Relate Fraction Division To Fraction Multiplication.Which Equation Shows The Same Relationship As $72 \times \frac{1}{8}=9$?Choose 1 Answer:A. $72=9 \div \frac{1}{8}$B. $72=\frac{1}{8} \div 9$C. $72 \times 9=\frac{1}{8}$

Feb 28, 2025 by ADMIN 221 views

**Relating Fraction Division to Fraction Multiplication**

Understanding the Relationship Between Division and Multiplication

In mathematics, division and multiplication are two fundamental operations that are closely related. While they may seem like distinct concepts, they are actually two sides of the same coin. In this article, we will explore the relationship between fraction division and fraction multiplication, and examine which equation shows the same relationship as $72 \times \frac{1}{8}=9$ .

The Concept of Division as the Inverse of Multiplication

Division is often thought of as the inverse operation of multiplication. In other words, if we have a product of two numbers, we can divide one of the numbers by the other to obtain the other factor. For example, if we have $72 \times \frac{1}{8}=9$ , we can divide 72 by $\frac{1}{8}$ to obtain 9.

The Relationship Between Fraction Division and Fraction Multiplication

When we divide a fraction by another fraction, we are essentially finding the reciprocal of the second fraction and multiplying it by the first fraction. In other words, if we have $\frac{a}{b} \div \frac{c}{d}$ , we can rewrite it as $\frac{a}{b} \times \frac{d}{c}$ .

Analyzing the Given Equation

The given equation is $72 \times \frac{1}{8}=9$ . To find the relationship between this equation and the concept of division, we need to examine the equation more closely. We can start by rewriting the equation as a division problem:

72 \div \frac{1}{8}=9

This equation shows that 72 divided by $\frac{1}{8}$ is equal to 9. But what does this mean in terms of fraction division?

Rewriting the Equation as a Fraction Division Problem

To rewrite the equation as a fraction division problem, we need to find the reciprocal of $\frac{1}{8}$ . The reciprocal of a fraction is obtained by swapping the numerator and denominator. Therefore, the reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ .

Now, we can rewrite the equation as:

72 \div \frac{1}{8}=72 \times \frac{8}{1}=9

This equation shows that 72 divided by $\frac{1}{8}$ is equal to 72 multiplied by $\frac{8}{1}$ , which is equal to 9.

Choosing the Correct Equation

Based on our analysis, we can see that the correct equation is:

72=9 \div \frac{1}{8}

This equation shows the same relationship as $72 \times \frac{1}{8}=9$ . The other options do not show the same relationship.

Conclusion

In conclusion, the relationship between fraction division and fraction multiplication is closely tied to the concept of division as the inverse of multiplication. By understanding this relationship, we can rewrite division problems as multiplication problems and vice versa. In this article, we analyzed the given equation $72 \times \frac{1}{8}=9$ and rewrote it as a division problem. We then found the reciprocal of $\frac{1}{8}$ and rewrote the equation as a fraction division problem. Finally, we chose the correct equation that shows the same relationship as the given equation.

Key Takeaways

Division is the inverse operation of multiplication.
Fraction division can be rewritten as fraction multiplication by finding the reciprocal of the second fraction.
The correct equation that shows the same relationship as $72 \times \frac{1}{8}=9$ is $72=9 \div \frac{1}{8}$ .

Q: What is the relationship between fraction division and fraction multiplication?

A: The relationship between fraction division and fraction multiplication is closely tied to the concept of division as the inverse of multiplication. When we divide a fraction by another fraction, we are essentially finding the reciprocal of the second fraction and multiplying it by the first fraction.

Q: How do I rewrite a division problem as a multiplication problem?

A: To rewrite a division problem as a multiplication problem, you need to find the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, if you have $\frac{a}{b} \div \frac{c}{d}$ , you can rewrite it as $\frac{a}{b} \times \frac{d}{c}$ .

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ .

Q: How do I find the reciprocal of a fraction?

A: To find the reciprocal of a fraction, you simply need to swap the numerator and denominator. For example, if you have $\frac{a}{b}$ , the reciprocal is $\frac{b}{a}$ .

Q: Can you give me an example of rewriting a division problem as a multiplication problem?

A: Let's say we have the division problem $\frac{1}{2} \div \frac{3}{4}$ . To rewrite this as a multiplication problem, we need to find the reciprocal of $\frac{3}{4}$ , which is $\frac{4}{3}$ . Therefore, we can rewrite the division problem as a multiplication problem as follows:

\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3}

Q: How do I know which fraction to multiply by the other fraction?

A: When rewriting a division problem as a multiplication problem, you need to multiply the first fraction by the reciprocal of the second fraction. In other words, if you have $\frac{a}{b} \div \frac{c}{d}$ , you can rewrite it as $\frac{a}{b} \times \frac{d}{c}$ .

Q: Can you give me an example of a real-world application of relating fraction division to fraction multiplication?

A: Let's say you are baking a cake and you need to divide a recipe into 8 equal parts. The recipe calls for 1 cup of sugar, but you only have 1/8 cup measuring cups. To find out how much sugar you need to use for each part, you can divide 1 cup by 1/8 cup. This can be rewritten as a multiplication problem as follows:

1 \div \frac{1}{8} = 1 \times \frac{8}{1} = 8

Therefore, you need to use 8 times 1/8 cup of sugar for each part of the recipe.

Q: What are some common mistakes to avoid when relating fraction division to fraction multiplication?

A: Some common mistakes to avoid when relating fraction division to fraction multiplication include:

Not finding the reciprocal of the second fraction
Not multiplying the first fraction by the reciprocal of the second fraction
Not simplifying the resulting fraction

By avoiding these common mistakes, you can ensure that you are accurately relating fraction division to fraction multiplication.