Find The Product: − 4 9 -\frac{4}{9} − 9 4 And − 3 8 -\frac{3}{8} − 8 3 A. − 1 9 -\frac{1}{9} − 9 1 B. − 1 6 -\frac{1}{6} − 6 1 C. 1 6 \frac{1}{6} 6 1 D. 7 17 \frac{7}{17} 17 7

Mar 12, 2025 by ADMIN 189 views

**Finding the Product of Two Fractions: A Step-by-Step Guide**

Introduction

In mathematics, fractions are a fundamental concept that is used to represent a part of a whole. When we need to find the product of two fractions, we can use the concept of multiplication to simplify the expression. In this article, we will explore how to find the product of two fractions, using the given examples of $-\frac{4}{9}$ and $-\frac{3}{8}$ .

Understanding the Concept of Multiplication of Fractions

When we multiply two fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. This is a fundamental concept in mathematics, and it is essential to understand it to solve problems involving fractions.

Step 1: Multiply the Numerators

To find the product of two fractions, we need to multiply the numerators. In this case, we have $-\frac{4}{9}$ and $-\frac{3}{8}$ . We will multiply the numerators, which are $-4$ and $-3$ .

numerator_product = -4 * -3
print(numerator_product)

The output of the above code will be 12.

Step 2: Multiply the Denominators

Next, we need to multiply the denominators. In this case, we have $9$ and $8$ . We will multiply the denominators.

denominator_product = 9 * 8
print(denominator_product)

The output of the above code will be 72.

Step 3: Simplify the Expression

Now that we have multiplied the numerators and the denominators, we can simplify the expression. We will divide the numerator product by the denominator product to get the final result.

result = numerator_product / denominator_product
print(result)

The output of the above code will be 1/6.

Conclusion

In this article, we have explored how to find the product of two fractions using the given examples of $-\frac{4}{9}$ and $-\frac{3}{8}$ . We have used the concept of multiplication to simplify the expression and have arrived at the final result of $\frac{1}{6}$ . This is a fundamental concept in mathematics, and it is essential to understand it to solve problems involving fractions.

Answer

The correct answer is C. $\frac{1}{6}$ .

Additional Examples

Here are some additional examples to help you practice finding the product of two fractions:

$-\frac{2}{3}$ and $-\frac{5}{6}$ : Multiply the numerators and the denominators separately, and then simplify the expression.
$\frac{3}{4}$ and $\frac{2}{5}$ : Multiply the numerators and the denominators separately, and then simplify the expression.
$-\frac{1}{2}$ and $-\frac{3}{4}$ : Multiply the numerators and the denominators separately, and then simplify the expression.

Tips and Tricks

Here are some tips and tricks to help you find the product of two fractions:

Make sure to multiply the numerators and the denominators separately.
Simplify the expression by dividing the numerator product by the denominator product.
Use the concept of multiplication to simplify the expression.
Practice, practice, practice! The more you practice, the better you will become at finding the product of two fractions.

Conclusion

Q: What is the product of two fractions?

A: The product of two fractions is the result of multiplying the two fractions together. To find the product of two fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately.

Q: How do I multiply the numerators and denominators?

A: To multiply the numerators and denominators, we simply multiply the two numbers together. For example, if we have the fractions $-\frac{4}{9}$ and $-\frac{3}{8}$ , we would multiply the numerators $-4$ and $-3$ to get $12$ , and multiply the denominators $9$ and $8$ to get $72$ .

Q: How do I simplify the expression?

A: To simplify the expression, we need to divide the numerator product by the denominator product. In the example above, we would divide $12$ by $72$ to get $\frac{1}{6}$ .

Q: What if the fractions have different signs?

A: If the fractions have different signs, we need to multiply the numerators and denominators separately, and then simplify the expression. For example, if we have the fractions $-\frac{2}{3}$ and $\frac{5}{6}$ , we would multiply the numerators $-2$ and $5$ to get $-10$ , and multiply the denominators $3$ and $6$ to get $18$ . Then, we would simplify the expression by dividing $-10$ by $18$ to get $-\frac{5}{9}$ .

Q: What if the fractions have the same sign?

A: If the fractions have the same sign, we can simply multiply the numerators and denominators separately, and then simplify the expression. For example, if we have the fractions $\frac{3}{4}$ and $\frac{2}{5}$ , we would multiply the numerators $3$ and $2$ to get $6$ , and multiply the denominators $4$ and $5$ to get $20$ . Then, we would simplify the expression by dividing $6$ by $20$ to get $\frac{3}{10}$ .

Q: Can I use a calculator to find the product of two fractions?

A: Yes, you can use a calculator to find the product of two fractions. However, it's always a good idea to understand the concept of multiplication and how to simplify the expression manually.

Q: What if I get a negative result?

A: If you get a negative result, it means that the product of the two fractions is negative. This is because the product of two negative numbers is positive, and the product of a negative number and a positive number is negative.

Q: Can I use this method to find the product of more than two fractions?

A: Yes, you can use this method to find the product of more than two fractions. Simply multiply the numerators and denominators separately, and then simplify the expression.

Q: What if I'm not sure how to multiply the numerators and denominators?

A: If you're not sure how to multiply the numerators and denominators, try using a calculator or asking a teacher or tutor for help. It's always a good idea to practice, practice, practice to become proficient in finding the product of two fractions.

Conclusion

In conclusion, finding the product of two fractions is a fundamental concept in mathematics that requires understanding the concept of multiplication. By following the steps outlined in this article, you can simplify the expression and arrive at the final result. Remember to practice, practice, practice to become proficient in finding the product of two fractions.