How Will The Product Of 72 × 3 7 72 \times \frac{3}{7} 72 × 7 3 ​ Compare To 72, And Why?Choose One Answer:A. It Will Be Less Because We Are Multiplying 72 By A Fraction That Is Less Than 1.B. It Will Be Equal Because We Are Multiplying 72 By A Fraction That Is

When it comes to multiplying a whole number by a fraction, it's essential to understand how the result compares to the original whole number. In this article, we'll delve into the concept of multiplying a whole number by a fraction and explore how the product compares to the original number.

What is a Fraction?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction 3/7 represents three parts out of seven equal parts.

Multiplying a Whole Number by a Fraction

When we multiply a whole number by a fraction, we are essentially finding a part of the whole number. The result of this multiplication is a fraction that represents the part of the whole number.

The Product of $72 \times \frac{3}{7}$

Let's consider the product of $72 \times \frac{3}{7}$. To find the product, we multiply the whole number 72 by the fraction 3/7.

Step 1: Multiply the Numerator and the Whole Number

To multiply the numerator and the whole number, we multiply 3 (the numerator) by 72 (the whole number).

3 × 72 = 216

Step 2: Divide the Product by the Denominator

Now, we divide the product (216) by the denominator (7) to get the final result.

216 ÷ 7 = 30.86 (approximately)

Comparing the Product to the Original Whole Number

Now that we have the product of $72 \times \frac{3}{7}$, let's compare it to the original whole number 72.

Why is the Product Less than the Original Whole Number?

The product of $72 \times \frac{3}{7}$ is less than the original whole number 72 because we are multiplying 72 by a fraction that is less than 1. The fraction 3/7 is less than 1, so when we multiply 72 by this fraction, the result is less than 72.

Conclusion

In conclusion, when we multiply a whole number by a fraction that is less than 1, the product is less than the original whole number. This is because the fraction represents a part of the whole number, and multiplying by a fraction less than 1 results in a smaller part of the whole number.

Why is this Important?

Understanding how to multiply a whole number by a fraction is essential in various mathematical operations, such as finding percentages, calculating proportions, and solving equations. By grasping this concept, you'll be better equipped to tackle complex mathematical problems and make informed decisions in real-world applications.

Real-World Applications

Multiplying a whole number by a fraction has numerous real-world applications, including:

• Finance: When calculating interest rates or investment returns, you may need to multiply a whole number by a fraction to find the total amount.
• Science: In scientific calculations, you may need to multiply a whole number by a fraction to find the result of a chemical reaction or a physical process.
• Engineering: In engineering applications, you may need to multiply a whole number by a fraction to find the result of a mechanical or electrical calculation.

Final Thoughts

In our previous article, we explored the concept of multiplying a whole number by a fraction and how the product compares to the original whole number. In this article, we'll address some frequently asked questions related to this topic.

Q: What happens when we multiply a whole number by a fraction that is greater than 1?

A: When we multiply a whole number by a fraction that is greater than 1, the product is greater than the original whole number. This is because the fraction represents a part of the whole number that is larger than the whole number itself.

Q: Can we multiply a whole number by a fraction that is equal to 1?

A: Yes, we can multiply a whole number by a fraction that is equal to 1. In this case, the product will be equal to the original whole number. For example, 72 × 1 = 72.

Q: What is the difference between multiplying a whole number by a fraction and multiplying a fraction by a whole number?

A: When we multiply a whole number by a fraction, we are essentially finding a part of the whole number. When we multiply a fraction by a whole number, we are essentially finding a multiple of the fraction. For example, 3/7 × 4 = 12/7, while 4 × 3/7 = 12/7.

Q: Can we multiply a whole number by a fraction that has a negative sign?

A: Yes, we can multiply a whole number by a fraction that has a negative sign. In this case, the product will have a negative sign. For example, 72 × (-3/7) = -216/7.

Q: What is the relationship between multiplying a whole number by a fraction and dividing a whole number by a fraction?

A: When we multiply a whole number by a fraction, we are essentially finding a part of the whole number. When we divide a whole number by a fraction, we are essentially finding the whole number that is equal to the fraction. For example, 72 ÷ (3/7) = 72 × (7/3) = 168.

Q: Can we multiply a whole number by a fraction that has a decimal value?

A: Yes, we can multiply a whole number by a fraction that has a decimal value. In this case, we can convert the decimal value to a fraction and then multiply the whole number by the fraction. For example, 72 × 0.4 = 72 × (4/10) = 28.8.

Q: What is the importance of understanding how to multiply a whole number by a fraction?

A: Understanding how to multiply a whole number by a fraction is essential in various mathematical operations, such as finding percentages, calculating proportions, and solving equations. By grasping this concept, you'll be better equipped to tackle complex mathematical problems and make informed decisions in real-world applications.

Conclusion

In conclusion, multiplying a whole number by a fraction is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to multiply a whole number by a fraction, you'll be better equipped to tackle complex mathematical problems and make informed decisions in various fields.

Common Mistakes to Avoid

When multiplying a whole number by a fraction, it's essential to avoid common mistakes such as:

• Forgetting to multiply the numerator and the whole number: Make sure to multiply the numerator and the whole number before dividing the product by the denominator.
• Dividing the numerator by the denominator instead of multiplying: Remember to multiply the numerator and the whole number, and then divide the product by the denominator.
• Not considering the sign of the fraction: Make sure to consider the sign of the fraction when multiplying a whole number by a fraction.

Final Thoughts

In conclusion, multiplying a whole number by a fraction is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to multiply a whole number by a fraction, you'll be better equipped to tackle complex mathematical problems and make informed decisions in various fields.