Solving: (1 2/3 Of 3/10) - (50/8 * 3/5) Expression

Hey guys! Let's break down this math problem step by step. We've got to solve the expression: (1 2/3 of 3/10) - (50/8 × 3/5). It looks a bit intimidating, but don't worry, we'll get through it together. Grab your calculators or a piece of paper, and let's dive in!

Step 1: Convert Mixed Fraction to Improper Fraction

First, we need to convert the mixed fraction 1 2/3 into an improper fraction. To do this, we multiply the whole number (1) by the denominator (3) and then add the numerator (2). So, 1 × 3 + 2 = 5. We then put this result over the original denominator, which gives us 5/3. So, 1 2/3 becomes 5/3. This conversion is crucial because it makes multiplication and other operations much easier to handle. Improper fractions are our friends in these situations!

Why do we do this? Well, dealing with mixed fractions directly can be a bit messy when performing multiplication or division. Converting them to improper fractions simplifies the process and reduces the chance of making errors. Think of it as preparing our ingredients before we start cooking – it just makes everything smoother and more efficient.

So, now our expression looks like this: (5/3 of 3/10) - (50/8 × 3/5). We’re one step closer to solving it! Remember, the key is to take it one step at a time and not get overwhelmed by the entire problem. Each small conversion or calculation brings us closer to the final answer. Keep this approach in mind, and you'll find that even complex problems become manageable.

Step 2: Calculate "of"

In mathematics, the term "of" often means multiplication. So, when we see "5/3 of 3/10", we need to multiply 5/3 by 3/10. Let's do that: (5/3) × (3/10). When multiplying fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So, 5 × 3 = 15 and 3 × 10 = 30. This gives us 15/30.

Now, we can simplify this fraction. Both 15 and 30 are divisible by 15. So, we divide both the numerator and the denominator by 15: 15 ÷ 15 = 1 and 30 ÷ 15 = 2. Therefore, 15/30 simplifies to 1/2. So, (5/3 of 3/10) is equal to 1/2. This simplification is important because it makes our calculations easier later on. Dealing with smaller numbers reduces the risk of errors and keeps things manageable.

Remember, always look for opportunities to simplify fractions whenever you can. It's a good habit to develop in mathematics, and it will save you a lot of time and effort in the long run. Plus, it makes the problem look less intimidating! So, now our expression looks like this: (1/2) - (50/8 × 3/5). We’ve simplified the first part, and we’re ready to move on to the next step. Keep up the great work!

Step 3: Perform the Multiplication

Next, we need to calculate 50/8 × 3/5. Again, we multiply the numerators together and the denominators together. So, 50 × 3 = 150 and 8 × 5 = 40. This gives us 150/40. Now, let's simplify this fraction. Both 150 and 40 are divisible by 10. So, we divide both the numerator and the denominator by 10: 150 ÷ 10 = 15 and 40 ÷ 10 = 4. This simplifies to 15/4.

We can leave it as an improper fraction (15/4) or convert it to a mixed fraction. To convert it to a mixed fraction, we divide 15 by 4. The quotient is 3, and the remainder is 3. So, 15/4 is equal to 3 3/4. For the sake of simplicity, let’s stick with the improper fraction 15/4 for now. It will make our next calculation a bit easier.

Understanding how to simplify and convert fractions is a fundamental skill in mathematics. It allows us to work with numbers in their simplest form, which reduces the chance of making mistakes. So, make sure you're comfortable with these concepts. Our expression now looks like this: (1/2) - (15/4). We’re getting closer to the final answer! Just one more step to go.

Step 4: Perform the Subtraction

Now, we need to subtract 15/4 from 1/2. To subtract fractions, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. So, we need to convert 1/2 into an equivalent fraction with a denominator of 4. To do this, we multiply both the numerator and the denominator of 1/2 by 2: (1 × 2) / (2 × 2) = 2/4.

Now we can subtract: 2/4 - 15/4. When subtracting fractions with a common denominator, we subtract the numerators and keep the denominator the same. So, 2 - 15 = -13. Therefore, 2/4 - 15/4 = -13/4.

Finally, we can convert -13/4 into a mixed fraction. We divide 13 by 4. The quotient is 3, and the remainder is 1. So, -13/4 is equal to -3 1/4. Therefore, the final answer is -13/4 or -3 1/4.

Remember, when subtracting fractions, it's important to pay attention to the signs. In this case, we were subtracting a larger number from a smaller number, so the result was negative. Always double-check your work to make sure you haven't made any errors with the signs. And that's it! We've solved the expression. You did it! You are awesome!

Conclusion

So, (1 2/3 of 3/10) - (50/8 × 3/5) = -13/4 or -3 1/4. Great job working through this problem with me! Remember, the key to solving complex math problems is to break them down into smaller, manageable steps. Convert mixed fractions, simplify when possible, and find common denominators when adding or subtracting fractions. With practice and patience, you can tackle any math problem that comes your way. Keep practicing, and you'll become a math whiz in no time! If you have any questions, feel free to ask. Keep up the great work, and I'll see you in the next problem!