Have you ever found yourself needing to divide 200 by 6 but weren’t sure about the exact result? Division plays a crucial role in mathematics and everyday problem-solving, from financial calculations to real-world applications. This article provides a detailed breakdown of the division of 200 by 6, presenting the answer in decimal, fraction, and mixed number formats, along with its real-life implications.
Understanding the Division of 200 by 6
Mathematically, when we divide 200 by 6, we express it as:
Performing the division, we get:
(repeating decimal)
This result means that the number 33.3 continues infinitely, with the digit 3 repeating. It can be written as 33.3̅, where the bar denotes the repeating sequence.
Fraction Representation
Instead of writing the result in decimal form, we can also express 200 ÷ 6 as a fraction:
To simplify, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
Thus, the simplified fraction form of 200 ÷ 6 is 100/3.
Mixed Number Representation
An improper fraction like 100/3 can also be written as a mixed number. To do this:
- Divide 100 by 3:
- 3 goes into 100 33 times (since 3 × 33 = 99).
- The remainder is 1.
- Express the remainder as a fraction:
- The remainder 1 over the divisor 3 gives 1/3.
Thus, 100/3 is written as 33 1/3 in mixed number form.
Step-by-Step Long Division
For those who want a detailed breakdown, let’s go through the long division process:
- Divide: 6 fits into 20 three times (6 × 3 = 18).
- Subtract: 20 – 18 = 2.
- Bring down: The next digit in 200 is 0, making it 20.
- Divide again: 6 fits into 20 three times (6 × 3 = 18).
- Repeat: This cycle continues infinitely, giving 33.3̅ as the quotient.
Real-Life Applications
Understanding the division of 200 by 6 is useful in many practical scenarios, such as:
- Splitting a Budget: If you have $200 and need to distribute it equally among 6 people, each person gets $33.33.
- Time Management: If you have 200 minutes to complete 6 tasks, each task should take approximately 33.33 minutes.
- Product Packaging: If a company needs to package 200 items into boxes of 6, they will completely fill 33 boxes, with 2 items left over.
Conclusion
Dividing 200 by 6 results in a repeating decimal of 33.3̅, a simplified fraction of 100/3, and a mixed number of 33 1/3. Understanding different representations of division is essential for both mathematical learning and real-world applications. Whether working with decimals, fractions, or mixed numbers, knowing how to manipulate these values can make calculations easier and more efficient.
