Solving 1 + (12/13) * (3/18): A Math Problem

by Dimemap Team 45 views

Hey guys! Let's dive into this math problem together and break it down step by step. We've got a mix of fractions and whole numbers, but don't worry, it's totally manageable. We’ll make sure to clarify every step so you can easily follow along and understand the process. Let's get started!

Understanding the Problem

The problem we're tackling is: 1 + (12/13) * (3/18). At first glance, it might look a bit intimidating with the fractions, but remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order is super important to get the correct answer.

So, according to the order of operations, we need to handle the multiplication part first. That means we'll multiply (12/13) by (3/18) before we do any addition. This is a crucial step, because doing addition first would completely change the outcome. Once we've taken care of the multiplication, we'll add the result to 1. Easy peasy, right? Let's break down the multiplication part next.

Step-by-Step Solution

1. Multiply the Fractions

Okay, first things first, let's multiply those fractions: (12/13) * (3/18). When you multiply fractions, you simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So, we have:

  • Numerator: 12 * 3 = 36
  • Denominator: 13 * 18 = 234

So, the result of the multiplication is 36/234. But hold on a second! We're not done yet. This fraction looks like it can be simplified, and simplifying fractions makes things much easier to work with in the long run. Simplifying means reducing the fraction to its lowest terms, which we'll do in the next step.

2. Simplify the Fraction

Now, let's simplify 36/234. To do this, we need to find the greatest common divisor (GCD) of 36 and 234. The GCD is the largest number that divides both 36 and 234 without leaving a remainder. Figuring out the GCD might seem tricky, but there are a few ways to do it. You can list the factors of each number and find the largest one they have in common, or you can use the Euclidean algorithm, which is a more systematic approach.

In this case, the GCD of 36 and 234 is 18. That means we can divide both the numerator and the denominator by 18 to simplify the fraction:

  • 36 ÷ 18 = 2
  • 234 ÷ 18 = 13

So, 36/234 simplifies to 2/13. See? Much easier to handle! Now that we've simplified the fraction, we're ready to move on to the next step, which is adding this simplified fraction to 1.

3. Add to 1

Alright, we've simplified the multiplication part to 2/13. Now we need to add this to 1. So, the problem now looks like this: 1 + (2/13). To add a whole number and a fraction, we need to express the whole number as a fraction with the same denominator as the other fraction. In this case, we want the denominator to be 13.

So, we can rewrite 1 as 13/13 because any number divided by itself is 1. Now we have:

13/13 + 2/13

Now that the denominators are the same, we can simply add the numerators and keep the denominator the same:

  • (13 + 2) / 13 = 15/13

So, 1 + (2/13) = 15/13. We're almost there! We have our answer, but sometimes it's helpful to express the answer as a mixed number, especially if the fraction is improper (meaning the numerator is greater than the denominator). Let's convert 15/13 to a mixed number in the next step.

4. Convert to a Mixed Number (Optional)

We have the answer as 15/13, which is an improper fraction. To convert it to a mixed number, we need to see how many times 13 goes into 15. Well, 13 goes into 15 one time with a remainder.

  • 15 ÷ 13 = 1 with a remainder of 2

So, the whole number part of our mixed number is 1, and the remainder 2 becomes the numerator of the fractional part, with the denominator staying the same (13). Therefore, 15/13 as a mixed number is 1 2/13.

Final Answer

So, guys, after breaking it down step by step, we've found that 1 + (12/13) * (3/18) = 15/13, which can also be expressed as the mixed number 1 2/13. See? Not so scary after all!

Key Takeaways

  • Order of Operations: Remember PEMDAS/BODMAS! Always handle multiplication and division before addition and subtraction.
  • Simplifying Fractions: Always simplify fractions to their lowest terms to make calculations easier.
  • Adding Fractions: Make sure the denominators are the same before adding the numerators.
  • Improper Fractions and Mixed Numbers: Know how to convert between improper fractions and mixed numbers.

Practice Makes Perfect

Math can seem tough sometimes, but the more you practice, the easier it becomes. Try working through similar problems to reinforce what you've learned here. You can even change the numbers in this problem and solve it again to test your understanding. And remember, there are tons of resources out there to help you, like online calculators, math websites, and even tutors if you need some extra support. Keep practicing, and you'll be a math whiz in no time!

Conclusion

I hope this step-by-step solution helped you understand how to solve this problem! Remember, math is all about breaking things down into smaller, manageable steps. Don't be afraid to tackle those fractions and mixed numbers – you've got this! If you have any more math questions, feel free to ask. Keep up the great work, and happy calculating!