What Equation Represents The Given Verbal Expression: Half The Product Of 7 And A Number?Select One:a. $2(7n$\]b. $\frac{7n}{2}$c. $\frac{7+2}{2}$d. $\frac{7}{2}n$

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What Equation Represents the Given Verbal Expression: "Half the Product of 7 and a Number"?

Understanding the Problem

The problem requires us to translate a verbal expression into a mathematical equation. The verbal expression is "Half the product of 7 and a number." This means we need to find an equation that represents this expression.

Breaking Down the Expression

To solve this problem, we need to break down the verbal expression into its individual components. The expression "Half the product of 7 and a number" can be broken down into three parts:

  1. Product of 7 and a number: This means we need to multiply 7 by a number. Let's call this number "n". So, the product of 7 and n is 7n.
  2. Half: This means we need to divide the product by 2.

Translating the Expression into an Equation

Now that we have broken down the expression, we can translate it into an equation. The equation should represent the product of 7 and n, and then divide it by 2.

The correct equation is: 7n2\frac{7n}{2}

Analyzing the Options

Let's analyze the options given:

a. 2(7n)2(7n): This option is incorrect because it multiplies 7n by 2, which is the opposite of what we want.

b. 7n2\frac{7n}{2}: This option is correct because it represents the product of 7 and n, and then divides it by 2.

c. 7+22\frac{7+2}{2}: This option is incorrect because it adds 7 and 2, and then divides the result by 2. This does not represent the product of 7 and a number.

d. 72n\frac{7}{2}n: This option is incorrect because it divides 7 by 2, and then multiplies the result by n. This does not represent the product of 7 and a number.

Conclusion

The correct equation that represents the verbal expression "Half the product of 7 and a number" is 7n2\frac{7n}{2}. This equation represents the product of 7 and n, and then divides it by 2.

Understanding the Concept of Product and Half

The concept of product and half is a fundamental concept in mathematics. The product of two numbers is the result of multiplying them together. For example, the product of 7 and 3 is 21. The half of a number is the result of dividing it by 2. For example, the half of 10 is 5.

Real-World Applications

The concept of product and half has many real-world applications. For example, if you are buying a product that costs $7 and you want to pay half of the price, you would pay $3.50. If you are dividing a pizza among 7 people, and you want to give each person half of the pizza, you would give each person 3.5 slices.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

  • Read the problem carefully and break it down into its individual components.
  • Use variables to represent unknown values.
  • Translate the verbal expression into a mathematical equation.
  • Analyze the options given and choose the correct one.

Common Mistakes

Here are some common mistakes to avoid when solving problems like this:

  • Not reading the problem carefully and breaking it down into its individual components.
  • Not using variables to represent unknown values.
  • Not translating the verbal expression into a mathematical equation.
  • Not analyzing the options given and choosing the correct one.

Conclusion

In conclusion, the correct equation that represents the verbal expression "Half the product of 7 and a number" is 7n2\frac{7n}{2}. This equation represents the product of 7 and n, and then divides it by 2. The concept of product and half is a fundamental concept in mathematics, and it has many real-world applications. By following the tips and tricks and avoiding common mistakes, you can solve problems like this with ease.
What Equation Represents the Given Verbal Expression: "Half the Product of 7 and a Number"? - Q&A

Q: What is the product of 7 and a number?

A: The product of 7 and a number is the result of multiplying 7 by the number. Let's call the number "n". So, the product of 7 and n is 7n.

Q: What does "half" mean in the context of the verbal expression?

A: In the context of the verbal expression, "half" means to divide the product of 7 and n by 2.

Q: How do I translate the verbal expression into a mathematical equation?

A: To translate the verbal expression into a mathematical equation, you need to break it down into its individual components. In this case, the components are:

  1. Product of 7 and a number (7n)
  2. Half (divide by 2)

So, the equation would be: 7n2\frac{7n}{2}

Q: What is the difference between multiplying and dividing?

A: Multiplying and dividing are two different operations. Multiplying means to add a number a certain number of times, while dividing means to share a number into equal parts.

Q: Can you give an example of how to use the concept of product and half in real life?

A: Yes, here's an example:

Let's say you are buying a product that costs $7 and you want to pay half of the price. You would pay $3.50. If you are dividing a pizza among 7 people, and you want to give each person half of the pizza, you would give each person 3.5 slices.

Q: What are some common mistakes to avoid when solving problems like this?

A: Here are some common mistakes to avoid:

  • Not reading the problem carefully and breaking it down into its individual components.
  • Not using variables to represent unknown values.
  • Not translating the verbal expression into a mathematical equation.
  • Not analyzing the options given and choosing the correct one.

Q: How can I practice solving problems like this?

A: Here are some tips to help you practice solving problems like this:

  • Start with simple problems and gradually move on to more complex ones.
  • Practice breaking down verbal expressions into their individual components.
  • Practice translating verbal expressions into mathematical equations.
  • Practice analyzing options and choosing the correct one.

Q: What are some real-world applications of the concept of product and half?

A: Here are some real-world applications of the concept of product and half:

  • Shopping: When you are buying a product, you may want to pay half of the price.
  • Cooking: When you are dividing a pizza among a group of people, you may want to give each person half of the pizza.
  • Science: When you are measuring the volume of a liquid, you may need to divide it by 2 to get the half volume.

Q: Can you give an example of how to use the concept of product and half in a word problem?

A: Yes, here's an example:

Tom has 7 boxes of cookies, and he wants to share them equally among his 7 friends. How many cookies will each friend get?

To solve this problem, you need to find the product of 7 and 7, which is 49. Then, you need to divide 49 by 2 to get the half product, which is 24.5. Since you can't divide cookies into fractions, you can round down to 24 cookies per friend.

Conclusion

In conclusion, the concept of product and half is a fundamental concept in mathematics that has many real-world applications. By practicing solving problems like this and avoiding common mistakes, you can become proficient in solving problems that involve the concept of product and half.