Solving Math Problems: Even-Numbered Calculations

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Solving Math Problems: Even-Numbered Calculations

Hey math enthusiasts! Today, we're diving into a set of interesting math problems. Specifically, we'll be tackling the even-numbered questions from a problem set, applying our skills in fractions, mixed numbers, and basic arithmetic operations. Let's get started and break down these problems step-by-step. This approach helps in understanding the concepts and building a solid foundation in mathematics. We'll focus on clarity, ensuring that each step is easy to follow. Our main objective is not just to find the answers, but also to explain how we arrive at those answers. So, buckle up, grab your pens and paper, and let's conquer these problems together! We're going to ensure that we approach each problem systematically. This approach is key to accuracy and understanding. Let's make sure our math journey is both enjoyable and educational.

Problem 2: (7/12 - 1/3) × 16/19

Alright, guys, let's tackle this fraction problem. The first step involves subtracting the fractions inside the parentheses. To do this, we need a common denominator. The least common multiple (LCM) of 12 and 3 is 12, so we'll convert 1/3 to an equivalent fraction with a denominator of 12. Remember, when we are dealing with fractions, it is vital to apply the basic rules of arithmetic operations such as addition, subtraction, multiplication, and division. First, we need to convert the fractions so they can be subtracted and added. We will rewrite 1/3 as 4/12. This makes our problem (7/12 - 4/12) × 16/19. Now that both fractions have the same denominator, we can easily subtract them. 7/12 minus 4/12 equals 3/12. So, our problem now looks like this: (3/12) × 16/19. Next, before multiplying, we can simplify 3/12. This fraction can be reduced to 1/4. We divide both the numerator and denominator by 3. Our expression is now (1/4) × 16/19. To multiply fractions, we multiply the numerators together and the denominators together. 1 multiplied by 16 equals 16. 4 multiplied by 19 equals 76. Therefore, the result of (1/4) × 16/19 is 16/76. Finally, we simplify this fraction. Both 16 and 76 are divisible by 4. So, we divide both the numerator and the denominator by 4. This results in the final answer of 4/19. This detailed breakdown ensures you understand every step and the reasoning behind each calculation. We encourage you to always double-check your work to avoid any potential errors.

Step-by-Step Breakdown of Problem 2

Here’s a simplified breakdown to clarify the process.

  1. Find a Common Denominator: Convert 1/3 to 4/12.
  2. Subtract Fractions: (7/12 - 4/12) = 3/12.
  3. Simplify: Reduce 3/12 to 1/4.
  4. Multiply Fractions: (1/4) × 16/19 = 16/76.
  5. Simplify: Reduce 16/76 to 4/19. The final answer is 4/19!

Problem 4: (11/24 + 1/6) × 1 3/5

Time for another fraction adventure, folks! This problem involves both addition and multiplication, along with a mixed number. First things first, we must handle the operation inside the parentheses. The fractions 11/24 and 1/6 need to be added. To add them, we need a common denominator. The LCM of 24 and 6 is 24, so we will convert 1/6 to an equivalent fraction with a denominator of 24. This conversion transforms 1/6 into 4/24. Our problem becomes (11/24 + 4/24) × 1 3/5. Add the fractions within the parentheses: 11/24 + 4/24 equals 15/24. Now, we have (15/24) × 1 3/5. Before we proceed, let's convert the mixed number 1 3/5 into an improper fraction. Multiply the whole number (1) by the denominator (5), which gives us 5. Add the numerator (3) to get 8. Place this over the original denominator to get 8/5. Our problem is now (15/24) × 8/5. To multiply these fractions, we multiply the numerators (15 and 8) and the denominators (24 and 5). 15 multiplied by 8 equals 120. 24 multiplied by 5 equals 120. This gives us 120/120, which simplifies to 1. Therefore, the solution to this problem is 1. Remember that consistent practice with these types of problems will boost your speed and accuracy. Always remember to simplify your fractions to their lowest terms whenever possible. This will make your calculations easier and will reduce the chance of errors.

Step-by-Step Breakdown of Problem 4

Let’s make it easier to follow:

  1. Find a Common Denominator: Convert 1/6 to 4/24.
  2. Add Fractions: (11/24 + 4/24) = 15/24.
  3. Convert Mixed Number: 1 3/5 to 8/5.
  4. Multiply Fractions: (15/24) × 8/5 = 120/120.
  5. Simplify: 120/120 = 1. The final answer is 1!

Problem 6: (7 - 2 5/16) × 4/25

Alright, friends, let's wrap this up with problem 6. This one includes subtraction with a mixed number and multiplication. The first step here is to deal with the subtraction inside the parentheses. We are subtracting a mixed number from a whole number. To perform this, we need to convert the whole number (7) to a form that allows us to subtract the fraction 5/16. We can rewrite 7 as 6 16/16. Now, the problem becomes (6 16/16 - 2 5/16) × 4/25. Subtract the whole numbers (6 - 2 = 4) and subtract the fractions (16/16 - 5/16 = 11/16). This results in 4 11/16. Our problem now looks like this: 4 11/16 × 4/25. Convert the mixed number 4 11/16 into an improper fraction. Multiply 4 by 16 which is 64. Add 11 to get 75. Keep the denominator the same to get 75/16. So now we have (75/16) × 4/25. Multiply the numerators: 75 multiplied by 4 is 300. Multiply the denominators: 16 multiplied by 25 is 400. This gives us 300/400. Finally, simplify the fraction 300/400. Both the numerator and the denominator are divisible by 100. So, 300 divided by 100 is 3, and 400 divided by 100 is 4. Therefore, the final answer is 3/4. This concludes our math problem journey. Keep practicing and keep up the great work. Math can be fun when approached systematically and with a positive attitude.

Step-by-Step Breakdown of Problem 6

Let's break down the steps to make it easier to digest:

  1. Rewrite Whole Number: 7 as 6 16/16.
  2. Subtract Mixed Number: (6 16/16 - 2 5/16) = 4 11/16.
  3. Convert to Improper Fraction: 4 11/16 to 75/16.
  4. Multiply Fractions: (75/16) × 4/25 = 300/400.
  5. Simplify: Reduce 300/400 to 3/4. The final answer is 3/4!

Conclusion

Congratulations, everyone, for successfully completing these math problems! We've covered a lot of ground today, from fraction subtraction and addition to mixed numbers and simplifying. Remember, practice is key. The more you practice, the more comfortable and confident you will become with these types of problems. Each problem is an opportunity to learn and hone your math skills. Also, it’s beneficial to review each step to find if there are any mistakes and to get familiar with mathematical principles. Understanding the why behind each step is just as important as getting the correct answer. So, keep up the excellent work, and always keep exploring the world of math! Keep practicing, and you'll become a math whiz in no time!