3/4 divided by 1/2 as a fraction

Guri Bee

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17-10-2024

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Dividing Fractions: Unlocking the Mystery of 3/4 ÷ 1/2

Dividing fractions can seem daunting, but it's actually quite simple with the right approach. Let's break down the classic example: 3/4 divided by 1/2. We'll explore the steps and delve into the "why" behind the process.

Understanding the Problem

Imagine you have a pizza cut into fourths. You want to divide those fourths into halves – essentially, how many half-sized pieces can you get from the three fourths you have? This is the essence of 3/4 ÷ 1/2.

The Flip-and-Multiply Rule

The key to dividing fractions lies in a simple trick: flip the second fraction and multiply.

• Step 1: Flip the second fraction (the divisor): 1/2 becomes 2/1.
• Step 2: Multiply the first fraction by the flipped second fraction: 3/4 x 2/1

Solving the Multiplication

Now we have a standard multiplication problem:

• (3 x 2) / (4 x 1) = 6/4

Simplifying the Answer

The fraction 6/4 can be simplified by dividing both numerator and denominator by their greatest common factor (2):

• 6/4 = 3/2

Therefore, 3/4 divided by 1/2 equals 3/2.

Visualizing the Solution

Let's relate this back to our pizza example:

• You start with 3/4 of a pizza (3 out of 4 slices).
• Dividing by 1/2 means you're trying to see how many half-slices fit into those 3/4.
• The answer, 3/2, tells us you can get one and a half (3/2) half-slices from the three fourths of the pizza.

Why Does This Work?

The "flip and multiply" method is a shortcut for understanding what division actually means. Dividing by a fraction is the same as multiplying by its reciprocal (the flipped version). This allows us to express the division problem as a multiplication, which is often easier to solve.

Further Exploration

Source: Github discussion thread - Replace with the actual link to the relevant Github discussion.

You can apply this same "flip-and-multiply" rule to any fraction division problem. Try it out with different examples to solidify your understanding.

Remember: Understanding the "why" behind mathematical rules makes them easier to remember and apply in various contexts.