Which Statement Describes The Product Of The Expression $5 \times \frac{1}{2}$?A. It Is Less Than $\frac{1}{2}$.B. It Is Greater Than 5.C. It Is Between 5 And 6.D. It Is Between \$\frac{1}{2}$[/tex\] And 5.
Introduction
In mathematics, expressions are used to represent a value or a relationship between values. When we multiply two numbers, we are essentially finding the product of those numbers. In this article, we will analyze the product of the expression $5 \times \frac{1}{2}$ and determine which statement describes it.
The Expression: 5 × 1/2
The given expression is $5 \times \frac{1}{2}$. To find the product, we need to multiply 5 by 1/2. Multiplication is a commutative operation, meaning that the order of the numbers being multiplied does not change the result. Therefore, we can rewrite the expression as $\frac{1}{2} \times 5$.
Multiplying Fractions
When multiplying fractions, we multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom). In this case, we have:
Analyzing the Result
Now that we have found the product of the expression, let's analyze the result. The product is $\frac{5}{2}$. This is a fraction, and we can convert it to a decimal by dividing the numerator by the denominator:
Comparing the Result to the Options
Now that we have found the product of the expression, let's compare it to the options:
A. It is less than $\frac{1}{2}$. B. It is greater than 5. C. It is between 5 and 6. D. It is between $\frac{1}{2}$ and 5.
Option A: It is less than 1/2
The product of the expression is $\frac{5}{2}$, which is equal to 2.5. This is greater than $\frac{1}{2}$, which is equal to 0.5. Therefore, option A is incorrect.
Option B: It is greater than 5
The product of the expression is $\frac{5}{2}$, which is equal to 2.5. This is less than 5, not greater than 5. Therefore, option B is incorrect.
Option C: It is between 5 and 6
The product of the expression is $\frac{5}{2}$, which is equal to 2.5. This is between 5 and 6, but it is closer to 5 than 6. Therefore, option C is partially correct, but it is not the most accurate description of the product.
Option D: It is between 1/2 and 5
The product of the expression is $\frac{5}{2}$, which is equal to 2.5. This is between $\frac{1}{2}$ and 5, and it is closer to 5 than $\frac{1}{2}$. Therefore, option D is the most accurate description of the product.
Conclusion
In conclusion, the product of the expression $5 \times \frac{1}{2}$ is $\frac{5}{2}$, which is equal to 2.5. This is between $\frac{1}{2}$ and 5, making option D the correct answer.
Final Answer
The final answer is:
Q&A: Product of an Expression
In the previous article, we analyzed the product of the expression $5 \times \frac{1}{2}$. In this article, we will answer some frequently asked questions related to the product of an expression.
Q: What is the product of the expression 3 × 1/4?
A: To find the product of the expression 3 × 1/4, we need to multiply 3 by 1/4. Multiplication is a commutative operation, meaning that the order of the numbers being multiplied does not change the result. Therefore, we can rewrite the expression as 1/4 × 3.
When multiplying fractions, we multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom). In this case, we have:
1/4 × 3 = (1 × 3) / (4 × 1) = 3/4
Q: What is the product of the expression 2 × 3/5?
A: To find the product of the expression 2 × 3/5, we need to multiply 2 by 3/5. Multiplication is a commutative operation, meaning that the order of the numbers being multiplied does not change the result. Therefore, we can rewrite the expression as 3/5 × 2.
When multiplying fractions, we multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom). In this case, we have:
3/5 × 2 = (3 × 2) / (5 × 1) = 6/5
Q: What is the product of the expression 4 × 2/3?
A: To find the product of the expression 4 × 2/3, we need to multiply 4 by 2/3. Multiplication is a commutative operation, meaning that the order of the numbers being multiplied does not change the result. Therefore, we can rewrite the expression as 2/3 × 4.
When multiplying fractions, we multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom). In this case, we have:
2/3 × 4 = (2 × 4) / (3 × 1) = 8/3
Q: How do I multiply fractions with different denominators?
A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.
For example, let's say you want to multiply 1/4 and 3/5. The LCM of 4 and 5 is 20. So, you can rewrite the fractions as:
1/4 = 5/20 3/5 = 12/20
Now you can multiply the fractions:
5/20 × 12/20 = (5 × 12) / (20 × 20) = 60/400
Q: Can I multiply fractions with decimals?
A: Yes, you can multiply fractions with decimals. To do this, you need to convert the decimal to a fraction. For example, let's say you want to multiply 2.5 and 3/4. You can convert 2.5 to a fraction by dividing it by 1:
2.5 = 5/2
Now you can multiply the fractions:
5/2 × 3/4 = (5 × 3) / (2 × 4) = 15/8
Conclusion
In conclusion, multiplying fractions is a simple process that involves multiplying the numerators and denominators. You can also multiply fractions with different denominators by finding the least common multiple (LCM) of the denominators. Additionally, you can multiply fractions with decimals by converting the decimal to a fraction.
Final Answer
The final answer is:
- The product of the expression 3 × 1/4 is 3/4.
- The product of the expression 2 × 3/5 is 6/5.
- The product of the expression 4 × 2/3 is 8/3.
- To multiply fractions with different denominators, find the least common multiple (LCM) of the denominators.
- You can multiply fractions with decimals by converting the decimal to a fraction.