Complete The Blanks.${ \frac{7}{8} \times \frac{3}{5} = \begin{array}{c} \square \ \square \end{array} }$
Understanding the Basics of Multiplying Fractions
Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to get a product. In this article, we will focus on multiplying two fractions, specifically the product of 7/8 and 3/5. To begin with, let's understand the basics of multiplying fractions.
What are Fractions?
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 3/4 represents 3 parts out of a total of 4 parts.
How to Multiply Fractions
To multiply fractions, we simply multiply the numerators together and multiply the denominators together. This is a straightforward process that can be applied to any two fractions.
Multiplying 7/8 and 3/5
Now that we have a basic understanding of multiplying fractions, let's apply this concept to the given problem: 7/8 × 3/5.
To multiply these fractions, we multiply the numerators (7 and 3) together and multiply the denominators (8 and 5) together.
7/8 × 3/5 = ?
To find the product, we multiply the numerators and denominators separately:
- Numerator: 7 × 3 = 21
- Denominator: 8 × 5 = 40
Therefore, the product of 7/8 and 3/5 is 21/40.
Simplifying the Product
In some cases, the product of two fractions may be able to be simplified. Simplifying a fraction involves reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).
To simplify the product 21/40, we need to find the GCD of 21 and 40. The GCD of 21 and 40 is 1, since they have no common factors other than 1.
Since the GCD is 1, the product 21/40 is already in its simplest form.
Real-World Applications of Multiplying Fractions
Multiplying fractions has numerous real-world applications in various fields, including science, engineering, and finance.
For example, in science, multiplying fractions can be used to calculate the concentration of a solution. In engineering, it can be used to calculate the stress on a material. In finance, it can be used to calculate the interest on an investment.
Conclusion
In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to get a product. By understanding the basics of multiplying fractions and applying this concept to the given problem, we can find the product of 7/8 and 3/5 to be 21/40. This concept has numerous real-world applications in various fields, making it an essential skill to possess.
Frequently Asked Questions
Q: What is the product of 7/8 and 3/5?
A: The product of 7/8 and 3/5 is 21/40.
Q: How do I multiply fractions?
A: To multiply fractions, you multiply the numerators together and multiply the denominators together.
Q: Can the product of two fractions be simplified?
A: Yes, the product of two fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
Q: What are some real-world applications of multiplying fractions?
A: Multiplying fractions has numerous real-world applications in various fields, including science, engineering, and finance.
Additional Resources
For more information on multiplying fractions, check out the following resources:
- Khan Academy: Multiplying Fractions
- Mathway: Multiplying Fractions
- Wolfram Alpha: Multiplying Fractions
By following these resources and practicing multiplying fractions, you can become proficient in this essential math concept.
Understanding the Basics of Multiplying Fractions
Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to get a product. In this article, we will focus on providing answers to frequently asked questions about multiplying fractions.
Q: What is the product of 7/8 and 3/5?
A: The product of 7/8 and 3/5 is 21/40.
Q: How do I multiply fractions?
A: To multiply fractions, you multiply the numerators together and multiply the denominators together. For example, to multiply 7/8 and 3/5, you would multiply the numerators (7 and 3) together and multiply the denominators (8 and 5) together.
Q: Can the product of two fractions be simplified?
A: Yes, the product of two fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, the product 21/40 can be simplified by dividing both the numerator and denominator by 1, since they have no common factors other than 1.
Q: What are some real-world applications of multiplying fractions?
A: Multiplying fractions has numerous real-world applications in various fields, including science, engineering, and finance. For example, in science, multiplying fractions can be used to calculate the concentration of a solution. In engineering, it can be used to calculate the stress on a material. In finance, it can be used to calculate the interest on an investment.
Q: How do I multiply a fraction by a whole number?
A: To multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number. For example, to multiply 1/2 by 3, you would multiply the numerator (1) by 3 to get 3, and keep the denominator (2) the same.
Q: Can I multiply a fraction by a decimal?
A: Yes, you can multiply a fraction by a decimal. To do this, you can convert the decimal to a fraction and then multiply the fractions together. For example, to multiply 1/2 by 0.5, you can convert 0.5 to a fraction (1/2) and then multiply the fractions together to get 1/4.
Q: How do I multiply a fraction by a fraction with a negative sign?
A: To multiply a fraction by a fraction with a negative sign, you multiply the numerators together and multiply the denominators together, just like you would with two positive fractions. However, you must also multiply the result by -1 to account for the negative sign. For example, to multiply 1/2 by -3/4, you would multiply the numerators (1 and -3) together to get -3, and multiply the denominators (2 and 4) together to get 8. Then, you would multiply the result by -1 to get 24/8, which can be simplified to 3/1 or simply 3.
Q: Can I multiply a fraction by a fraction with a variable?
A: Yes, you can multiply a fraction by a fraction with a variable. To do this, you multiply the numerators together and multiply the denominators together, just like you would with two fractions with numbers. For example, to multiply 1/2 by x/4, you would multiply the numerators (1 and x) together to get x, and multiply the denominators (2 and 4) together to get 8. The result would be x/8.
Q: How do I multiply a fraction by a fraction with a mixed number?
A: To multiply a fraction by a fraction with a mixed number, you can convert the mixed number to an improper fraction and then multiply the fractions together. For example, to multiply 1/2 by 2 3/4, you can convert 2 3/4 to an improper fraction (11/4) and then multiply the fractions together to get 11/8.
Conclusion
In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to get a product. By understanding the basics of multiplying fractions and applying this concept to various scenarios, you can become proficient in this essential math concept.
Frequently Asked Questions
Q: What is the product of 7/8 and 3/5?
A: The product of 7/8 and 3/5 is 21/40.
Q: How do I multiply fractions?
A: To multiply fractions, you multiply the numerators together and multiply the denominators together.
Q: Can the product of two fractions be simplified?
A: Yes, the product of two fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
Q: What are some real-world applications of multiplying fractions?
A: Multiplying fractions has numerous real-world applications in various fields, including science, engineering, and finance.
Additional Resources
For more information on multiplying fractions, check out the following resources:
- Khan Academy: Multiplying Fractions
- Mathway: Multiplying Fractions
- Wolfram Alpha: Multiplying Fractions
By following these resources and practicing multiplying fractions, you can become proficient in this essential math concept.