Solving Math: Expression Calculation Guide

Hey math enthusiasts! Let's dive into the fascinating world of mathematical expressions and learn how to solve them step-by-step. Today, we're going to break down the expression: (-6 2/5 + 3) * (3 - 4.5) * 5/17. Don't worry, it might look a little intimidating at first, but trust me, it's totally manageable! We'll go through each part of the problem, explaining the concepts and calculations in a way that's easy to grasp. We'll start with converting mixed numbers to improper fractions, then tackle the operations inside the parentheses, and finally, we'll simplify the entire expression. So, grab your pencils, and let's get started. By the end of this guide, you'll be able to solve similar expressions with confidence. This guide will help build a strong foundation for future math concepts and boost your problem-solving skills, and we'll transform this seemingly complex expression into a simple, understandable solution. Ready? Let's go!

Step 1: Convert Mixed Numbers to Improper Fractions

Okay, guys, the first thing we need to do is deal with that pesky mixed number, which is -6 2/5. Remember, a mixed number is a whole number combined with a fraction. To make our lives easier, we need to convert this into an improper fraction. An improper fraction is simply a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). So, how do we convert -6 2/5? Here's the trick: Multiply the whole number (-6) by the denominator (5) and then add the numerator (2). Keep the same denominator (5). So, -6 * 5 = -30. Then, -30 + 2 = -28. Therefore, -6 2/5 becomes -28/5. Awesome!

Now our expression looks like this: (-28/5 + 3) * (3 - 4.5) * 5/17. See? Not so scary anymore. This step is crucial because it allows us to perform arithmetic operations more efficiently. Working with improper fractions makes it easier to add, subtract, multiply, and divide. Always make sure to check your work; a small mistake here can throw off the entire calculation. Double-checking each conversion can prevent larger errors later on. When converting mixed numbers to improper fractions, keep in mind the sign of the original mixed number. In our case, the mixed number was negative, so the resulting improper fraction will also be negative. This is a common mistake, so pay close attention! Mastering this skill will not only help you solve this specific problem but will also boost your overall math abilities. Keep practicing, and you'll become a pro in no time! Remember, consistency and attention to detail are key in math. The more you practice converting mixed numbers, the easier and faster it will become.

Why Convert to Improper Fractions?

• Simplifies Operations: Working with improper fractions often simplifies addition and subtraction, especially when dealing with different denominators.
• Consistency: It provides a consistent format for all fractions, making calculations less prone to errors.
• Foundation: This step is fundamental to further math concepts like multiplying and dividing fractions.

Step 2: Solve the Operations Within Parentheses

Alright, now that we've taken care of the mixed number, let's tackle the parentheses. This is where we perform the operations inside the brackets. We have two sets of parentheses: (-28/5 + 3) and (3 - 4.5). Let's start with the first set, (-28/5 + 3). To add -28/5 and 3, we first need to convert 3 into a fraction with the same denominator as -28/5, which is 5. So, 3 becomes 15/5. Now we have -28/5 + 15/5. Adding these two fractions, we get (-28 + 15) / 5 = -13/5. So, the first set of parentheses simplifies to -13/5. Great job!

Next, let's look at the second set of parentheses: (3 - 4.5). This one is much simpler. 3 - 4.5 = -1.5. However, to keep everything consistent with fractions, let's convert -1.5 into a fraction. We can rewrite -1.5 as -3/2. So, the second set of parentheses simplifies to -3/2. Now, our expression looks like this: (-13/5) * (-3/2) * 5/17. We're getting closer to the final answer, and it's starting to look much more manageable. Remember, the order of operations is crucial. Always solve operations within parentheses first, then move on to multiplication and division. Now we are ready to multiply the simplified terms. This stage is all about precision and focus. Always double-check your calculations. Ensure each step is carried out carefully to avoid any errors. Practicing these kinds of calculations helps improve your accuracy and speed. This stage reinforces the foundational principles of arithmetic and ensures that each step flows smoothly into the next. Remember that understanding the order of operations helps you solve more complex math problems. Taking your time here will help make the final calculation easier. By practicing these steps, you build a solid understanding of how to work with fractions and decimal numbers.

Tips for Solving Parentheses Operations

• Order of Operations: Always follow the order of operations (PEMDAS/BODMAS).
• Common Denominators: Make sure fractions have a common denominator before adding or subtracting.
• Decimal to Fraction: Convert decimals to fractions for easier calculations.

Step 3: Multiply the Fractions

Okay, guys, we're in the home stretch! Now it's time to multiply the fractions. Our expression is now (-13/5) * (-3/2) * 5/17. When multiplying fractions, we multiply the numerators together and the denominators together. So, first, let's multiply (-13/5) * (-3/2). A negative times a negative is a positive, so (-13 * -3) = 39 and (5 * 2) = 10. That simplifies to 39/10. Our expression now looks like this: (39/10) * (5/17).

Next, multiply the numerators: 39 * 5 = 195. Then, multiply the denominators: 10 * 17 = 170. This gives us 195/170. But wait! We can simplify this fraction further. Both 195 and 170 are divisible by 5. So, divide the numerator and the denominator by 5. 195 / 5 = 39 and 170 / 5 = 34. Therefore, 195/170 simplifies to 39/34. That's our final answer! The original, seemingly complicated expression simplifies to a relatively straightforward fraction. Congratulations, you've successfully solved the expression! Now you can confidently tackle similar math problems. Remember that math is all about practice and understanding. The more problems you solve, the more comfortable you'll become. Keep up the great work, and you'll be a math whiz in no time. This final step brings together all the previous steps, showcasing how each part of the process contributes to the overall solution. Simplifying the fraction is always the last thing to do. Always reduce your fractions to their simplest forms. This not only makes your answer neater but also ensures that you have found the most accurate solution. Keep in mind that math is a journey, not a destination. Celebrate each small win, and don't be discouraged by challenges; they are opportunities to learn and grow. Practice consistently, and you will become proficient in solving mathematical expressions.

Simplifying Fractions

• Find the Greatest Common Divisor (GCD): Divide both the numerator and the denominator by their GCD.
• Reduce to Lowest Terms: Always simplify your fractions to their simplest form.

Conclusion: Practice and Mastery

So, there you have it, guys! We've successfully solved the expression (-6 2/5 + 3) * (3 - 4.5) * 5/17, and our final answer is 39/34. It might seem tricky at first, but by breaking it down into smaller, manageable steps, we can solve any expression. Remember, practice makes perfect. The more you work through different problems, the more comfortable you'll become with various mathematical concepts. Don't be afraid to make mistakes; they are a crucial part of the learning process. Each time you stumble, you learn something new and gain a deeper understanding. So, keep practicing, keep learning, and keep challenging yourself. Math is a rewarding subject that opens doors to endless possibilities. I hope this guide has helped you understand how to solve this expression. Keep exploring the world of mathematics and enjoy the journey!

Disclaimer: This guide is for educational purposes. Always double-check your calculations and consult with a teacher or tutor if you need further assistance.