Solve: 3/4 Is 60% Of What Number?

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Hey guys! Let's dive into this math problem together and figure out what number 3/4 represents when it's 60% of the total. This is a classic percentage problem, and we'll break it down step-by-step so it’s super clear. So, grab your thinking caps, and let's get started!

Understanding the Problem

Before we jump into calculations, let's make sure we understand what the question is asking. We're given that 3/4 is 60% of some unknown number. Our mission is to find that mystery number. To do this, we need to translate the words into a mathematical equation. Think of it like turning a riddle into a solvable puzzle. We'll use the concepts of percentages and fractions to crack the code. Remember, percentages are just fractions out of 100, and fractions represent parts of a whole. Combining these ideas will lead us to the solution.

Keywords here are “is” which often means equals (=) in math, and “of” which usually indicates multiplication (*). So, we’re looking to set up an equation where we can isolate the unknown variable, which will represent the number we're trying to find. Breaking it down like this makes the problem way less intimidating, right? Now, let's move on to the next part and set up the equation!

Setting Up the Equation

The key to solving percentage problems is translating the words into a mathematical equation. Let's break down the sentence "3/4 is 60% of what number?" piece by piece.

  • "3/4 is" can be written as 3/4 =
  • "60% of" can be written as 60/100 *
  • "what number?" can be represented by a variable, let's use x

Putting it all together, our equation looks like this:

3/4 = (60/100) * x

Now, we have a clear equation that we can solve. The next step involves simplifying the equation to make it easier to work with. We'll start by dealing with the percentage and then isolate x to find our answer. Remember, the goal is to get x all by itself on one side of the equation. This is where our algebra skills come in handy! So, don’t worry, we've got this. Let’s move on to simplifying and solving!

Simplifying the Equation

Before we start isolating x, let's simplify the equation to make our calculations easier. We have:

3/4 = (60/100) * x

The fraction 60/100 can be simplified. Both 60 and 100 are divisible by 20, so we can reduce the fraction:

60 Ă· 20 = 3 100 Ă· 20 = 5

So, 60/100 simplifies to 3/5. Now our equation looks like this:

3/4 = (3/5) * x

This is much cleaner and easier to work with! Simplifying fractions before diving into the algebra is always a good move. It reduces the chances of making errors and keeps the numbers manageable. The next step is to isolate x. To do this, we need to get rid of the 3/5 that’s being multiplied by x. How do we do that? We'll use the magic of inverse operations! Let’s jump into the next section and see how it’s done.

Isolating the Variable

Alright, we're at the crucial step where we isolate the variable x. Our simplified equation is:

3/4 = (3/5) * x

To isolate x, we need to get rid of the 3/5 that's being multiplied by it. We can do this by multiplying both sides of the equation by the reciprocal of 3/5, which is 5/3. Remember, whatever we do to one side of the equation, we must do to the other to keep it balanced.

So, we multiply both sides by 5/3:

(5/3) * (3/4) = (5/3) * (3/5) * x

On the right side, (5/3) * (3/5) cancels out, leaving us with just x. On the left side, we multiply the fractions:

(5 * 3) / (3 * 4) = 15/12

So our equation now looks like this:

15/12 = x

We're almost there! Now, we just need to simplify the fraction 15/12 to get our final answer. Let’s head to the next section to see how it's done.

Simplifying the Result

Okay, we've reached the final stretch! We've got:

x = 15/12

Now we need to simplify the fraction 15/12. Both 15 and 12 are divisible by 3, so let's divide both the numerator and the denominator by 3:

15 Ă· 3 = 5 12 Ă· 3 = 4

So, 15/12 simplifies to 5/4.

Therefore, x = 5/4.

We can also express 5/4 as a mixed number. To do this, we divide 5 by 4:

5 Ă· 4 = 1 with a remainder of 1

So, 5/4 is equal to 1 and 1/4.

And there you have it! We've found the number that 3/4 is 60% of. But before we wrap up, let's make sure we’ve answered the question completely and clearly. In the next section, we'll summarize our solution.

Final Answer

Alright, let's wrap this up with a nice, clear answer. We started with the question: “3/4 is 60% of what number?” After working through the steps, we found that:

x = 5/4 or 1 1/4

So, 3/4 is 60% of 5/4 (or 1 1/4). We can state our final answer clearly:

Answer: 3/4 is 60% of 5/4 (or 1 1/4).

To double-check, we can calculate 60% of 5/4 to see if it equals 3/4:

(60/100) * (5/4) = (3/5) * (5/4) = 15/20 = 3/4

Yep, it checks out! We’ve successfully solved the problem. Give yourselves a pat on the back, guys! We took a potentially tricky problem and broke it down into manageable steps. Now, let's do a quick recap of our journey.

Recap

Wow, we've covered quite a bit in this math problem! Let's do a quick recap of the steps we took to solve "3/4 is 60% of what number?"

  1. Understanding the Problem: We made sure we understood what the question was asking and identified the unknown variable.
  2. Setting Up the Equation: We translated the words into a mathematical equation: 3/4 = (60/100) * x.
  3. Simplifying the Equation: We simplified 60/100 to 3/5, making our equation 3/4 = (3/5) * x.
  4. Isolating the Variable: We multiplied both sides of the equation by 5/3, the reciprocal of 3/5, to isolate x.
  5. Simplifying the Result: We simplified 15/12 to 5/4.
  6. Final Answer: We clearly stated our answer: 3/4 is 60% of 5/4 (or 1 1/4).

By breaking down the problem into these steps, we made it much easier to solve. Remember, tackling math problems is all about taking things one step at a time and staying organized. And most importantly, don't be afraid to ask questions and seek help when you need it. Math can be fun and rewarding when you approach it with the right mindset! So, keep practicing, keep learning, and keep shining!