Solve: (3 / X) * (2 / 9) = 1 / 6 - Find The Missing Number!

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Alright, guys, let's dive into this math problem! We've got an equation with a missing number, and our mission is to find out what that number is. The equation looks like this: (3 / x) * (2 / 9) = (1 / 6). It might seem a bit tricky at first, but don't worry, we'll break it down step by step so it's super easy to understand. So, grab your pencils, and let's get started!

Understanding the Equation

Let's start by really understanding what this equation is telling us. We have a fraction, 3 divided by an unknown number x, multiplied by another fraction, 2 divided by 9. The result of this multiplication is supposed to be 1 divided by 6. Our goal is to figure out what number x needs to be for this whole thing to make sense.

Why is this important, you ask? Well, equations like these show up all over the place in math and science. Whether you're calculating how much pizza each person gets at a party or figuring out the speed of a rocket, understanding how to solve for unknowns is a crucial skill. Plus, it's a great way to flex those brain muscles!

So, let's recap the key parts:

  • 3 / x: This is the first fraction. We need to find out what x is.
  • 2 / 9: This is the second fraction. We know both the numerator (2) and the denominator (9).
  • 1 / 6: This is the result of multiplying the first two fractions. We want to make the left side of the equation equal to this.

Now that we've got a good handle on what the equation means, let's move on to simplifying it. By simplifying, we can make the equation easier to work with and get closer to finding our missing number.

Simplifying the Equation

Okay, let's make this equation a bit less intimidating. Right now, we have (3 / x) * (2 / 9) = (1 / 6). The first thing we can do is simplify the left side by multiplying the two fractions together. When you multiply fractions, you multiply the numerators (the top numbers) and the denominators (the bottom numbers).

So, we have:

(3 * 2) / (x * 9) = 1 / 6

This simplifies to:

6 / (9x) = 1 / 6

Now, the equation looks much cleaner! We've combined the two fractions on the left into a single fraction. The equation now tells us that 6 divided by 9 times x is equal to 1 divided by 6.

But wait, there's more we can do! Notice that both 6 and 9 have a common factor: 3. We can simplify the fraction 6 / 9 by dividing both the numerator and the denominator by 3. This gives us:

(6 / 3) / (9 / 3) = 2 / 3

So, we can rewrite our equation as:

2 / (3x) = 1 / 6

This is even better! By simplifying the fraction, we've made the numbers smaller and easier to work with. Our equation now says that 2 divided by 3 times x is equal to 1 divided by 6. Believe it or not, we're getting closer to solving for x! The key to simplifying equations is to break them down into smaller, more manageable parts. By doing this, we can make the problem much less daunting and increase our chances of finding the correct answer. So, take a deep breath, and let's keep going!

Solving for x

Alright, now for the fun part: solving for x! We've simplified our equation to 2 / (3x) = 1 / 6. There are a couple of ways we can tackle this. One common method is to use cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting them equal to each other.

So, we multiply 2 by 6 and 1 by 3x:

2 * 6 = 1 * (3x)

This simplifies to:

12 = 3x

Now we're getting somewhere! We have a simple equation that relates 12 to 3 times x. To isolate x, we need to get rid of the 3 that's multiplying it. We can do this by dividing both sides of the equation by 3:

12 / 3 = (3x) / 3

This gives us:

4 = x

Ta-da! We've found our missing number! x is equal to 4. This means that if we plug 4 back into our original equation, it should all work out. Let's check our answer to make sure we didn't make any mistakes.

Checking the Answer

Okay, so we think that x = 4. To make sure we're right, let's plug that value back into our original equation: (3 / x) * (2 / 9) = (1 / 6).

Replacing x with 4, we get:

(3 / 4) * (2 / 9) = 1 / 6

Now, let's multiply the fractions on the left side:

(3 * 2) / (4 * 9) = 1 / 6

This simplifies to:

6 / 36 = 1 / 6

We can simplify the fraction 6 / 36 by dividing both the numerator and the denominator by 6:

(6 / 6) / (36 / 6) = 1 / 6

This gives us:

1 / 6 = 1 / 6

Success! The left side of the equation is equal to the right side. This means that our answer, x = 4, is correct. High five! Checking your answer is always a good idea to make sure you haven't made any silly mistakes along the way. Plus, it gives you that extra bit of confidence that you've nailed the problem. So, remember to always double-check your work, guys!

Conclusion

So, there you have it! We successfully solved the equation (3 / x) * (2 / 9) = (1 / 6) and found that the missing number, x, is equal to 4. We did this by:

  1. Understanding the equation: We made sure we knew what each part of the equation meant.
  2. Simplifying the equation: We made the equation easier to work with by multiplying and reducing fractions.
  3. Solving for x: We used cross-multiplication to isolate x and find its value.
  4. Checking the answer: We plugged our answer back into the original equation to make sure it worked.

By following these steps, you can solve all sorts of equations with missing numbers. Remember, math is all about breaking down complex problems into smaller, more manageable steps. So, don't be afraid to take your time, ask questions, and practice, practice, practice! With a little bit of effort, you'll be solving equations like a pro in no time. Keep up the great work, guys!