This article provides a comprehensive explanation of how to divide 7500 by 12, covering various methods and applications. We'll explore both long division and the use of calculators, highlighting the importance of understanding the process regardless of the tool used. Understanding division is fundamental to many areas of mathematics, from simple budgeting to complex engineering calculations. This exploration will solidify your understanding of division and its practical applications.
I. Understanding the Problem: 7500 ÷ 12
The problem "7500 divided by 12" asks: "How many times does 12 fit into 7500?" This question can arise in numerous real-world situations. For example, if you have 7500 candies to distribute evenly among 12 children, how many candies would each child receive? Or, if a company produces 7500 units of a product in 12 months, what is the average monthly production? Solving this problem involves finding the quotient (the result of the division).
II. Method 1: Long Division
Long division is a fundamental arithmetic process. Let's break down how to solve 7500 ÷ 12 using this method:
1. Set up the problem: Write 7500 inside the long division symbol (⟌) and 12 outside.
2. Divide the first digit(s): 12 doesn't go into 7, so consider the first two digits, 75. How many times does 12 go into 75? It goes 6 times (6 x 12 = 72). Write the 6 above the 5 in 7500.
3. Multiply and subtract: Multiply the quotient (6) by the divisor (12): 6 x 12 = 72. Subtract this from 75: 75 - 72 = 3.
4. Bring down the next digit: Bring down the next digit from the dividend (0) to create 30.
5. Repeat the process: How many times does 12 go into 30? It goes 2 times (2 x 12 = 24). Write the 2 above the 0 in 7500.
6. Multiply and subtract again: 2 x 12 = 24. Subtract this from 30: 30 - 24 = 6.
7. Bring down the last digit: Bring down the last digit (0) to create 60.
8. Final division: How many times does 12 go into 60? It goes 5 times (5 x 12 = 60). Write the 5 above the last 0 in 7500.
9. Subtract: 60 - 60 = 0. There is no remainder.
Therefore, 7500 ÷ 12 = 625.
III. Method 2: Using a Calculator
Calculators provide a quick and efficient way to perform division. Simply input "7500 ÷ 12" into your calculator, and the answer, 625, will be displayed. While calculators are convenient, understanding the underlying process of long division is crucial for developing a strong mathematical foundation.
IV. Real-world Applications
The result of 7500 ÷ 12 = 625 has numerous practical applications. Returning to our earlier examples:
Candy distribution: Each of the 12 children would receive 625 candies.
Monthly production: The company produces an average of 625 units per month.
Other applications include calculating unit prices, splitting bills amongst friends, and determining average speeds or rates.
V. Checking Your Answer
It's always good practice to check your answer. You can do this by multiplying the quotient (625) by the divisor (12): 625 x 12 = 7500. Since this matches the original dividend, our answer is correct.
VI. Summary
Dividing 7500 by 12 results in a quotient of 625. We explored two methods to solve this problem: long division, which provides a detailed step-by-step process, and the use of a calculator, which offers a faster solution. Understanding both methods is crucial for developing strong mathematical skills and for applying division to various real-world scenarios.
VII. FAQs
1. What if there was a remainder in the division? If there was a remainder, it would represent the amount left over after the division. For example, if dividing 7503 by 12, you would get a quotient of 625 with a remainder of 3.
2. Can I use a different method to solve this problem? Yes, other methods include repeated subtraction or using prime factorization, though these are less efficient for larger numbers like 7500.
3. Why is understanding long division important? Long division helps you grasp the fundamental principles of division, enhancing your mathematical understanding and problem-solving abilities. It also allows you to perform calculations without relying solely on technology.
4. What are some common errors made when performing long division? Common errors include misplacing digits, incorrect multiplication or subtraction, and not bringing down the correct digits. Careful and organized work is crucial.
5. How can I practice my division skills? Practice with various division problems, starting with smaller numbers and gradually increasing the difficulty. Online resources and workbooks offer numerous practice exercises.
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