Division is a fundamental arithmetic operation that involves splitting a quantity into equal parts. This article delves into the specific calculation of 50 divided by 6, exploring the process, the result, and its practical applications. Understanding this seemingly simple calculation lays the groundwork for more complex mathematical concepts. We will unpack this problem, exploring different approaches and providing context to make the concept clear and accessible to all learners.
1. The Long Division Method: A Step-by-Step Approach
The most common method for solving 50 ÷ 6 is long division. This method breaks down the division into manageable steps, providing a clear understanding of the process.
1. Set up the problem: Write the dividend (50) inside the long division symbol (⟌) and the divisor (6) outside.
```
_____
6 | 50
```
2. Determine the quotient's first digit: How many times does 6 go into 5? It doesn't go in at all, so we move to the next digit (50). How many times does 6 go into 50? It goes in 8 times (6 x 8 = 48). Write the 8 above the 0 in 50.
```
8
6 | 50
```
3. Multiply and subtract: Multiply the quotient digit (8) by the divisor (6): 8 x 6 = 48. Write 48 below 50 and subtract: 50 - 48 = 2.
```
8
6 | 50
48
--
2
```
4. The remainder: The result of the subtraction (2) is the remainder. This indicates that 6 goes into 50 eight times with 2 left over.
Therefore, 50 ÷ 6 = 8 with a remainder of 2. This can also be expressed as a mixed number: 8 2/6, which can be simplified to 8 1/3.
2. Understanding the Remainder
The remainder in division represents the portion of the dividend that is left over after dividing by the divisor. In our example, the remainder of 2 signifies that if we had 50 items to divide equally among 6 groups, each group would receive 8 items, and 2 items would be left undistributed.
Imagine you have 50 candies to distribute equally amongst 6 friends. Each friend would get 8 candies (8 x 6 = 48), and you would have 2 candies left over.
3. Expressing the Result as a Fraction or Decimal
The result of 50 ÷ 6 can be represented in several ways:
Mixed Number: 8 1/3 (eight and one-third) - this combines the whole number quotient with the remainder expressed as a fraction.
Improper Fraction: 25/3 – This represents the total number of thirds. To obtain this, multiply the whole number by the denominator and add the numerator (83 +1 = 25) and place this over the denominator (3).
Decimal: Approximately 8.333... – This is the result obtained by converting the fraction 1/3 to a decimal. The three repeats infinitely, indicating a recurring decimal.
4. Real-world Applications
Division is crucial in various daily scenarios. Understanding 50 ÷ 6 can help in situations like:
Sharing resources: Dividing 50 toys equally among 6 children.
Calculating costs: Determining the price per unit when 6 units cost 50 dollars.
Measurement conversions: Converting 50 inches into feet (since there are 12 inches in a foot).
5. Beyond the Basic Calculation
While this article focuses on the basic calculation, understanding 50 ÷ 6 paves the way for grasping more complex division problems involving larger numbers, decimals, and fractions.
Summary:
Dividing 50 by 6 yields a quotient of 8 with a remainder of 2. This can be expressed as 8 1/3, 25/3, or approximately 8.333... The remainder signifies the portion left undivided. This seemingly simple calculation has broad applications in everyday life and forms a building block for more advanced mathematical concepts.
Frequently Asked Questions (FAQs):
1. What is the exact decimal value of 50 divided by 6? There is no exact decimal value, as the result is a repeating decimal (8.333...).
2. Can I round the answer to 8.33? While 8.33 is a close approximation, it's important to acknowledge the repeating nature of the decimal. The accuracy needed will determine the appropriateness of rounding.
3. Why is the remainder important? The remainder indicates the portion not fully divided, crucial for understanding the complete result and its context (e.g., leftover candies).
4. How can I check my answer in long division? Multiply the quotient (8) by the divisor (6) and add the remainder (2). If the result is the dividend (50), your calculation is correct.
5. What if the dividend was less than the divisor (e.g., 6 divided by 50)? In this case, the quotient would be 0, and the remainder would be the dividend itself (6). The result can be expressed as the fraction 6/50.
Note: Conversion is based on the latest values and formulas.
Formatted Text:
how much is 500 grams 32 centimeters in inches 54 inches to feet 220 grams to ounces 400 g to lbs 5ft9 in cm 176cm to ft 70 pounds to kilograms 70cm to mm 49 lb to kg 6 8 in cm 63cm to inch 20l to gallons 2 10 in inches 5 8 in centimeters
