Math Problem: Detailed Solution With Example

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Hey guys! Let's dive into solving this math problem step-by-step. I'll show you exactly how to break it down, just like it would be on a sheet of paper. We're aiming for a crystal-clear solution to get those 80 points! So, the problem we're tackling is similar to this example: +2.1 + 3 â…— + (1 7/15). Sounds fun, right? Let's make sure we understand each part and tackle it properly to get to the answer. Understanding the basics is key to solving this type of problem. We will be using the concepts of fractions, decimals, and mixed numbers. Let's not waste any time and get started!

Understanding the Problem and Breaking it Down

Alright, first things first, let's look closely at the problem. We have a mix of decimals, whole numbers, and fractions. The main goal here is to understand how to add these different types of numbers together. The example we have is: +2.1 + 3 ⅗ + (1 7/15). It’s super important to understand what each part of the problem means. Here's a quick rundown:

  • Decimals: Like +2.1. These are numbers with a decimal point, representing parts of a whole.
  • Fractions: Like â…— and 7/15. These represent parts of a whole as well, but in a different format.
  • Mixed Numbers: Like 1 7/15. This is a combination of a whole number and a fraction. We will need to convert all mixed numbers to fractions to calculate the sum. The mixed numbers are also known as the improper fraction. The main thing to remember is to keep everything in the same format. We can either turn everything into fractions or convert everything to decimals. I will be converting everything into fractions.

To make things easier, we'll convert everything into fractions or decimals. This lets us add everything together more smoothly. This approach helps us avoid any confusion and ensures that we get the right answer! Converting all the mixed numbers into improper fractions will make the calculation process a lot easier and more precise. First, we need to convert the decimal number to a fraction. The first number is 2.1, the fraction format of this number is 21/10. Next, we need to convert the mixed numbers into improper fractions. The first mixed number to be converted is 3 â…—, which is converted to 18/5, and the last mixed number is 1 7/15, converted to 22/15. This process ensures we can perform the addition correctly. Let's make sure we're on the right track and convert everything over for a unified approach.

Converting Decimals to Fractions

Let’s start with the decimal. Converting a decimal to a fraction is pretty straightforward. For +2.1, you write it as 21/10. The number after the decimal becomes the numerator, and the denominator is a power of 10. The digits after the decimal point determine the power of 10. We have one digit after the decimal in 2.1, so we use 10 as the denominator. This is a critical step because it ensures we are adding like units. It's all about making sure everything is in a format that we can easily work with. Now, we can move forward with this approach!

Converting Mixed Numbers to Improper Fractions

Now, let's convert the mixed numbers into improper fractions. For example, the mixed number 3 â…—. To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, add the numerator, and put that over the original denominator. In this case, 3 x 5 = 15, plus the numerator 3, which equals 18. So, 3 â…— becomes 18/5. Similarly, for the mixed number 1 7/15, multiply the whole number 1 by the denominator 15, which is 15. Then add the numerator 7, which equals 22. So, 1 7/15 becomes 22/15. These steps are super important for consistency. This process allows us to combine everything into a common format!

Solving the Math Problem: Step-by-Step

Now that we have everything in fraction form, we can get to the core of the problem: actually solving it! Let's refresh our memory on what we have:

  • 2.1 becomes 21/10
  • 3 â…— becomes 18/5
  • 1 7/15 becomes 22/15

The full problem, in fraction form, becomes 21/10 + 18/5 + 22/15. Let’s make sure we find a common denominator for all these fractions. We can then add them together. Let's get started!

Finding a Common Denominator

To add fractions, we need a common denominator. The least common multiple (LCM) of 10, 5, and 15 is 30. We’ll convert each fraction to an equivalent fraction with a denominator of 30. This process is key to getting the correct answer. The main goal here is to make sure we're dealing with consistent units. So, here’s how we do it:

  • For 21/10, multiply both the numerator and denominator by 3: (21 x 3) / (10 x 3) = 63/30.
  • For 18/5, multiply both the numerator and denominator by 6: (18 x 6) / (5 x 6) = 108/30.
  • For 22/15, multiply both the numerator and denominator by 2: (22 x 2) / (15 x 2) = 44/30.

We now have the fractions 63/30, 108/30, and 44/30. We're ready to move to the next step, which is adding the fractions!

Adding the Fractions

Now we can add the numerators of the fractions and keep the common denominator. This step is pretty straightforward. It is important to know the steps to get to the answer. Here's how to add the fractions:

63/30 + 108/30 + 44/30 = (63 + 108 + 44) / 30 = 215/30.

We add the numerators and keep the same denominator. This gives us 215/30. We are now closer to the correct answer. This process leads us straight to our final answer. The key here is to keep everything consistent. It is important to remember what we did in the previous steps. Let's take a look at the final answer!

Simplifying the Answer and Final Result

We now have the answer as 215/30. We can simplify this fraction. Now, we'll try to simplify the fraction to its lowest terms. Both the numerator and denominator are divisible by 5.

  • 215 ÷ 5 = 43
  • 30 ÷ 5 = 6

So, 215/30 simplifies to 43/6. We can convert this improper fraction back into a mixed number. 43 divided by 6 is 7 with a remainder of 1. So, 43/6 is equal to 7 1/6. This is our final, simplified answer. Always make sure to simplify your fractions! It’s a good practice, and it will help you a lot in mathematics. Congrats, we solved the problem! If you follow these steps, you should get the same answer too!

Final Answer

The solution to the math problem +2.1 + 3 â…— + (1 7/15) is 7 1/6. Great job, guys! You did it!

Tips and Tricks for Similar Problems

  • Always convert all numbers to the same format: Whether you prefer fractions or decimals, stick to one. It keeps things clear.
  • Find the Least Common Denominator (LCD): This makes adding fractions a breeze.
  • Simplify, Simplify, Simplify: Always reduce your fractions to their simplest form.
  • Practice, Practice, Practice: The more you practice, the easier it gets. Try different examples to get better.
  • Double-Check Your Work: Make sure you haven't made any mistakes during the calculations. It’s easy to do, so be careful!

Conclusion

Awesome work, everyone! We successfully solved the math problem. Remember, breaking down the problem into smaller steps is essential. Make sure you practice, and don’t be afraid to ask for help! I hope this helps you get those 80 points. Good luck, and keep up the great work, everyone! I hope you liked this tutorial and can follow it to solve other problems as well. If you liked this tutorial, then give it a thumbs up!