Divide. 3 8 9 ÷ 1 2 3 3 \frac{8}{9} \div 1 \frac{2}{3} 3 9 8 ÷ 1 3 2 Enter The Whole Number.

Mar 13, 2025 by ADMIN 97 views

Divide Fractions: A Step-by-Step Guide to Solving $3 \frac{8}{9} \div 1 \frac{2}{3}$

When it comes to dividing fractions, many of us struggle to understand the concept and apply it correctly. However, with a clear understanding of the steps involved, dividing fractions can be a straightforward process. In this article, we will explore the concept of dividing fractions and provide a step-by-step guide on how to solve the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ .

What is Dividing Fractions?

Dividing fractions is the process of finding the quotient of two fractions. It involves inverting the second fraction (i.e., flipping the numerator and denominator) and then multiplying the two fractions together. This process is also known as "inverting and multiplying."

Why Do We Need to Invert and Multiply?

When we divide one fraction by another, we are essentially asking how many times the first fraction fits into the second fraction. To find this out, we need to compare the two fractions. By inverting the second fraction, we are essentially making it easier to compare the two fractions. This is because the inverted fraction has the same value as the original fraction, but with the numerator and denominator swapped.

Step-by-Step Guide to Dividing Fractions

To divide fractions, follow these steps:

Invert the second fraction: Flip the numerator and denominator of the second fraction.
Multiply the two fractions: Multiply the first fraction by the inverted second fraction.
Simplify the result: Simplify the resulting fraction, if possible.

Solving $3 \frac{8}{9} \div 1 \frac{2}{3}$

To solve the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ , we will follow the steps outlined above.

Step 1: Invert the Second Fraction

The second fraction is $1 \frac{2}{3}$ . To invert it, we need to flip the numerator and denominator. The inverted fraction is $\frac{3}{2}$ .

Step 2: Multiply the Two Fractions

Now that we have the inverted second fraction, we can multiply the two fractions together. The first fraction is $3 \frac{8}{9}$ , and the inverted second fraction is $\frac{3}{2}$ . To multiply these fractions, we need to multiply the numerators and denominators separately.

$3 \frac{8}{9} \div 1 \frac{2}{3} = \frac{3 \times 9 + 8}{9} \div \frac{3}{2}$

$= \frac{27 + 8}{9} \div \frac{3}{2}$

$= \frac{35}{9} \div \frac{3}{2}$

Step 3: Simplify the Result

Now that we have multiplied the two fractions together, we need to simplify the result. To do this, we can divide the numerator by the denominator.

$\frac{35}{9} \div \frac{3}{2} = \frac{35}{9} \times \frac{2}{3}$

$= \frac{35 \times 2}{9 \times 3}$

$= \frac{70}{27}$

Dividing fractions can be a challenging concept, but with a clear understanding of the steps involved, it can be a straightforward process. By inverting the second fraction and then multiplying the two fractions together, we can find the quotient of two fractions. In this article, we have provided a step-by-step guide on how to solve the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ .

The final answer to the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ is $\boxed{2}$ .

Why is the Final Answer 2?

The final answer is 2 because when we divide $3 \frac{8}{9}$ by $1 \frac{2}{3}$ , we are essentially asking how many times $1 \frac{2}{3}$ fits into $3 \frac{8}{9}$ . To find this out, we need to compare the two fractions. By inverting the second fraction and then multiplying the two fractions together, we can find the quotient of the two fractions. In this case, the quotient is 2.

Common Mistakes to Avoid

When dividing fractions, there are several common mistakes to avoid. These include:

Not inverting the second fraction: Failing to invert the second fraction can lead to incorrect results.
Not multiplying the two fractions together: Failing to multiply the two fractions together can also lead to incorrect results.
Not simplifying the result: Failing to simplify the result can lead to incorrect answers.

Tips and Tricks

When dividing fractions, there are several tips and tricks to keep in mind. These include:

Use a common denominator: When multiplying fractions, it is often helpful to use a common denominator.
Simplify the fractions: Before multiplying fractions, it is often helpful to simplify the fractions.
Check your work: Before giving an answer, it is often helpful to check your work to ensure that it is correct.

In our previous article, we explored the concept of dividing fractions and provided a step-by-step guide on how to solve the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ . However, we know that sometimes, the best way to learn is through practice and asking questions. In this article, we will provide a Q&A guide to help you better understand the concept of dividing fractions and how to solve problems like $3 \frac{8}{9} \div 1 \frac{2}{3}$ .

Q: What is the first step in dividing fractions?

A: The first step in dividing fractions is to invert the second fraction. This means flipping the numerator and denominator of the second fraction.

Q: Why do we need to invert the second fraction?

A: We need to invert the second fraction because it makes it easier to compare the two fractions. By inverting the second fraction, we are essentially making it easier to find the quotient of the two fractions.

Q: How do we invert a fraction?

A: To invert a fraction, we simply flip the numerator and denominator. For example, if we have the fraction $\frac{3}{4}$ , the inverted fraction would be $\frac{4}{3}$ .

Q: What is the next step in dividing fractions?

A: The next step in dividing fractions is to multiply the two fractions together. This means multiplying the numerators and denominators separately.

Q: How do we multiply fractions?

A: To multiply fractions, we simply multiply the numerators and denominators separately. For example, if we have the fractions $\frac{2}{3}$ and $\frac{3}{4}$ , we would multiply the numerators and denominators as follows:

$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}$

Q: What is the final step in dividing fractions?

A: The final step in dividing fractions is to simplify the result. This means simplifying the fraction to its simplest form.

Q: How do we simplify a fraction?

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

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction.

Q: How do we find the GCD?

A: To find the GCD, we can use a variety of methods, including listing the factors of the numerator and denominator, using the Euclidean algorithm, or using a calculator.

Q: What is the final answer to the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ ?

A: The final answer to the problem $3 \frac{8}{9} \div 1 \frac{2}{3}$ is $\boxed{2}$ .

Q: Why is the final answer 2?

A: The final answer is 2 because when we divide $3 \frac{8}{9}$ by $1 \frac{2}{3}$ , we are essentially asking how many times $1 \frac{2}{3}$ fits into $3 \frac{8}{9}$ . To find this out, we need to compare the two fractions. By inverting the second fraction and then multiplying the two fractions together, we can find the quotient of the two fractions. In this case, the quotient is 2.

Dividing fractions can be a challenging concept, but with a clear understanding of the steps involved, it can be a straightforward process. By inverting the second fraction and then multiplying the two fractions together, we can find the quotient of two fractions. In this article, we have provided a Q&A guide to help you better understand the concept of dividing fractions and how to solve problems like $3 \frac{8}{9} \div 1 \frac{2}{3}$ .