Dividing Fractions: 34 3/4 Divided By 2

by Jhon Lennon 40 views

Hey guys! Let's break down how to divide the mixed number 34 3/4 by 2 and express the result as a fraction. This might seem a bit tricky at first, but don't worry, we'll go through it step by step to make sure you understand exactly how it's done. So, grab your pencils and let's dive in!

Converting Mixed Numbers to Improper Fractions

First things first, we need to convert the mixed number 34 3/4 into an improper fraction. An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This makes it much easier to perform division. To convert 34 3/4, we multiply the whole number part (34) by the denominator (4) and then add the numerator (3). This result becomes our new numerator, and we keep the same denominator.

So, the calculation looks like this:

(34 * 4) + 3 = 136 + 3 = 139

Therefore, 34 3/4 as an improper fraction is 139/4. Now that we have our mixed number converted into an improper fraction, we can move on to the division step. Remember, converting to an improper fraction is crucial because it simplifies the process of dividing by a whole number. Trying to divide a mixed number directly can be confusing, but with this conversion, we're setting ourselves up for success. Make sure you take your time with this step and double-check your calculations to ensure accuracy. Understanding this conversion is fundamental not just for this problem, but for many other fraction-related calculations you'll encounter. Once you've mastered converting mixed numbers to improper fractions, you'll find that many seemingly complex problems become much more manageable. Keep practicing, and you'll get the hang of it in no time!

Dividing by a Whole Number

Now that we have 34 3/4 represented as the improper fraction 139/4, we can divide it by 2. Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of that whole number. The reciprocal of 2 is 1/2. So, we're essentially multiplying 139/4 by 1/2.

The calculation looks like this:

(139/4) / 2 = (139/4) * (1/2)

When multiplying fractions, we multiply the numerators together and the denominators together:

139 * 1 = 139 4 * 2 = 8

So, (139/4) * (1/2) = 139/8. Therefore, 34 3/4 divided by 2 is 139/8. This might seem like a straightforward step, but understanding why we multiply by the reciprocal is crucial. Dividing by a number is the same as multiplying by its inverse, and for whole numbers, the inverse is simply 1 divided by that number. This concept extends to all types of fractions and numbers, so grasping it now will help you in more advanced math later on. Also, remember that multiplying fractions is generally easier than dividing them, which is why converting the division problem into a multiplication problem simplifies things so much. Always double-check your multiplication to avoid errors, and make sure you're clear on which numbers are the numerators and which are the denominators. With practice, dividing fractions will become second nature, and you'll be able to tackle these problems with confidence.

Simplifying the Improper Fraction

Okay, so we've found that 34 3/4 divided by 2 is 139/8. Now, let's simplify this improper fraction into a mixed number. An improper fraction, as we mentioned earlier, has a numerator larger than its denominator. To convert it back to a mixed number, we need to divide the numerator (139) by the denominator (8).

When we divide 139 by 8, we get 17 with a remainder of 3. This means that 8 goes into 139 seventeen times, with 3 left over. The quotient (17) becomes the whole number part of our mixed number, the remainder (3) becomes the new numerator, and we keep the same denominator (8).

So, 139/8 as a mixed number is 17 3/8. Therefore, 34 3/4 divided by 2 is 17 3/8. Simplifying improper fractions to mixed numbers is often preferred because it gives a clearer sense of the quantity. While 139/8 is technically correct, 17 3/8 provides a more intuitive understanding of the value. Think of it like having 139 slices of a pie that's cut into 8 slices each; it's easier to visualize 17 whole pies and 3 extra slices. This step is particularly useful when you need to compare quantities or use the result in a real-world context. Always remember to check if your improper fraction can be simplified further. Sometimes, both the numerator and denominator can be divided by a common factor, which would simplify the fraction even more before converting it to a mixed number. Practice these conversions regularly, and you'll become proficient at quickly and accurately simplifying fractions.

Final Answer

So, to recap, we started with the problem of dividing 34 3/4 by 2. We converted the mixed number 34 3/4 into the improper fraction 139/4. Then, we divided 139/4 by 2, which is the same as multiplying 139/4 by 1/2, resulting in 139/8. Finally, we simplified the improper fraction 139/8 into the mixed number 17 3/8.

Therefore, 34 3/4 divided by 2 is 17 3/8.

Practice Problems

To make sure you've really got this down, try these practice problems:

  1. 25 1/2 divided by 3
  2. 16 2/3 divided by 4
  3. 42 5/8 divided by 5

Work through each problem step by step, converting mixed numbers to improper fractions, dividing, and then simplifying. Check your answers with a calculator if you need to, but try to do the calculations by hand to reinforce your understanding.

Tips for Success

  • Always convert mixed numbers to improper fractions first. This makes the division process much smoother.
  • Remember that dividing by a number is the same as multiplying by its reciprocal.
  • Simplify your fractions whenever possible. This makes the answer easier to understand and work with.
  • Practice regularly! The more you practice, the more comfortable you'll become with these types of problems.

Conclusion

Dividing fractions might seem a little daunting at first, but with a clear understanding of the steps involved and plenty of practice, you'll be solving these problems like a pro in no time. Remember, the key is to break down the problem into smaller, manageable steps and to take your time to ensure accuracy. Keep practicing, and you'll master dividing fractions in no time! You've got this!