Cracking the Code: How to Divide Mixed Numbers Like a Pro

Got a math question that’s been bugging you? Let’s tackle it together! Today’s puzzle asks, “What is the result of dividing (2 \frac{6}{7}) by (\frac{3}{4})?” Now, you’re probably thinking that sounds a bit tricky, but don’t fret! We’re going to break it down step by step.

First off, the answer choices are:

• A. (20/7)
• B. (80/21)
• C. (10/3)
• D. (24/5)

The correct answer, spoiler alert, is B. (80/21). But how do we get there? Let’s talk about transforming that mixed number into something a little less daunting.

Turning Mixed Numbers into Improper Fractions

Here’s the deal: to divide mixed numbers, it’s usually easiest to convert them into improper fractions first. So, what’s a mixed number? Think of it as a blend of whole numbers and fractions—in this case, (2 \frac{6}{7}).

To convert it into an improper fraction, we follow a simple formula:

1. Multiply the whole number (2) by the denominator (7). That gives us (2 \times 7 = 14).
2. Add the numerator (6): (14 + 6 = 20).
3. Hence, we can rewrite (2 \frac{6}{7}) as the improper fraction (\frac{20}{7}).

Let’s Get Dividing!

Now, let’s tackle the division: we want to divide (\frac{20}{7}) by (\frac{3}{4}). Remember this golden rule: dividing by a fraction is the same as multiplying by its reciprocal. So instead of dividing, we’ll flip (\frac{3}{4}) and multiply:

[ \frac{20}{7} \div \frac{3}{4} = \frac{20}{7} \times \frac{4}{3} ]

Next, we multiply the numerators and denominators together:

(\frac{20 \times 4}{7 \times 3} = \frac{80}{21})

And there you have it! When you multiply it out, you get (B. \frac{80}{21}).

A Quick Recap

So remember, when faced with complex fractions or mixed numbers:

• Convert them into improper fractions.
• Flip the second fraction (the one you’re dividing by) and change that division into multiplication.
• Multiply across the top and bottom.

And just like that, you’ve cracked the code!

Why is This Important?

If you’re preparing for exams, especially something as rigorous as the Kaplan Nursing Entrance Exam, mastering basic math skills is crucial. Nurses often deal with medication dosages, calculations, and patient information, where math plays a significant role. So, being comfortable with dividing fractions not only helps in exams but also prepares you for real-life scenarios!

So, next time someone asks you, "Can you divide a mixed number?" you'll confidently respond, "Absolutely! Here’s how!" It’s all about practice and keeping those math skills sharp.

Got it? Good! Remember, practice makes perfect, so don’t hesitate to reach out if you hit a snag. You’ve got this!