Comparing the Product to the Options

Oct 13, 2025 by vinooalluri.com 50 views

Introduction

When dealing with fractions and multiplication, it's essential to understand the properties of fractions and how they interact with other numbers. In this case, we're given the product $\frac{14}{25} \times 3$ and asked to determine which statement is true about it. To approach this problem, we need to first calculate the product and then compare it to the given options.

Calculating the Product

To calculate the product $\frac{14}{25} \times 3$ , we can start by multiplying the numerator (14) by 3, which gives us 42. Then, we multiply the denominator (25) by 3, which gives us 75. So, the product is $\frac{42}{75}$ .

Comparing the Product to the Options

Now that we have the product $\frac{42}{75}$ , we can compare it to the given options to determine which statement is true.

Option A: The Product is Greater than 1

To determine if the product is greater than 1, we need to compare it to 1. We can do this by converting the fraction to a decimal or by comparing it to a whole number. Let's convert the fraction to a decimal by dividing the numerator (42) by the denominator (75). This gives us a decimal value of approximately 0.56. Since 0.56 is less than 1, we can conclude that the product is not greater than 1.

Option B: The Product is Equal to 3

To determine if the product is equal to 3, we can compare it to 3. We can do this by converting the fraction to a decimal or by comparing it to a whole number. Let's convert the fraction to a decimal by dividing the numerator (42) by the denominator (75). This gives us a decimal value of approximately 0.56. Since 0.56 is not equal to 3, we can conclude that the product is not equal to 3.

Option C: The Product is Less than 3

To determine if the product is less than 3, we can compare it to 3. We can do this by converting the fraction to a decimal or by comparing it to a whole number. Let's convert the fraction to a decimal by dividing the numerator (42) by the denominator (75). This gives us a decimal value of approximately 0.56. Since 0.56 is less than 3, we can conclude that the product is indeed less than 3.

Conclusion

In conclusion, the product $\frac{14}{25} \times 3$ is less than 3. This is because the decimal value of the product (approximately 0.56) is less than 3. Therefore, the correct statement is:

The product is less than 3.

Frequently Asked Questions

Q: What is the product of $\frac{14}{25} \times 3$ ?

A: The product is $\frac{42}{75}$ .

Q: Is the product greater than 1?

A: No, the product is not greater than 1.

Q: Is the product equal to 3?

A: No, the product is not equal to 3.

Q: Is the product less than 3?

A: Yes, the product is less than 3.

Final Thoughts

When dealing with fractions and multiplication, it's essential to understand the properties of fractions and how they interact with other numbers. In this case, we calculated the product $\frac{14}{25} \times 3$ and compared it to the given options to determine which statement is true. We found that the product is indeed less than 3. This demonstrates the importance of understanding fractions and how to work with them in mathematical operations.

Additional Resources

For more information on fractions and multiplication, you can refer to the following resources:

Introduction

Fractions and multiplication can be a challenging topic for many students. In our previous article, we discussed the product $\frac{14}{25} \times 3$ and determined that it is less than 3. In this article, we will answer some frequently asked questions about fractions and multiplication.

Q&A

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I multiply fractions?

A: To multiply fractions, you multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). Then, simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator.

Q: What is the product of $\frac{3}{4} \times 2$ ?

A: To find the product, multiply the numerator (3) by 2, which gives 6. Then, multiply the denominator (4) by 2, which gives 8. So, the product is $\frac{6}{8}$ , which can be simplified to $\frac{3}{4}$ .

Q: Is the product of $\frac{3}{4} \times 2$ equal to 2?

A: No, the product of $\frac{3}{4} \times 2$ is not equal to 2. As we calculated earlier, the product is $\frac{6}{8}$ , which can be simplified to $\frac{3}{4}$ .

Q: Is the product of $\frac{3}{4} \times 2$ greater than 2?

A: No, the product of $\frac{3}{4} \times 2$ is not greater than 2. As we calculated earlier, the product is $\frac{6}{8}$ , which can be simplified to $\frac{3}{4}$ , which is less than 2.

Q: Can I multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number. To do this, multiply the numerator (the number on top) by the whole number, and multiply the denominator (the number on the bottom) by 1.

Q: What is the product of $\frac{1}{2} \times 5$ ?

A: To find the product, multiply the numerator (1) by 5, which gives 5. Then, multiply the denominator (2) by 1, which gives 2. So, the product is $\frac{5}{2}$ .

Q: Is the product of $\frac{1}{2} \times 5$ equal to 5?

A: No, the product of $\frac{1}{2} \times 5$ is not equal to 5. As we calculated earlier, the product is $\frac{5}{2}$ .

Q: Is the product of $\frac{1}{2} \times 5$ greater than 5?

A: No, the product of $\frac{1}{2} \times 5$ is not greater than 5. As we calculated earlier, the product is $\frac{5}{2}$ , which is less than 5.

Conclusion

In conclusion, fractions and multiplication can be a challenging topic, but with practice and understanding, you can become proficient in working with fractions and multiplying them by whole numbers. Remember to multiply the numerators and denominators, simplify the resulting fraction, and convert fractions to decimals as needed.

Frequently Asked Questions

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I multiply fractions?

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator.

Final Thoughts

Fractions and multiplication are essential concepts in mathematics, and with practice and understanding, you can become proficient in working with fractions and multiplying them by whole numbers. Remember to multiply the numerators and denominators, simplify the resulting fraction, and convert fractions to decimals as needed.

Additional Resources

For more information on fractions and multiplication, you can refer to the following resources: