Find The Product: 1 1 4 × 5 3 5 1 \frac{1}{4} \times 5 \frac{3}{5} 1 4 1 × 5 5 3 A. 5 3 20 5 \frac{3}{20} 5 20 3 B. 6 C. 6 1 4 6 \frac{1}{4} 6 4 1 D. 7
Introduction
In mathematics, multiplication of fractions and mixed numbers is a fundamental operation that requires a clear understanding of the concept. When dealing with mixed numbers, it's essential to convert them into improper fractions to simplify the multiplication process. In this article, we will explore the multiplication of two mixed numbers, and , and find the product.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It can be represented as , where is the whole number part, and is the fractional part. To multiply mixed numbers, we need to convert them into improper fractions.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. The result is then written as the new numerator over the original denominator.
For example, to convert to an improper fraction, we multiply the whole number part (1) by the denominator (4) and add the numerator (1). This gives us:
So, can be written as .
Similarly, to convert to an improper fraction, we multiply the whole number part (5) by the denominator (5) and add the numerator (3). This gives us:
So, can be written as .
Multiplying Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can multiply them together.
To multiply fractions, we multiply the numerators together and the denominators together.
This simplifies to:
Simplifying the Result
The resulting fraction, , can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 140 and 20 is 20.
So, the product of and is 7.
Conclusion
In this article, we have explored the multiplication of two mixed numbers, and . We converted both mixed numbers to improper fractions and then multiplied them together. The resulting fraction was simplified to find the final product, which is 7.
Discussion
The multiplication of fractions and mixed numbers is a fundamental operation in mathematics. It requires a clear understanding of the concept and the ability to convert mixed numbers to improper fractions. In this article, we have demonstrated how to multiply two mixed numbers and find the product.
Answer
The correct answer is D. 7.
Related Topics
- Multiplication of fractions
- Mixed numbers
- Improper fractions
- Greatest common divisor (GCD)
References
- [1] Khan Academy. (n.d.). Multiplying fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals/fractions-and-decimals-multiplication-and-division/multiplying-fractions/v/multiplying-fractions
- [2] Math Open Reference. (n.d.). Mixed numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html
- [3] Purplemath. (n.d.). Multiplying mixed numbers. Retrieved from https://www.purplemath.com/modules/mixedmult.htm
Introduction
In our previous article, we explored the multiplication of two mixed numbers, and . We converted both mixed numbers to improper fractions and then multiplied them together to find the product. In this article, we will answer some frequently asked questions related to the multiplication of fractions and mixed numbers.
Q&A
Q: What is the difference between a mixed number and an improper fraction?
A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator. The result is then written as the new numerator over the original denominator.
Q: Can I multiply mixed numbers directly?
A: No, you cannot multiply mixed numbers directly. You need to convert them to improper fractions first.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
Q: How do I simplify a fraction?
A: To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).
Q: What is the product of and ?
A: The product of and is 7.
Q: Can I use a calculator to multiply fractions?
A: Yes, you can use a calculator to multiply fractions. However, it's always a good idea to understand the concept and do it manually to ensure accuracy.
Q: What are some real-life applications of multiplying fractions?
A: Multiplying fractions has many real-life applications, such as calculating the area of a rectangle, the volume of a cube, and the cost of a product.
Conclusion
In this article, we have answered some frequently asked questions related to the multiplication of fractions and mixed numbers. We have also provided some tips and tricks to help you understand the concept better.
Discussion
Multiplying fractions and mixed numbers is a fundamental operation in mathematics. It requires a clear understanding of the concept and the ability to convert mixed numbers to improper fractions. In this article, we have demonstrated how to multiply two mixed numbers and find the product.
Answer
The correct answer is D. 7.
Related Topics
- Multiplication of fractions
- Mixed numbers
- Improper fractions
- Greatest common divisor (GCD)
- Simplifying fractions
- Real-life applications of multiplying fractions
References
- [1] Khan Academy. (n.d.). Multiplying fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals/fractions-and-decimals-multiplication-and-division/multiplying-fractions/v/multiplying-fractions
- [2] Math Open Reference. (n.d.). Mixed numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html
- [3] Purplemath. (n.d.). Multiplying mixed numbers. Retrieved from https://www.purplemath.com/modules/mixedmult.htm