Solving Complex Mathematical Expressions: A Step-by-Step Guide

Hey guys! Math can sometimes feel like navigating a maze, especially when you're faced with a bunch of different numbers and operations all jumbled together. But don't sweat it! We're going to break down some complex mathematical expressions step by step, so you can tackle them with confidence. This guide will walk you through each problem, explaining the process in a way that's easy to understand. So, grab your pencils, and let's dive in!

1) -0.25 - 3

In tackling the first expression, -0.25 - 3, it's crucial to grasp the fundamentals of subtracting numbers, including decimals and integers. So, how do we make sense of this? Think of it like this: You're starting at -0.25 on the number line, and you need to move 3 units further to the left because you're subtracting 3. When you subtract a positive number from a negative number, you're essentially adding the magnitudes and keeping the negative sign. To solve this, we simply add the absolute values of the numbers (0.25 and 3) and keep the negative sign. 0. 25 plus 3 equals 3.25. Therefore, the final answer is -3.25. Remember, the key is to visualize the movement on the number line or think about combining debts. It's like owing 0.25 and then owing another 3 – you end up owing a total of 3.25.

Understanding this basic principle is vital because it forms the groundwork for more intricate calculations. By mastering the subtraction of decimals and integers, you're setting yourself up for success in higher-level math problems. Always remember to consider the signs of the numbers carefully and apply the rules of addition and subtraction accordingly. With practice, these types of calculations will become second nature, and you'll be solving them in no time! So, let's keep this momentum going as we move on to the next expression.

2) -91 - 0.75

Now, let's get into the second expression, -91 - 0.75. This one might look a little intimidating because we're dealing with a larger integer and a decimal. But don't worry, the same principles apply as before! We're still subtracting, which means we're moving further into the negative territory on the number line. Imagine you're starting way back at -91, and now you need to subtract another 0.75. This is similar to owing 91 dollars and then adding another debt of 0.75 dollars. To solve this, we add the absolute values of the numbers (91 and 0.75) and keep the negative sign. Adding these values is pretty straightforward: 91 plus 0.75 equals 91.75. Therefore, the final answer is -91.75. See? Not so scary after all!

The key here is to not let the size of the numbers throw you off. Whether you're working with small decimals or large integers, the rules of subtraction remain the same. Keeping track of the signs is crucial, and in this case, since we're subtracting a positive number from a negative number, the result will be even more negative. This type of problem reinforces the importance of understanding number relationships and how they behave on the number line. By consistently practicing these concepts, you'll build a solid foundation for tackling more advanced mathematical challenges. Let's move on to the next one and keep building our skills!

3) -3 - 2 - 9/20

The third expression, -3 - 2 - 9/20, introduces a fraction into the mix! Don't let that fraction scare you, though. We can handle this. The expression involves a series of subtractions, so we'll tackle them step by step. First, let's focus on the integers: -3 minus 2. As we discussed before, subtracting a positive number from a negative number means we move further into the negative zone. So, -3 minus 2 equals -5. Now, we have -5 - 9/20. To subtract the fraction 9/20 from -5, we need to convert -5 into a fraction with a denominator of 20. To do this, we multiply -5 by 20/20, which gives us -100/20. Now our expression looks like this: -100/20 - 9/20. Since both fractions have the same denominator, we can easily subtract the numerators. -100 minus 9 equals -109. So, we have -109/20. This fraction can be left as is, or we can convert it into a mixed number. -109/20 is equal to -5 9/20. This problem highlights the importance of understanding fractions and how they interact with integers. By breaking it down step by step, we were able to navigate the subtractions and arrive at the solution. Keep practicing, and fractions will become your friends in no time!

4) -27 - 5/4

Okay, let's tackle the fourth expression, -27 - 5/4. Just like the previous one, we've got an integer and a fraction hanging out together. The key here is to combine them properly using subtraction. We have -27 and we're subtracting 5/4. To do this, we'll need to convert -27 into a fraction with a denominator of 4. Multiply -27 by 4/4, and we get -108/4. Now our expression looks like this: -108/4 - 5/4. With a common denominator of 4, we can easily subtract the numerators: -108 minus 5 equals -113. So, our fraction is -113/4. If we want, we can convert this improper fraction into a mixed number. To do that, we divide 113 by 4. 113 divided by 4 is 28 with a remainder of 1. So, -113/4 is equal to -28 1/4. Or, we can keep it as the improper fraction -113/4. Both answers are perfectly valid! This problem shows us again how important it is to be comfortable working with fractions and converting between improper fractions and mixed numbers. The more you practice these skills, the easier they'll become. Let's keep moving forward!

