Simplifying 4 Divided By 3/4 In Fraction Form

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Mastering fraction arithmetic is a fundamental skill in mathematics, and one operation that can be a bit tricky is dividing fractions. When we encounter a problem like simplifying 4 divided by 3/4, it's essential to understand the steps involved in simplifying such expressions.

Understanding the Problem

Before we dive into the solution, let's break down the problem statement. We have the expression 4 ÷ 3/4, which means we're dividing the whole number 4 by the fraction 3/4. Our goal is to simplify this expression into a more manageable form.

Step 1: Invert and Multiply

To divide fractions, we use the invert-and-multiply method. This involves flipping the second fraction (i.e., inverting it) and then multiplying it by the first fraction. So, in this case, we'll invert the fraction 3/4 to get 4/3, and then multiply it by the whole number 4.

Inverting the Fraction

The inverted fraction of 3/4 is 4/3. We simply swap the numerator and denominator to get the inverted fraction.

Multiplying the Fractions

Now, we'll multiply the whole number 4 by the inverted fraction 4/3. To do this, we multiply the numerators (4 and 4) to get 16, and multiply the denominators (1 and 3) to get 3. The resulting fraction is 16/3.

Step 2: Simplifying the Result

We have the fraction 16/3, which can be simplified further. Since the numerator (16) is greater than the denominator (3), we can convert this improper fraction to a mixed number.

Converting to a Mixed Number

To convert the improper fraction 16/3 to a mixed number, we divide the numerator (16) by the denominator (3). This gives us a quotient of 5 and a remainder of 1. So, the mixed number equivalent of 16/3 is 5 1/3.

Final Answer

The simplified form of the expression 4 divided by 3/4 is 5 1/3.

Real-World Applications

Understanding how to simplify fraction expressions like this has numerous real-world applications. For example, in cooking, you may need to divide a recipe that serves 4 people by 3/4 to accommodate a smaller group. In finance, you may need to calculate interest rates or investment returns using fraction arithmetic.

Common Mistakes

When simplifying fraction expressions, it's essential to avoid common mistakes. One of the most common errors is to multiply the fractions directly, without inverting the second fraction. This can lead to incorrect results and confusion.

Best Practices

To avoid mistakes, follow these best practices:

• Always invert the second fraction before multiplying.
• Multiply the numerators and denominators separately.
• Simplify the resulting fraction, if possible.
• Double-check your work to ensure accuracy.

Conclusion

Simplifying fraction expressions like 4 divided by 3/4 requires a solid understanding of fraction arithmetic and the invert-and-multiply method. By following the steps outlined in this article, you'll be able to tackle even the most complex fraction expressions with confidence.

We hope you've found this article informative and helpful. If you have any questions or topics you'd like us to cover, please leave a comment below.