Math Problems: Calculations And Percentage Solutions

Hey everyone! Today, we're diving into a bunch of math problems. We've got calculations involving fractions, decimals, and order of operations, followed by some percentage problems. Let's break it down step by step, making sure everyone understands the process. No worries if you're not a math whiz; we'll go through everything nice and easy. Let's get started, guys!

Solving Arithmetic Expressions: A Detailed Guide

Alright, let's tackle these arithmetic expressions. We'll follow the order of operations (PEMDAS/BODMAS – Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) to get the right answers. Remember, understanding the order is key! Let's start with the first set:

1. 4 x 6, 1-2, 2b. (5,8-3,7) x 7c. (6+3,3) ÷3d. $\frac{10}{5}$ x 2

   • a. 4 x 6,1-2: This is a bit tricky because of the way it's written. It appears there might be a typo, but we'll interpret it as (4 * 6.1) - 2. First, we multiply 4 by 6.1, which equals 24.4. Then, we subtract 2, giving us 22.4. Easy peasy!
   • b. (5.8 - 3.7) x 7: First, we solve the parentheses: 5.8 - 3.7 = 2.1. Next, we multiply 2.1 by 7, resulting in 14.7. Doing well, guys!
   • c. (6 + 3.3) ÷ 3: Inside the parentheses, 6 + 3.3 = 9.3. Then, we divide 9.3 by 3, which equals 3.1.
   • d. $\frac{10}{5}$ x 2: First, the fraction $\frac{10}{5}$ simplifies to 2. Then, we multiply 2 by 2, giving us 4.

   So, the solutions for this part are 22.4, 14.7, 3.1, and 4. This first part covers a mix of multiplication, subtraction, and division, reminding us to be careful with the order of operations.

Mastering Decimals and Operations

Now, let's move on to a new set of problems, still focusing on different arithmetic operations, paying special attention to decimals. These problems involve a combination of addition, subtraction, multiplication, and division, offering us a good chance to practice our skills. Don't be intimidated – we'll break down each step to ensure clarity. Let's see what we've got:

2. a. 2,5-4,1+2,8b. 25,5×4÷5c. 3-1÷4d. (5-6,4) x 1,5

   • a. 2.5 - 4.1 + 2.8: We start with the subtraction: 2.5 - 4.1 = -1.6. Then, we add 2.8: -1.6 + 2.8 = 1.2. Remember, the trick is to handle the positive and negative signs accurately.
   • b. 25.5 x 4 ÷ 5: We can do this in order from left to right. First, 25.5 x 4 = 102. Then, divide by 5: 102 ÷ 5 = 20.4. Another way is to divide 4 by 5 first (4 ÷ 5 = 0.8) and then multiply 25.5 by 0.8, also resulting in 20.4. Choose the method that feels easiest for you.
   • c. 3 - 1 ÷ 4: Here, we must follow the order of operations. We do the division first: 1 ÷ 4 = 0.25. Then, subtract: 3 - 0.25 = 2.75.
   • d. (5 - 6.4) x 1.5: Inside the parentheses, 5 - 6.4 = -1.4. Multiply by 1.5: -1.4 x 1.5 = -2.1. Remember to keep an eye on the negative signs!

   So, for this part, we've got 1.2, 20.4, 2.75, and -2.1. We're doing awesome! This set of problems requires careful attention to both the operations and the decimal points.

Unveiling Percentage Calculations: Your Step-by-Step Guide

Alright, now it's time to tackle some percentage problems! Percentages are super useful in real life, from calculating discounts to understanding statistics. We'll break down each calculation into easy steps. The core concept is converting the percentage to a decimal and then multiplying. Let's see how it works:

3. a. 10% of 75. b. 30% of 9. c. 32% of 10. d. 14% of 50

   • a. 10% of 75: Convert 10% to a decimal (0.10) and multiply by 75: 0.10 x 75 = 7.5.
   • b. 30% of 9: Convert 30% to a decimal (0.30) and multiply by 9: 0.30 x 9 = 2.7.
   • c. 32% of 10: Convert 32% to a decimal (0.32) and multiply by 10: 0.32 x 10 = 3.2.
   • d. 14% of 50: Convert 14% to a decimal (0.14) and multiply by 50: 0.14 x 50 = 7.

   Therefore, the solutions for this section are 7.5, 2.7, 3.2, and 7. You're doing great, guys! The key here is remembering how to convert percentages to decimals: just move the decimal point two places to the left.

Advanced Percentage Problems: Taking It Up a Notch

Now, let's crank it up a notch with some more complex percentage problems. These will help you master the skill of calculating percentages. Remember, practice makes perfect. So, let's work through these step-by-step to build your confidence. Here we go:

4. a. 150% of 60. b. 0,5% of 1 000. c. 14,4% of 200. d. 230% of 20

   • a. 150% of 60: Convert 150% to a decimal (1.50) and multiply by 60: 1.50 x 60 = 90. This means you're finding one and a half times 60.
   • b. 0.5% of 1 000: Convert 0.5% to a decimal (0.005) and multiply by 1000: 0.005 x 1000 = 5.
   • c. 14.4% of 200: Convert 14.4% to a decimal (0.144) and multiply by 200: 0.144 x 200 = 28.8.
   • d. 230% of 20: Convert 230% to a decimal (2.30) and multiply by 20: 2.30 x 20 = 46. This is like finding more than double the number 20.

   So, our final answers for this section are 90, 5, 28.8, and 46. Great job, everyone! This section shows how percentages can go above 100% and how to deal with them effectively.

Key Takeaways and Final Thoughts

Alright, guys, we've covered a lot of ground today! We started with basic arithmetic operations, moved on to working with decimals, and then got into percentage calculations. Here are the key takeaways:

• Order of Operations: Always remember PEMDAS/BODMAS to solve expressions correctly.
• Decimal Points: Pay close attention to decimal points when adding, subtracting, multiplying, and dividing.
• Percentage Conversions: To calculate a percentage, convert it to a decimal (by dividing by 100) and then multiply.

I hope this detailed guide was helpful and made the problems clearer. Keep practicing, and you'll become a math whiz in no time! Remember, math is all about practice and understanding the underlying principles. If you have any more questions, feel free to ask. See you in the next lesson, and keep up the great work!