5) -16 - 7.3

Now let's dive into the fifth expression, -16 - 7.3. This one brings us back to working with decimals, which is a nice change of pace! We're subtracting a decimal from an integer, but the same basic principle applies: when you subtract a positive number from a negative number, you're moving further into the negative territory. Imagine starting at -16 on the number line and then moving 7.3 units to the left. To solve this, we add the absolute values of the numbers (16 and 7.3) and keep the negative sign. Adding 16 and 7.3 is pretty straightforward: 16 + 7.3 = 23.3. So, the final answer is -23.3. It's like owing 16 dollars and then owing another 7.3 dollars – you end up owing a total of 23.3 dollars. This problem highlights how decimals fit into the same mathematical rules as integers. By understanding this, you can confidently tackle subtraction problems involving any combination of numbers. Keep up the great work, and let's move on to the next expression!

6) -5.8 - 17

Let's tackle the sixth expression: -5.8 - 17. Here, we're subtracting an integer from a decimal, but don't let that mix-up throw you off! The underlying principle remains the same. Think of it like this: We're starting at -5.8, and we need to subtract 17, which means moving 17 units further to the left on the number line. To solve this, we add the absolute values of the numbers (5.8 and 17) and keep the negative sign. 5. 8 plus 17 equals 22.8. Therefore, the answer is -22.8. It's just like owing 5.8 dollars and then owing another 17 dollars – your total debt is 22.8 dollars. This problem reinforces the idea that the rules of subtraction apply consistently, regardless of whether you're dealing with integers or decimals. The more you practice, the more natural these calculations will become. So, let's keep that momentum going and move on to the next challenge!

7) -4.75 - 3 - 9/20

Alright, let's dive into the seventh expression: -4.75 - 3 - 9/20. This one's a bit of a combination – we've got a decimal, an integer, and a fraction all in one place! No problem, we can handle this by breaking it down step by step. First, let's combine the decimal and the integer: -4.75 minus 3. This means we're moving 3 units further to the left from -4.75 on the number line. Adding the absolute values (4.75 and 3) gives us 7.75, so this part becomes -7.75. Now we have -7.75 - 9/20. To subtract the fraction, we need to convert everything into the same format. Let's convert 9/20 into a decimal. 9 divided by 20 is 0.45. So, we now have -7.75 - 0.45. Subtracting 0.45 from -7.75 means we add the absolute values and keep the negative sign. 7. 75 plus 0.45 equals 8.2. Therefore, the final answer is -8.2. This problem demonstrates the importance of being flexible with different types of numbers and knowing how to convert between them. By taking it one step at a time, we were able to conquer this mixed-number challenge! Keep practicing these skills, and you'll be a math whiz in no time.

8) -2 - 9.4

Last but not least, let's tackle the eighth expression: -2 - 9.4. We're back to subtracting a decimal from an integer, which we've done before, so this should feel familiar! We're starting at -2, and we need to subtract 9.4, meaning we move 9.4 units further to the left on the number line. To solve this, we add the absolute values of the numbers (2 and 9.4) and keep the negative sign. 2 plus 9.4 equals 11.4. So, the final answer is -11.4. Think of it as owing 2 dollars and then owing another 9.4 dollars – your total debt is 11.4 dollars. This problem reinforces the basic principle of subtracting numbers with different signs. By now, you've probably noticed a pattern: when subtracting a positive number from a negative number, we simply add their magnitudes and keep the negative sign. Mastering this concept is key to handling a wide range of mathematical expressions. Great job sticking with it till the end! You've tackled some challenging problems, and with practice, you'll continue to improve your math skills.

Wrapping it up, guys, I hope this step-by-step guide has helped you feel more confident in tackling complex mathematical expressions. Remember, the key is to break down each problem into smaller, manageable steps, and don't forget the importance of understanding the basic principles of subtraction and number relationships. Keep practicing, and you'll be amazed at how far you can go! You've got this!