Select The Two Correct Statements.A. The Product Of 3 5 \frac{3}{5} 5 3 ​ And 4 Is Greater Than 4.B. The Product Of 3 5 \frac{3}{5} 5 3 ​ And 4 Is Less Than 3 5 \frac{3}{5} 5 3 ​ .C. The Product Of 1 1 2 1 \frac{1}{2} 1 2 1 ​ And 2 Is Greater Than

Understanding the Problem

In this article, we will be discussing two statements related to mathematical operations. We will analyze each statement and determine whether it is correct or incorrect. The statements involve multiplication and comparison of fractions and mixed numbers.

Statement A: The Product of $\frac{3}{5}$ and 4 is Greater than 4

To determine whether statement A is correct, we need to calculate the product of $\frac{3}{5}$ and 4.

$\frac{3}{5} \times 4 = \frac{3 \times 4}{5} = \frac{12}{5}$

Since $\frac{12}{5}$ is greater than 4, statement A is correct.

Statement B: The Product of $\frac{3}{5}$ and 4 is Less than $\frac{3}{5}$

To determine whether statement B is correct, we need to compare the product of $\frac{3}{5}$ and 4 with $\frac{3}{5}$.

$\frac{3}{5} \times 4 = \frac{12}{5}$

Since $\frac{12}{5}$ is greater than $\frac{3}{5}$, statement B is incorrect.

Statement C: The Product of $1 \frac{1}{2}$ and 2 is Greater than

To determine whether statement C is correct, we need to calculate the product of $1 \frac{1}{2}$ and 2.

First, we need to convert the mixed number $1 \frac{1}{2}$ to an improper fraction.

$1 \frac{1}{2} = \frac{3}{2}$

Now, we can calculate the product.

$\frac{3}{2} \times 2 = \frac{3 \times 2}{2} = 3$

Since 3 is greater than 2, statement C is correct.

Conclusion

In conclusion, we have analyzed three statements related to mathematical operations. We have determined that statement A is correct, statement B is incorrect, and statement C is correct.

Key Takeaways

• The product of $\frac{3}{5}$ and 4 is greater than 4.
• The product of $\frac{3}{5}$ and 4 is not less than $\frac{3}{5}$.
• The product of $1 \frac{1}{2}$ and 2 is greater than 2.

Final Thoughts

In this article, we have discussed the importance of understanding mathematical operations and their applications. We have analyzed three statements related to multiplication and comparison of fractions and mixed numbers. By following the steps outlined in this article, readers can develop a deeper understanding of mathematical concepts and improve their problem-solving skills.

Additional Resources

For readers who want to learn more about mathematical operations and their applications, we recommend the following resources:

• Khan Academy: A free online platform that offers video lessons and practice exercises on various mathematical topics.
• Mathway: A math problem solver that can help readers solve mathematical problems and equations.
• Wolfram Alpha: A computational knowledge engine that can provide readers with information on various mathematical topics.

Q: What is the difference between a fraction and a mixed number?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, $\frac{3}{5}$ is a fraction. A mixed number, on the other hand, is a combination of a whole number and a fraction. For example, $1 \frac{1}{2}$ is a mixed number.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. Then, you need to write the result as a fraction with the denominator as the new denominator.

For example, to convert $1 \frac{1}{2}$ to an improper fraction, you need to multiply 1 by 2 and add 1. This gives you 3. Then, you need to write the result as a fraction with 2 as the denominator.

$1 \frac{1}{2} = \frac{3}{2}$

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators and multiply the denominators. Then, you need to simplify the result.

For example, to multiply $\frac{3}{5}$ and $\frac{4}{7}$, you need to multiply 3 by 4 and multiply 5 by 7. This gives you $\frac{12}{35}$.

$\frac{3}{5} \times \frac{4}{7} = \frac{12}{35}$

Q: How do I compare fractions?

A: To compare fractions, you need to compare the numerators and denominators. If the numerators are the same, then the fraction with the smaller denominator is larger. If the denominators are the same, then the fraction with the larger numerator is larger.

For example, to compare $\frac{3}{5}$ and $\frac{4}{5}$, you need to compare the numerators. Since 3 is less than 4, $\frac{3}{5}$ is smaller than $\frac{4}{5}$.

Q: How do I add fractions?

A: To add fractions, you need to have the same denominator. Then, you need to add the numerators and keep the denominator the same.

For example, to add $\frac{3}{5}$ and $\frac{4}{5}$, you need to have the same denominator, which is 5. Then, you need to add the numerators, which gives you 7.

$\frac{3}{5} + \frac{4}{5} = \frac{7}{5}$

Q: How do I subtract fractions?

A: To subtract fractions, you need to have the same denominator. Then, you need to subtract the numerators and keep the denominator the same.

For example, to subtract $\frac{3}{5}$ from $\frac{4}{5}$, you need to have the same denominator, which is 5. Then, you need to subtract the numerators, which gives you 1.

$\frac{4}{5} - \frac{3}{5} = \frac{1}{5}$

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. Then, you need to divide both the numerator and denominator by the GCD.

For example, to simplify $\frac{12}{18}$, you need to find the GCD of 12 and 18, which is 6. Then, you need to divide both the numerator and denominator by 6.

$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

Conclusion

In conclusion, we have discussed some frequently asked questions on mathematical operations. We have covered topics such as converting mixed numbers to improper fractions, multiplying fractions, comparing fractions, adding fractions, subtracting fractions, the order of operations, and simplifying fractions. By following the steps outlined in this article, readers can develop a deeper understanding of mathematical concepts and improve their problem-solving skills.