much more smoothly with improper fractions than with mixed numbers directly. Remember, a mixed number has a whole number part and a fractional part. An improper fraction, on the other hand, has a numerator that is greater than or equal to its denominator. So, let's tackle our first mixed number: $1 rac{4}{7}$ . To convert this, we multiply the whole number (1) by the denominator (7) and then add the numerator (4). That gives us $(1 imes 7) + 4 = 7 + 4 = 11$ . This new number, 11, becomes our new numerator. The denominator stays the same, which is 7. So, $1 rac{4}{7}$ becomes the improper fraction $rac{11}{7}$ .

Now, let's do the same for our second mixed number: $2 rac{3}{5}$ . We multiply the whole number (2) by the denominator (5) and add the numerator (3). So, $(2 imes 5) + 3 = 10 + 3 = 13$ . Again, 13 is our new numerator, and the denominator remains 5. Thus, $2 rac{3}{5}$ is converted to the improper fraction $rac{13}{5}$ .

So now, our original problem $1 rac{4}{7} imes 2 rac{3}{5}$ has been transformed into $rac{11}{7} imes rac{13}{5}$ . See? It already looks a bit simpler, right? This conversion is the foundation for solving the rest of the problem. Making sure you get this step right is key to accurate results. Always double-check your conversion – multiply the whole number by the denominator, add the numerator, and keep the original denominator. It's a simple process but one where a small slip-up can throw off your entire answer. We've got this, team! Keep that momentum going!

Step 2: Multiply the Numerators and Denominators

Alright, mathletes, we've successfully converted our mixed numbers into improper fractions: $rac{11}{7}$ and $rac{13}{5}$ . Now comes the fun part – the actual multiplication! When you're multiplying fractions, the process is straightforward: you multiply the numerators together to get the new numerator, and you multiply the denominators together to get the new denominator. It's as simple as that! No need to find common denominators here, which is a big advantage of working with improper fractions. Let's apply this to our converted fractions.

We'll start with the numerators. We have 11 from the first fraction and 13 from the second. So, we calculate $11 imes 13$ . If you need to do this on the side, remember $11 imes 10 = 110$ and $11 imes 3 = 33$ . Adding those together, $110 + 33 = 143$ . So, our new numerator is 143.

Next, we multiply the denominators. We have 7 from the first fraction and 5 from the second. So, we calculate $7 imes 5$ . This one's a classic multiplication table fact: $7 imes 5 = 35$ . This is our new denominator.

Putting it all together, the result of multiplying $rac{11}{7} imes rac{13}{5}$ is $rac{143}{35}$ . So, the product of our original mixed numbers is the improper fraction $rac{143}{35}$ . Remember this step: multiply straight across – numerator to numerator, denominator to denominator. It's the core of fraction multiplication. We're well on our way to the final answer, guys! Keep that focus sharp!

Step 3: Convert the Improper Fraction Back to a Mixed Number

We've done the hard work of converting and multiplying, and now we have our answer as an improper fraction: $rac{143}{35}$ . But, like most math problems involving mixed numbers, the final answer is usually expected in mixed number form. So, the final step is to convert this improper fraction back into a mixed number. This involves a bit of division, but don't worry, it's straightforward.

To convert $rac{143}{35}$ into a mixed number, we need to find out how many times 35 fits into 143. This is where division comes in. We divide 143 by 35. Let's think about multiples of 35: $35 imes 1 = 35$ , $35 imes 2 = 70$ , $35 imes 3 = 105$ , $35 imes 4 = 140$ . Aha! 35 goes into 143 a total of 4 times. This '4' will be the whole number part of our mixed number.

Now, we need to find the remainder. We know that $35 imes 4 = 140$ . To find the remainder, we subtract this product from our original numerator: $143 - 140 = 3$ . This remainder, 3, becomes the numerator of the fractional part of our mixed number.

The denominator of the fractional part stays the same as the denominator of the original improper fraction, which is 35. So, our remainder of 3 over the denominator 35 gives us the fraction $rac{3}{35}$ .

Putting it all together, the improper fraction $rac{143}{35}$ converts to the mixed number $4 rac{3}{35}$ . This is our final answer! We've successfully multiplied $1 rac{4}{7}$ by $2 rac{3}{5}$ and arrived at $4 rac{3}{35}$ . Always remember to convert back to a mixed number if the question implies it or if the options are in mixed number format. You guys crushed it!

Checking the Options

Now that we've diligently worked through the problem and arrived at our answer of $4 rac{3}{35}$ , let's take a peek at the options provided to make sure we're on the right track. We're looking for the option that matches our calculated result.

(A) $4 rac{3}{35}$ - This looks exactly like what we calculated! Bingo!
(B) $4 rac{12}{35}$ - This is close, but the fractional part is different. This might happen if there was a mistake in multiplying the numerators or in finding the remainder after division.
(C) $3 rac{7}{12}$ - This is quite different from our answer. This could indicate a misunderstanding of the process, perhaps confusing multiplication with addition or having errors in the initial conversion to improper fractions.
(D) $4 rac{6}{35}$ - Similar to option (B), this has the correct whole number but an incorrect fractional part. This could stem from an error in the division or subtraction step.

Since our calculated answer is $4 rac{3}{35}$ , option (A) is the correct choice. It’s always a good strategy to review the given options after solving a problem, especially in a test scenario, to confirm your answer and identify potential errors if your result doesn't match any of them. Great job, everyone!

Conclusion

So there you have it, team! We've successfully tackled the multiplication of mixed numbers, specifically $1 rac{4}{7} imes 2 rac{3}{5}$ . The key takeaways are to first convert mixed numbers into improper fractions, then multiply the numerators and denominators straight across, and finally, convert the resulting improper fraction back into a mixed number. By following these steps carefully, you can confidently solve any mixed number multiplication problem that comes your way. Remember, practice makes perfect, so keep working through these problems, and you'll become a math whiz in no time. If you ever get stuck, just retrace these steps. You've got this! Happy calculating!