Let's dive into this math problem! Figuring out how many times one number goes into another is a fundamental concept in math, and it’s super useful in everyday life. Whether you're splitting a pizza, dividing up chores, or even planning a road trip, understanding division is key. So, let's break down how to solve the problem: How many times does 16 go into 672?

Understanding Division

Before we jump right into the problem, let's make sure we're all on the same page about what division really means. Division is essentially splitting a whole into equal parts. When we ask, "How many times does 16 go into 672?" we're really asking, "If we split 672 into groups of 16, how many groups would we have?"

Think of it like this: Suppose you have 672 candies, and you want to give 16 candies to each of your friends. The division problem 672 ÷ 16 will tell you exactly how many friends can get their sweet treat. This concept is crucial not just for math class, but for real-world scenarios where you need to distribute resources, calculate ratios, or understand proportions. Understanding the basics can make even complex problems feel manageable. So, with that in mind, let's solve the division problem.

Step-by-Step Solution: Dividing 672 by 16

Now, let's get down to business and solve this problem step by step. I'll walk you through the long division process to make it super clear.

1. Set up the problem: Write the division problem in the long division format. The number you're dividing into (672) goes inside the "house," and the number you're dividing by (16) goes outside.

   16 | 672
   

2. Divide the first digit(s): Look at the first digit of the number inside the house (6). Can 16 go into 6? Nope, 6 is too small. So, let's consider the first two digits together: 67. How many times does 16 go into 67? If you're not sure, you can try multiplying 16 by different numbers until you get close to 67 without going over. We know that 16 x 4 = 64, which is close to 67. So, 16 goes into 67 four times. Write the 4 above the 7 in the quotient.

      4
   16 | 672
   

3. Multiply and subtract: Multiply the number you wrote in the quotient (4) by the number outside the house (16). Write the result (64) under the 67, and subtract.

      4
   16 | 672
      -64
      ---
        3
   

4. Bring down the next digit: Bring down the next digit from the dividend (2) next to the remainder (3). Now you have 32.

      4
   16 | 672
      -64
      ---
        32
   

5. Repeat the process: How many times does 16 go into 32? Well, 16 x 2 = 32 exactly! So, 16 goes into 32 two times. Write the 2 next to the 4 in the quotient.

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      42
   16 | 672
      -64
      ---
        32
   

6. Multiply and subtract again: Multiply the number you just wrote in the quotient (2) by the number outside the house (16). Write the result (32) under the 32, and subtract. The remainder is 0.

      42
   16 | 672
      -64
      ---
        32
      -32
      ---
        0
   

7. Final answer: Since there's nothing left to bring down and the remainder is 0, you're done! The quotient (the number at the top) is your answer. So, 16 goes into 672 exactly 42 times.

Alternative Methods to Solve the Problem

While long division is a reliable method, it's always good to have other tricks up your sleeve. Here are a couple of alternative ways you could tackle the same problem:

Estimation and Approximation

If you're looking for a quick, rough answer, estimation can be your best friend. Round the numbers to make them easier to work with. For example, you could round 672 to 700 and 16 to 20. Now, the problem becomes: How many times does 20 go into 700? This is much easier to do mentally. 700 ÷ 20 = 35. So, you know the answer is somewhere around 35. This method is great for getting a ballpark figure and checking if your exact answer makes sense.

Using a Calculator

In this day and age, we've got amazing tools right at our fingertips. A calculator can give you the answer instantly! Simply type in 672 ÷ 16, and you'll get 42. Calculators are super handy for saving time and avoiding mistakes, especially when dealing with larger or more complicated numbers. But remember, it's still important to understand the underlying concepts. Don't rely on calculators so much that you forget how to do basic math on your own!

Real-World Applications of Division

So, now you know that 16 goes into 672 exactly 42 times. But why is this useful? Division problems pop up all the time in real life. Here are just a few examples:

• Splitting the Bill: Imagine you and 7 friends go out to dinner, and the total bill comes to $168. How do you figure out how much each person owes? You divide the total bill by the number of people: $168 ÷ 8 = $21. So, each person owes $21.
• Baking: Let's say a recipe calls for 3 cups of flour and makes 24 cookies. You only want to make 8 cookies. How much flour do you need? You need to figure out how much smaller you're making the recipe. Since 8 is one-third of 24 (24 ÷ 3 = 8), you need to use one-third of the flour. So, you'll need 1 cup of flour (3 cups ÷ 3 = 1 cup).
• Travel: You're planning a road trip of 450 miles, and you want to drive it in 2 days. How many miles do you need to drive each day? Divide the total distance by the number of days: 450 miles ÷ 2 days = 225 miles per day.
• Home Improvement: You're tiling a rectangular floor that's 12 feet long and 8 feet wide. Each tile is 1 square foot. How many tiles do you need? Find the area of the floor by multiplying the length and width: 12 feet x 8 feet = 96 square feet. Since each tile is 1 square foot, you need 96 tiles.

Practice Problems

Want to test your understanding? Try these practice problems:

1. How many times does 12 go into 384?
2. How many times does 25 go into 750?
3. How many times does 8 go into 512?

Conclusion

So, there you have it! Sixteen goes into 672 exactly 42 times. Understanding how to solve division problems like this is not just about getting the right answer in math class. It's a practical skill that you'll use throughout your life, from splitting costs with friends to planning events and managing resources. Mastering division is like unlocking a superpower that makes everyday tasks a little bit easier. Keep practicing, and you'll become a division whiz in no time!