Candy Distribution: Math Problem Solved!

Hey everyone! Today, we're diving into a fun math problem that involves sharing candies. This is a classic type of question that you might encounter in elementary or middle school math, and it's a great way to practice division and basic arithmetic. Let's break down the problem step-by-step and make sure we understand exactly what's going on.

Understanding the Problem: Candy Distribution

Okay, so here’s the scenario: A teacher has a bunch of candies – 90 delicious, sugary treats, to be exact! This teacher is super generous and wants to give each student in the class 3 candies. The question we need to answer is: how many students can the teacher share these candies with? This is a classic distribution problem where we're figuring out how many equal groups we can make from a larger quantity.

The main keyword here is distribution. In mathematical terms, when we distribute something equally, we're talking about division. We’re taking a total amount (the 90 candies) and splitting it into groups of a certain size (3 candies per student). So, the core concept we need to use here is division. Division helps us determine how many times one number (the divisor, which is 3 in this case) fits into another number (the dividend, which is 90). Imagine you have a big pile of something, and you want to share it fairly among a group of people. Division is the tool that helps you do that!

To visualize this, think of the 90 candies laid out in a big pile. The teacher starts handing out candies: one, two, three for the first student. Then another one, two, three for the next student. And so on. We want to figure out how many times the teacher can repeat this process of giving out three candies before running out. Another way to think about it is to group the candies into sets of three. Each set of three represents the candies given to one student. The number of these sets will tell us how many students can receive candies.

Understanding the problem thoroughly is the first and most important step. Before we jump into calculations, we need to be clear about what we're trying to find. In this case, we are trying to find the number of students who can receive candies. The keywords “how many students” are a clear indicator that our final answer should be a count of individuals. Now that we have a good grasp of the problem, let's move on to the next step: figuring out how to solve it. This involves choosing the right mathematical operation and setting up the equation.

Setting Up the Equation: Division is Key

So, as we’ve already discussed, this problem is all about division. We have a total number of candies, and we want to divide them equally among the students. The key here is to recognize that the total number of candies (90) is being divided into groups of 3 (the number of candies each student receives). Therefore, the mathematical operation we need to use is division. The phrase “reparte 3 caramelos a cada alumno” literally means distributes 3 candies to each student, clearly indicating the need for division.

The equation we need to set up is simple: we'll take the total number of candies and divide it by the number of candies per student. This will give us the number of students who can receive candies. In mathematical terms, it looks like this:

Number of students = Total candies / Candies per student

Now, let’s plug in the numbers we have from the problem:

Number of students = 90 / 3

This equation is the roadmap to our solution. It tells us exactly what we need to do: divide 90 by 3. It’s like saying, “Okay, math problem, I understand you! I know I need to split 90 into groups of 3, and the answer will tell me how many groups I can make.” This is where the magic of math starts to happen. We’ve translated a real-world scenario into a clear, actionable mathematical statement.

Setting up the equation correctly is crucial. If we were to use the wrong operation, like addition or multiplication, we’d end up with a completely incorrect answer. For instance, adding 90 and 3 wouldn’t make sense in this context. We're not combining quantities; we're dividing them. Similarly, multiplying 90 by 3 would give us a much larger number, which wouldn't represent the number of students. Once we have the correct equation, the next step is to actually perform the calculation. This is where our arithmetic skills come into play. We can use various methods to divide 90 by 3, whether it's long division, mental math, or even using a calculator. The goal is to arrive at the correct quotient, which will be the answer to our problem: the number of students who can get those delicious candies.

Solving the Equation: Finding the Answer

Alright, we've got our equation set up: 90 / 3 = ? Now comes the fun part – actually solving it! There are a few ways we can approach this division. Let’s explore a couple of them.

1. Mental Math:

If you're good with your times tables, you might already know the answer! Think: “What number times 3 equals 90?” You might recognize that 3 times 30 equals 90. So, 90 divided by 3 is 30. This is a quick and efficient way to solve the problem if you’re comfortable with mental math.

