2/3 divide 4/5

2 min read 23-10-2024

Understanding how to divide fractions is an essential math skill that often comes in handy in various fields, from cooking to construction. In this article, we will explore the division of two fractions specifically, 2/3 divided by 4/5. We will break down the process into simple steps and provide practical examples to enhance understanding.

What Does Dividing Fractions Mean?

When you divide one fraction by another, you are essentially determining how many times the second fraction fits into the first one. For instance, dividing 2/3 by 4/5 means you're asking: "How many 4/5's fit into 2/3?"

The Formula for Dividing Fractions

To divide fractions, you can use the following formula:

[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} ]

This means you will multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator.

Step-by-Step Calculation: 2/3 ÷ 4/5

Let's apply the formula to our specific problem:

Step 1: Identify the fractions

The fractions we are working with are:

First fraction ( \frac{2}{3} )
Second fraction ( \frac{4}{5} )

Step 2: Find the reciprocal of the second fraction

The reciprocal of ( \frac{4}{5} ) is ( \frac{5}{4} ).

Step 3: Multiply the first fraction by the reciprocal of the second

Now we will multiply ( \frac{2}{3} ) by ( \frac{5}{4} ):

[ \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} ]

Step 4: Simplify the resulting fraction

To simplify ( \frac{10}{12} ), we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

[ \frac{10 \div 2}{12 \div 2} = \frac{5}{6} ]

So, 2/3 divided by 4/5 equals 5/6.

Practical Applications

Understanding how to divide fractions can be beneficial in many real-world situations. Here are a few examples:

Cooking: If a recipe requires ( \frac{4}{5} ) of a cup of sugar for 2 servings, but you only need it for 1 serving, you might ask, "How much sugar do I need?" By dividing ( \frac{2}{3} ) cups of the available sugar by ( \frac{4}{5} ) cups required per serving, you'll determine how many servings you can make.
Construction: When dealing with measurements, you might encounter scenarios where you need to divide dimensions expressed as fractions.
Budgeting: You can use fraction division to allocate resources proportionally when dividing funds or materials.

Conclusion

In summary, dividing fractions might seem complex at first, but by following a structured method—finding the reciprocal and multiplying—you can easily tackle such problems. The example of dividing ( \frac{2}{3} ) by ( \frac{4}{5} ) and arriving at ( \frac{5}{6} ) is just one way of applying this technique.

Key Takeaways:

To divide fractions, multiply by the reciprocal.
Simplifying the resulting fraction makes it easier to understand and use.
Practical applications of dividing fractions can be found in everyday tasks.

Feel free to apply these steps to any fraction division problem you encounter, and you’ll quickly become proficient in this crucial math skill!

This article was created using a thorough review of relevant material and practical examples. Special thanks to the collaborative community on GitHub for inspiring educational discussions surrounding mathematical operations.