Evaluate $\frac{4}{3} \div 5$.Give Your Answer As A Fraction.$\frac{4}{3} \div 5 = \longdiv{ \text{Enter Your Next Step Here}}$

Feb 28, 2025 by ADMIN 128 views

$Evaluate $\frac{4}{3} \div 5$: A Step-by-Step Guide$

=====================================================

Introduction

When it comes to dividing fractions, it's essential to understand the concept of inverting the second fraction and then multiplying. In this article, we will evaluate the expression $\frac{4}{3} \div 5$ and provide a step-by-step guide on how to simplify it.

Understanding Division of Fractions

To divide a fraction by a whole number, we need to invert the fraction and then multiply. This means that we will flip the numerator and denominator of the fraction, and then multiply the result by the whole number.

Inverting the Fraction

To invert the fraction $\frac{4}{3}$ , we need to flip the numerator and denominator. This gives us $\frac{3}{4}$ .

Multiplying by the Whole Number

Now that we have inverted the fraction, we can multiply it by the whole number 5. This means that we will multiply the numerator and denominator of the fraction by 5.

Evaluating the Expression

Let's evaluate the expression $\frac{4}{3} \div 5$ using the steps outlined above.

Step 1: Invert the Fraction

$\frac{4}{3} \div 5 = \frac{3}{4} \times 5$

Step 2: Multiply the Numerator and Denominator

$\frac{3}{4} \times 5 = \frac{3 \times 5}{4 \times 5}$

Step 3: Simplify the Fraction

$\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Step 4: Reduce the Fraction

To reduce the fraction $\frac{15}{20}$ , we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 15 and 20 is 5.

$\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}$

Conclusion

In this article, we evaluated the expression $\frac{4}{3} \div 5$ using the concept of inverting the fraction and then multiplying. We simplified the fraction and reduced it to its lowest terms. The final answer is $\frac{3}{4}$ .

Frequently Asked Questions

Q: What is the concept of inverting a fraction?

A: Inverting a fraction means flipping the numerator and denominator.

Q: How do I multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, you need to multiply the numerator and denominator of the fraction by the whole number.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: How do I reduce a fraction?

A: To reduce a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Final Answer

The final answer is $\boxed{\frac{3}{4}}$ .

=====================================================

Introduction

In our previous article, we evaluated the expression $\frac{4}{3} \div 5$ using the concept of inverting the fraction and then multiplying. In this article, we will answer some frequently asked questions related to division of fractions.

Q&A

Q: What is the concept of inverting a fraction?

A: Inverting a fraction means flipping the numerator and denominator. For example, if you have the fraction $\frac{4}{3}$ , inverting it would give you $\frac{3}{4}$ .

Q: How do I multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, you need to multiply the numerator and denominator of the fraction by the whole number. For example, if you have the fraction $\frac{4}{3}$ and you want to multiply it by 5, you would get $\frac{4 \times 5}{3 \times 5} = \frac{20}{15}$ .

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, if you have the fraction $\frac{20}{15}$ , the GCD of 20 and 15 is 5. Dividing both numbers by 5 would give you $\frac{4}{3}$ .

Q: How do I reduce a fraction?

A: To reduce a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. This is the same as simplifying a fraction.

Q: What is the difference between simplifying and reducing a fraction?

A: Simplifying a fraction means finding the simplest form of the fraction, while reducing a fraction means finding the lowest terms of the fraction. For example, the fraction $\frac{20}{15}$ can be simplified to $\frac{4}{3}$ , but it can also be reduced to $\frac{4}{3}$ .

Q: Can I divide a fraction by a fraction?

A: Yes, you can divide a fraction by a fraction. To do this, you need to invert the second fraction and then multiply. For example, if you have the expression $\frac{4}{3} \div \frac{5}{6}$ , you would invert the second fraction to get $\frac{6}{5}$ and then multiply to get $\frac{4 \times 6}{3 \times 5} = \frac{24}{15}$ .

Q: Can I divide a fraction by a decimal?

A: Yes, you can divide a fraction by a decimal. To do this, you need to convert the decimal to a fraction and then divide. For example, if you have the expression $\frac{4}{3} \div 0.5$ , you would convert the decimal to a fraction to get $\frac{1}{2}$ and then divide to get $\frac{4 \times 2}{3 \times 1} = \frac{8}{3}$ .

Conclusion

In this article, we answered some frequently asked questions related to division of fractions. We covered topics such as inverting fractions, multiplying fractions by whole numbers, simplifying fractions, reducing fractions, and dividing fractions by fractions and decimals.

Final Answer

The final answer is $\boxed{\frac{3}{4}}$ .