what is 6 divided by 1/2

Guri Bee

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18-10-2024

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Why 6 Divided by 1/2 is 12: A Deep Dive into Fraction Division

We often encounter division problems in our daily lives, whether it's splitting a pizza among friends or calculating the cost per unit. But what happens when we divide a whole number by a fraction? This can be particularly confusing, especially when it comes to dividing by a fraction less than one, like 1/2.

Let's take a look at the question: What is 6 divided by 1/2?

Many people instinctively want to answer 3. However, the correct answer is 12. This is because dividing by a fraction is equivalent to multiplying by its reciprocal.

Here's why:

• Understanding the Relationship: Division is essentially the reverse of multiplication. If we divide 6 by 2, we are asking "how many times does 2 go into 6?". The answer is 3, because 2 x 3 = 6.
• Reciprocals: The reciprocal of a fraction is simply flipping it over. The reciprocal of 1/2 is 2/1, which is equivalent to 2.
• The Magic of Reciprocal Multiplication: When dividing by a fraction, we can multiply by its reciprocal instead. So, 6 divided by 1/2 is the same as 6 multiplied by 2.

Therefore, 6 divided by 1/2 is 6 x 2 = 12.

Let's explore this concept with a practical example:

Imagine you have 6 pizzas, and you want to divide them into portions that are each 1/2 of a pizza. How many portions would you get?

• Visualizing: You would cut each pizza in half, resulting in two portions per pizza.
• Calculation: Since you have 6 pizzas, you would get 6 x 2 = 12 portions.

Key Takeaways:

• Dividing by a fraction is the same as multiplying by its reciprocal.
• Understanding reciprocals and their relationship to division is essential for solving these problems.
• Applying these principles to real-world situations helps solidify the concept.

Remember, practice makes perfect! Try working through different division problems involving fractions to develop your understanding and confidence in solving them.

Source: This explanation is based on the principles of fraction division widely accepted in mathematics. While there may be many threads and discussions on platforms like Github discussing this concept, it's important to note that the fundamental mathematical rules remain consistent across resources.