How To Divide 4/5 By 3: Simple Steps Explained

gptAI

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11-14- 2024

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To divide fractions like ( \frac{4}{5} ) by a whole number such as 3 can be a little tricky if you don't know the right steps. However, with a clear explanation, you can easily grasp how to handle such division problems. Let’s explore the steps in detail and make the process as simple as possible! 📚✨

Understanding the Problem

Before diving into the solution, let's break down what it means to divide ( \frac{4}{5} ) by 3. When you see a problem like this, you can think of it as asking how many times the whole number (in this case, 3) fits into the fraction ( \frac{4}{5} ).

The Division of Fractions

Dividing fractions involves a few basic steps. The most important rule to remember is:

To divide by a fraction, multiply by its reciprocal.

This rule applies when we deal with whole numbers as well. We treat the whole number as a fraction with 1 in the denominator. So, 3 can be expressed as ( \frac{3}{1} ).

Steps to Divide ( \frac{4}{5} ) by 3

Now that we understand the concept, let’s break down the steps to divide ( \frac{4}{5} ) by 3.

Step 1: Write the Division as a Fraction

Express the division ( \frac{4}{5} \div 3 ) as ( \frac{4}{5} \div \frac{3}{1} ).

Step 2: Multiply by the Reciprocal

Now, instead of dividing, we will multiply by the reciprocal of ( \frac{3}{1} ). The reciprocal of ( \frac{3}{1} ) is ( \frac{1}{3} ).

So we rewrite the expression:

[ \frac{4}{5} \div \frac{3}{1} = \frac{4}{5} \times \frac{1}{3} ]

Step 3: Multiply the Fractions

To multiply fractions, simply multiply the numerators together and the denominators together:

[ \frac{4 \times 1}{5 \times 3} = \frac{4}{15} ]

Step 4: Simplify if Necessary

In this case, ( \frac{4}{15} ) is already in its simplest form. So our final answer remains:

[ \frac{4}{15} ]

Summary of Steps

Here’s a quick summary of the steps we took:

Important Notes

“Always remember that dividing by a whole number can be converted into multiplying by the reciprocal of that whole number.”

By following these steps, you can successfully divide any fraction by a whole number! 🎉

Additional Examples

To help solidify your understanding, let’s go through a few more examples:

Example 1: Dividing ( \frac{1}{2} ) by 4

1. Write as a fraction: ( \frac{1}{2} \div \frac{4}{1} )
2. Multiply by the reciprocal: ( \frac{1}{2} \times \frac{1}{4} )
3. Multiply: ( \frac{1 \times 1}{2 \times 4} = \frac{1}{8} )

Example 2: Dividing ( \frac{5}{6} ) by 2

1. Write as a fraction: ( \frac{5}{6} \div \frac{2}{1} )
2. Multiply by the reciprocal: ( \frac{5}{6} \times \frac{1}{2} )
3. Multiply: ( \frac{5 \times 1}{6 \times 2} = \frac{5}{12} )

Conclusion

Now you have a clear understanding of how to divide ( \frac{4}{5} ) by 3! 🎊 With practice and these simple steps, you'll become more confident in handling fraction division. Keep these methods in mind for future calculations, and don't hesitate to refer back to this guide whenever you need a reminder! Happy calculating! 🧮