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

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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, 1141 \frac{1}{4} and 5355 \frac{3}{5}, 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 abca \frac{b}{c}, where aa is the whole number part, and bc\frac{b}{c} 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 1141 \frac{1}{4} to an improper fraction, we multiply the whole number part (1) by the denominator (4) and add the numerator (1). This gives us:

1×4+1=51 \times 4 + 1 = 5

So, 1141 \frac{1}{4} can be written as 54\frac{5}{4}.

Similarly, to convert 5355 \frac{3}{5} to an improper fraction, we multiply the whole number part (5) by the denominator (5) and add the numerator (3). This gives us:

5×5+3=285 \times 5 + 3 = 28

So, 5355 \frac{3}{5} can be written as 285\frac{28}{5}.

Multiplying Improper Fractions

Now that we have converted both mixed numbers to improper fractions, we can multiply them together.

54×285\frac{5}{4} \times \frac{28}{5}

To multiply fractions, we multiply the numerators together and the denominators together.

5×284×5\frac{5 \times 28}{4 \times 5}

This simplifies to:

14020\frac{140}{20}

Simplifying the Result

The resulting fraction, 14020\frac{140}{20}, 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.

140÷2020÷20=71\frac{140 \div 20}{20 \div 20} = \frac{7}{1}

So, the product of 1141 \frac{1}{4} and 5355 \frac{3}{5} is 7.

Conclusion

In this article, we have explored the multiplication of two mixed numbers, 1141 \frac{1}{4} and 5355 \frac{3}{5}. 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

Introduction

In our previous article, we explored the multiplication of two mixed numbers, 1141 \frac{1}{4} and 5355 \frac{3}{5}. 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 1141 \frac{1}{4} and 5355 \frac{3}{5}?

A: The product of 1141 \frac{1}{4} and 5355 \frac{3}{5} 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