75 divided by 20

2025

2 min read

·

31-03-2025

19

0

Share

Introduction:

Dividing 75 by 20 might seem straightforward, but understanding the process is crucial for grasping division concepts. This article provides a comprehensive guide to solving 75 ÷ 20, explaining different methods and highlighting key mathematical principles. Whether you're a student brushing up on your math skills or an adult looking for a refresher, this guide will help you master this division problem and similar ones. We'll explore long division, decimal conversion, and the concept of remainders. By the end, you'll be confident in tackling 75 divided by 20 and similar division problems.

Understanding the Problem: 75 ÷ 20

The problem "75 divided by 20" asks: how many times does 20 go into 75? We can solve this using several methods. Let's explore a few.

Method 1: Long Division

Long division is a classic method for handling division problems. Here's how to solve 75 ÷ 20 using long division:

1. Set up the problem: Write 75 inside the long division symbol (÷) and 20 outside.
2. Divide: Ask yourself: how many times does 20 go into 75? It goes in 3 times (20 x 3 = 60).
3. Multiply: Write the 3 above the 5 in 75. Multiply 3 by 20 (3 x 20 = 60).
4. Subtract: Subtract 60 from 75 (75 - 60 = 15).
5. Remainder: The result, 15, is the remainder.

Therefore, 75 ÷ 20 = 3 with a remainder of 15.

Method 2: Converting to Decimals

Instead of a remainder, we can express the answer as a decimal. Here's how:

1. Perform long division as above. This gives us a quotient of 3 and a remainder of 15.
2. Express the remainder as a fraction: The remainder (15) becomes the numerator of a fraction, and the divisor (20) becomes the denominator. This gives us 15/20.
3. Simplify the fraction: Reduce 15/20 by dividing both the numerator and the denominator by their greatest common divisor, which is 5. This simplifies to 3/4.
4. Convert the fraction to a decimal: Divide the numerator (3) by the denominator (4). This gives 0.75.
5. Combine with the whole number: Add the whole number from the long division (3) to the decimal (0.75).

Therefore, 75 ÷ 20 = 3.75

Understanding Remainders and Decimals

The remainder in the long division method (15) indicates that after 20 goes into 75 three times (60), there are 15 units left over. The decimal representation (3.75) provides a more precise answer, showing the complete result of the division. Choosing between a remainder or a decimal depends on the context of the problem.

Real-World Applications

Understanding division is vital for various real-world scenarios. Imagine dividing 75 cookies among 20 people. Using the decimal result (3.75), each person gets 3.75 cookies. This means most people get 3 cookies, and a few get 4 (to account for the .75 portion).

Conclusion

Dividing 75 by 20 results in either 3 with a remainder of 15, or 3.75 as a decimal. Both answers are correct, but the most appropriate one depends on the context of the problem. By understanding both methods, you can confidently tackle similar division problems and apply your skills to real-world situations. Remember to always consider whether a remainder or decimal answer is more suitable for the problem at hand.