Identify The Coefficient Of $7xy$.A. $y$ B. 1 C. $x$ D. 7

Understanding Coefficients in Algebra

In algebra, a coefficient is a number or expression that is multiplied with a variable or a term. It is an essential concept in algebra that helps us simplify and manipulate expressions. In this article, we will focus on identifying the coefficient of a term in an algebraic expression.

What is a Term in Algebra?

A term in algebra is a single variable or a product of variables and constants. For example, in the expression $3x^2 + 2y - 4$, the terms are $3x^2$, $2y$, and $-4$. Each term has a coefficient associated with it.

Identifying the Coefficient of a Term

To identify the coefficient of a term, we need to look for the number or expression that is multiplied with the variable or variables in the term. Let's consider the term $7xy$. In this term, the variable is $xy$ and the coefficient is the number that is multiplied with it.

The Coefficient of $7xy$

The coefficient of $7xy$ is the number that is multiplied with the variable $xy$. In this case, the coefficient is $7$. Therefore, the correct answer is:

D. 7

Why is the Coefficient Important?

The coefficient of a term is important because it tells us how many times the variable or variables in the term are multiplied. In the expression $3x^2 + 2y - 4$, the coefficient of $x^2$ is $3$, which means that $x^2$ is multiplied by $3$. Similarly, the coefficient of $y$ is $2$, which means that $y$ is multiplied by $2$.

Real-World Applications of Coefficients

Coefficients have many real-world applications in science, engineering, and economics. For example, in physics, the coefficient of friction is a measure of the force that opposes the motion of an object. In economics, the coefficient of correlation is a measure of the relationship between two variables.

Conclusion

In conclusion, identifying the coefficient of a term in algebra is an essential concept that helps us simplify and manipulate expressions. By understanding the coefficient of a term, we can solve equations and inequalities, and make predictions about real-world phenomena. In this article, we identified the coefficient of the term $7xy$ as $7$.

Frequently Asked Questions

Q: What is a coefficient in algebra?

A: A coefficient is a number or expression that is multiplied with a variable or a term.

Q: How do I identify the coefficient of a term?

A: To identify the coefficient of a term, look for the number or expression that is multiplied with the variable or variables in the term.

Q: Why is the coefficient important?

A: The coefficient of a term is important because it tells us how many times the variable or variables in the term are multiplied.

Q: What are some real-world applications of coefficients?

A: Coefficients have many real-world applications in science, engineering, and economics, such as the coefficient of friction in physics and the coefficient of correlation in economics.

Q: Can you give an example of a term with a coefficient?

A: Yes, the term $3x^2$ has a coefficient of $3$, which means that $x^2$ is multiplied by $3$.

Q: Can you give an example of a term without a coefficient?

A: Yes, the term $x$ has no coefficient, which means that $x$ is multiplied by $1$.

Q: Can you give an example of a term with a negative coefficient?

A: Yes, the term $-4y$ has a coefficient of $-4$, which means that $y$ is multiplied by $-4$.

Q: Can you give an example of a term with a fractional coefficient?

A: Yes, the term $\frac{1}{2}x$ has a coefficient of $\frac{1}{2}$, which means that $x$ is multiplied by $\frac{1}{2}$.

Q: Can you give an example of a term with a coefficient that is a variable?

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Q: What is a coefficient in algebra?

A: A coefficient is a number or expression that is multiplied with a variable or a term. It is an essential concept in algebra that helps us simplify and manipulate expressions.

Q: How do I identify the coefficient of a term?

A: To identify the coefficient of a term, look for the number or expression that is multiplied with the variable or variables in the term. For example, in the expression $3x^2 + 2y - 4$, the coefficient of $x^2$ is $3$, the coefficient of $y$ is $2$, and the coefficient of $-4$ is $-4$.

Q: Why is the coefficient important?

A: The coefficient of a term is important because it tells us how many times the variable or variables in the term are multiplied. For example, in the expression $3x^2 + 2y - 4$, the coefficient of $x^2$ is $3$, which means that $x^2$ is multiplied by $3$.

Q: Can you give an example of a term with a coefficient?

A: Yes, the term $3x^2$ has a coefficient of $3$, which means that $x^2$ is multiplied by $3$.

Q: Can you give an example of a term without a coefficient?

A: Yes, the term $x$ has no coefficient, which means that $x$ is multiplied by $1$.

Q: Can you give an example of a term with a negative coefficient?

A: Yes, the term $-4y$ has a coefficient of $-4$, which means that $y$ is multiplied by $-4$.

Q: Can you give an example of a term with a fractional coefficient?

A: Yes, the term $\frac{1}{2}x$ has a coefficient of $\frac{1}{2}$, which means that $x$ is multiplied by $\frac{1}{2}$.

Q: Can you give an example of a term with a coefficient that is a variable?

A: Yes, the term $2x^2$ has a coefficient of $2$, which is a variable. However, it's worth noting that in this case, the coefficient is not a variable in the classical sense, but rather a numerical value that is multiplied by the variable $x^2$.

Q: How do I simplify an expression with coefficients?

A: To simplify an expression with coefficients, you can combine like terms by adding or subtracting the coefficients of the same variables. For example, in the expression $3x^2 + 2x^2$, you can combine the like terms by adding the coefficients: $3x^2 + 2x^2 = 5x^2$.

Q: Can you give an example of a real-world application of coefficients?

A: Yes, in physics, the coefficient of friction is a measure of the force that opposes the motion of an object. For example, if an object is moving with a force of $10$ Newtons and the coefficient of friction is $0.5$, then the force of friction is $10 \times 0.5 = 5$ Newtons.

Q: Can you give an example of a real-world application of coefficients in economics?

A: Yes, in economics, the coefficient of correlation is a measure of the relationship between two variables. For example, if the coefficient of correlation between the price of a product and its demand is $0.8$, then it means that there is a strong positive relationship between the two variables.

Q: Can you give an example of a real-world application of coefficients in engineering?

A: Yes, in engineering, the coefficient of thermal expansion is a measure of how much a material expands when it is heated. For example, if a material has a coefficient of thermal expansion of $0.00001$ per degree Celsius, then it means that the material will expand by $0.00001$ meters for every degree Celsius increase in temperature.

Q: Can you give an example of a real-world application of coefficients in science?

A: Yes, in science, the coefficient of viscosity is a measure of how much a fluid resists flow. For example, if a fluid has a coefficient of viscosity of $0.01$ Pascal-seconds, then it means that the fluid will resist flow by $0.01$ Newtons for every meter per second of flow.

Conclusion

In conclusion, identifying coefficients in algebra is an essential concept that helps us simplify and manipulate expressions. By understanding the coefficient of a term, we can solve equations and inequalities, and make predictions about real-world phenomena. We hope that this article has helped you to understand the concept of coefficients and their real-world applications.