2. Long Division:

If mental math isn't your thing, or if the numbers are bigger and more complex, long division is your best friend. Let’s walk through the steps:

• Set up the long division problem like this: 3 | 90
• First, look at the first digit of the dividend (90), which is 9. How many times does 3 go into 9? It goes in 3 times. Write the 3 above the 9.
• Multiply 3 (the quotient) by 3 (the divisor): 3 * 3 = 9. Write this 9 below the 9 in the dividend.
• Subtract the two 9s: 9 - 9 = 0. Write the 0 below the line.
• Bring down the next digit from the dividend, which is 0. Write it next to the 0 we just got, making it 00.
• How many times does 3 go into 0? It goes in 0 times. Write a 0 next to the 3 in the quotient.

So, the long division gives us 30 as the quotient.

3. Breaking It Down:

Another strategy is to break down the dividend (90) into smaller, more manageable parts. For example, you could think of 90 as 9 tens. So, we have 9 tens divided by 3. How many times does 3 go into 9? It goes in 3 times. So, 9 tens divided by 3 is 3 tens, which is 30.

No matter which method you choose, the answer is the same: 90 divided by 3 is 30. This means the teacher can distribute candies to 30 students. Isn't that cool? We've taken a bunch of candies and figured out exactly how many people can enjoy them. Now that we’ve calculated the answer, it’s super important to make sure it makes sense in the context of the problem. This is where we double-check our work and ensure our solution is logical.

Checking the Answer: Does It Make Sense?

We've crunched the numbers and found that the teacher can give candies to 30 students. But before we high-five ourselves and move on, let’s take a moment to make sure our answer makes sense. This is a crucial step in problem-solving – it’s like the quality control of math!

Here’s how we can check:

1. Reverse the Operation: Since we used division to solve the problem, we can use multiplication to check our answer. If we multiply the number of students (30) by the number of candies each student receives (3), we should get the total number of candies (90). So, let’s do it: 30 * 3 = 90. Bingo! Our answer checks out. This is like saying, “If 30 students each get 3 candies, then we'll use up all 90 candies.” It’s a great way to confirm our calculation is accurate.
2. Think Logically: Does the number 30 seem reasonable in the context of the problem? Well, the teacher has 90 candies, and each student gets 3. It makes sense that we’d be able to share with a decent number of students. If our answer had been something like 3 or 300, we’d know something went wrong. An answer of 3 would mean each student gets 30 candies, which is not what the problem says, and 300 students getting candies from only 90 candies is logically impossible. So, 30 feels like a sensible number. Using common sense is a powerful tool in math. It helps us catch errors and ensure our answers are realistic.
3. Use Estimation: We can also use estimation to get a rough idea of the answer. We know that 3 goes into 9 about 3 times, so 3 goes into 90 about 30 times. This quick estimate confirms that our answer of 30 is in the right ballpark. Estimating is like having a mental compass that guides us in the right direction. It prevents us from making huge errors and gives us confidence in our final answer.

Checking our answer isn’t just about getting a gold star; it’s about understanding the math and making sure we’re on the right track. It’s a habit that will serve you well in all sorts of problem-solving situations, not just in math class. So, always take that extra minute to double-check – your brain (and your grade) will thank you for it!

Final Answer: Sharing the Candy Joy!

Drumroll, please! After carefully setting up our equation, solving it with precision, and double-checking our answer to make sure it makes sense, we’ve arrived at our final answer. The teacher can share the 90 candies with 30 students!

So, there you have it! By using the simple yet powerful tool of division, we've solved a real-world problem about sharing and distribution. Math is all about finding these connections between numbers and everyday situations. Whether it's dividing candies, slicing a pizza, or figuring out how many buses you need for a field trip, the same mathematical principles apply.

The key takeaways from this problem are:

• Understanding the problem: Always read the problem carefully and make sure you know what you’re being asked to find.
• Choosing the right operation: Identify the mathematical operation that fits the situation (in this case, division).
• Setting up the equation: Translate the problem into a mathematical equation that you can solve.
• Solving the equation: Use your arithmetic skills to find the answer.
• Checking the answer: Make sure your answer makes sense in the context of the problem.

By following these steps, you can tackle all sorts of math challenges with confidence. And remember, math isn’t just about numbers; it’s about thinking logically and solving problems. So, keep practicing, keep exploring, and keep having fun with math!

If you have any questions or want to try more problems like this, feel free to ask. Happy candy sharing, everyone!