Subtracting Mixed Numbers: A Step-by-Step Guide

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Hey guys! Today, we're diving into the world of subtracting mixed numbers. Specifically, we're going to tackle the problem: $8 \frac{1}{6} - 4 \frac{3}{6}$. Don't worry if it looks a little intimidating at first. We'll break it down step-by-step so it's super easy to understand. Whether you're a student struggling with homework or just looking to brush up on your math skills, this guide is for you!

Understanding Mixed Numbers

Before we jump into the subtraction, let's make sure we're all on the same page about what mixed numbers actually are. A mixed number is simply a combination of a whole number and a fraction. Think of it like having a whole pizza and a slice or two left over. The whole pizza is the whole number, and the leftover slices represent the fraction.

In our problem, $8 \frac{1}{6}$ and $4 \frac{3}{6}$ are both mixed numbers. The whole numbers are 8 and 4, respectively, and the fractions are $ rac{1}{6}$ and $ rac{3}{6}$. Got it? Great! Now, let's get to the good stuff: subtracting these numbers.

Converting Mixed Numbers to Improper Fractions

The first key step in subtracting mixed numbers (especially when the fraction you're subtracting is larger than the first fraction) is to convert them into improper fractions. An improper fraction is one where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This might sound a little strange, but it makes subtraction much easier.

So, how do we do this conversion? It's a simple two-step process:

  1. Multiply the whole number by the denominator of the fraction.
  2. Add the numerator of the fraction to the result.
  3. Write this new number as the numerator, keeping the original denominator.

Let's apply this to our first mixed number, $8 \frac{1}{6}$:

  1. Multiply the whole number (8) by the denominator (6): 8 * 6 = 48
  2. Add the numerator (1) to the result: 48 + 1 = 49
  3. So, $8 \frac{1}{6}$ converted to an improper fraction is $ rac{49}{6}$.

Now, let's do the same for $4 \frac{3}{6}$:

  1. Multiply the whole number (4) by the denominator (6): 4 * 6 = 24
  2. Add the numerator (3) to the result: 24 + 3 = 27
  3. So, $4 \frac{3}{6}$ converted to an improper fraction is $ rac{27}{6}$.

Awesome! We've now transformed our mixed numbers into improper fractions: $ rac{49}{6} - \frac{27}{6}$.

Subtracting the Fractions

Now that we have improper fractions with the same denominator (which is 6 in this case), the subtraction becomes super straightforward. When the denominators are the same, all you have to do is subtract the numerators. The denominator stays the same.

So, we have $\frac{49}{6} - \frac{27}{6}$. Subtracting the numerators, we get 49 - 27 = 22. Therefore, the result is $\frac{22}{6}$.

Remember: When you are subtracting fractions, ensure they have the same denominator. If not, you need to find a common denominator before you can subtract.

Simplifying the Improper Fraction

We've got our answer as an improper fraction, $\frac{22}{6}$, but it's not quite in its simplest form yet. We need to simplify it. The first thing we can do is see if we can reduce the fraction. Both 22 and 6 are even numbers, so we can divide them both by their greatest common factor, which is 2.

Dividing both the numerator and the denominator by 2, we get: $\frac{22 \div 2}{6 \div 2} = \frac{11}{3}$.

So, our simplified improper fraction is $\frac{11}{3}$. But the original question asked us to write the answer as a mixed number, so we're not quite done yet!

Converting Back to a Mixed Number

To convert an improper fraction back to a mixed number, we need to divide the numerator by the denominator. The quotient (the whole number result) becomes the whole number part of our mixed number. The remainder becomes the numerator of the fraction, and we keep the original denominator.

Let's apply this to $\frac{11}{3}$. Divide 11 by 3:

  • 11 ÷ 3 = 3 with a remainder of 2

So:

  • The whole number part is 3.
  • The remainder is 2, which becomes the new numerator.
  • The denominator stays as 3.

Therefore, $\frac{11}{3}$ converted to a mixed number is $3 \frac{2}{3}$.

The Final Answer

We've done it! We've successfully subtracted the mixed numbers $8 \frac{1}{6} - 4 \frac{3}{6}$ and simplified the answer as a mixed number. The final answer is $3 \frac{2}{3}$.

So, the correct answer is B. $3 \frac{2}{3}$.

Key Takeaways

Let's recap the key steps we took to solve this problem:

  1. Convert Mixed Numbers to Improper Fractions: This is crucial for easier subtraction, especially when the fraction being subtracted is larger.
  2. Subtract the Fractions: Once you have improper fractions with a common denominator, subtract the numerators.
  3. Simplify the Resulting Fraction: Reduce the fraction if possible and convert it back to a mixed number if needed.

By following these steps, you can confidently subtract any mixed numbers that come your way!

Practice Makes Perfect

Now that you've seen how it's done, the best way to master subtracting mixed numbers is to practice! Try working through some similar problems on your own. You can even make up your own examples. The more you practice, the more comfortable you'll become with the process.

Remember, guys, math is like any other skill – it gets easier with practice. So, keep at it, and you'll be a pro at subtracting mixed numbers in no time!

Additional Tips and Tricks

  • Always double-check your work: It's easy to make a small mistake, so take a moment to review your calculations.
  • Use visual aids: If you're struggling to understand the concept, try drawing diagrams or using visual aids to represent the fractions.
  • Break down the problem: If the problem seems overwhelming, break it down into smaller, more manageable steps.
  • Don't be afraid to ask for help: If you're still stuck, don't hesitate to ask your teacher, a tutor, or a friend for help. We all need a little help sometimes!

Subtracting mixed numbers might seem tricky at first, but with a little practice and the right approach, you can conquer it. Just remember to convert to improper fractions, subtract, simplify, and convert back if necessary. You've got this! Keep practicing, and you'll become a subtraction superstar in no time.