7500 Divided By 12

Dividing 7500 by 12: A Step-by-Step Guide

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.

Search Results:

75 divided by 6.25? Step by step explanation - brainly.com Answer: 12. Step-by-step explanation: When dividing, you always want whole numbers, so by multiplying 100 by both numbers, makes it 7500 divided by 625. Now you can write this out the long division way. I don't know how to show the long division step by step, sorry!

Jack showed how he divided - Brainly.com 3 Dec 2024 · Breaking Down the Number: Jack separated the number 7,550 into two parts: 7,500 and 50. This is written as: 7, 550 = 7, 500 + 50. Dividing Each Part by 25: Jack then divided each part separately by 25. He did: 7, 500 ÷ 25 = 300 50 ÷ 25 = 2. Adding the Results: Finally, he added the results of the two divisions: 300 + 2 = 302

An audio amplifier has an output impedance of 7500 ohms. It must 13 Jun 2023 · The transformation ratio for coupling an audio amplifier with an output impedance of 7500 ohms to a speaker with an input impedance of 12 ohms is approximately 625:1. The transformation ratio, also known as the impedance matching ratio, is calculated by dividing the output impedance by the input impedance.

Divide $7500 in the ratio of 8:3:1. - Brainly.com 5 Oct 2021 · So, the money is divided as follows: First person gets $5000. Second person gets $1875. Third person gets $625. The sum of the amounts received by all three people adds up to $5000 + $1875 + $625 = $7500, which is the total amount that was divided. Therefore, the division is correct, and the three individuals receive amounts in the ratio of 8:3:1.

Your goal by the end of the year is to save $7500.00 How much … 5 Jun 2023 · To save $7500 by the end of the year, you would need to save $625 per month (7500 divided by 12 months). Therefore, the correct answer is e. $625.00. Therefore, the correct answer is e. $625.00. To calculate the monthly savings required to reach a goal of $7500 by the end of the year , we divide the total savings goal by the number of months in a year (12 months).

Rs. 7500 were divided equally among a certain number of … 31 Jan 2024 · Let's denote the original number of children as x. The amount each child receives is Rs. 7500 divided by x. If there were 20 less children, the equation would be Rs. 7500 divided by (x - 20), and each child would receive Rs. 100 more than before. We can set up the following equation: 7500/x + 100 = 7500/(x - 20) Now we'll solve for x:

[FREE] Malik purchased 7,500 square meters of riverfront … 12 Dec 2023 · Final answer: The varying quantities for Malik's riverfront property are the width, perimeter, and length. The length (l) is defined as 7500 divided by the width (w) and the fencing needed (F) is calculated using the formula F = 2w + (7500/w), excluding the river side.

Find each quotient. 7 500 ÷ 20 500 420 - brainly.com 30 Oct 2023 · To find the quotient of 7,500 ÷ 20, divide the two numbers to get 375. Explanation: To find the quotient of 7,500 divided by 20, you need to divide the two numbers. The quotient is the result of the division operation. In this case, 7,500 divided by 20 is equal to 375. Therefore, the quotient is 375. Learn more about Division and quotients here:

[FREE] Calculate the following expression: 7500 \div (-25) 12 Feb 2025 · This answer is FREE! See the answer to your question: Calculate the following expression: [tex]\[ 7500 \div (-25) \][/tex] - brainly.com

Franklin Co. borrowed $75,000 from a bank on August 1, 2006. 1 Aug 2006 · The nth payment is equally divided between int; You have received a $10,000 loan from your bank for 10 years. If the bank charges you 5% interest, calculate the total amount of money that you have to pay back to the bank if the loan is a discount loan. You have borrowed $6,000 from the ABC Bank for a period of 4 years. The annual interest rate ...