Simplify The Expression: \left(-\frac{7}{2} Z+4\right)+\left(\frac{1}{5} Z-15\right ]

Mar 13, 2025 by ADMIN 86 views

Simplify the Expression: A Step-by-Step Guide to Combining Like Terms

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Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable raised to the same power. In this article, we will focus on simplifying the given expression by combining like terms.

The Given Expression

The given expression is:

\left(-\frac{7}{2} z+4\right)+\left(\frac{1}{5} z-15\right)

Step 1: Identify Like Terms

To simplify the expression, we need to identify like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable $z$ .

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract their coefficients. The coefficient of a term is the number that multiplies the variable.

Combining the Coefficients of $z$

The coefficient of $z$ in the first term is $-\frac{7}{2}$ , and the coefficient of $z$ in the second term is $\frac{1}{5}$ . To combine these coefficients, we need to find a common denominator. The least common multiple of $2$ and $5$ is $10$ .

from fractions import Fraction
coeff1 = Fraction(-7, 2)
coeff2 = Fraction(1, 5)

common_denominator = 10

coeff1 = Fraction(coeff1.numerator * (common_denominator // coeff1.denominator), common_denominator)
coeff2 = Fraction(coeff2.numerator * (common_denominator // coeff2.denominator), common_denominator)

combined_coeff = coeff1 + coeff2
print(combined_coeff)

The output of the code is:

-\frac{33}{10}

Combining the Constants

The constants in the expression are $4$ and $-15$ . To combine these constants, we simply add them together.

4 + (-15) = -11

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression.

\left(-\frac{7}{2} z+4\right)+\left(\frac{1}{5} z-15\right) = -\frac{33}{10} z - 11

Conclusion

In this article, we simplified the given expression by combining like terms. We identified the like terms, combined their coefficients, and simplified the expression. The final simplified expression is:

-\frac{33}{10} z - 11

This expression is a simplified version of the original expression, and it is easier to work with.

Frequently Asked Questions

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients.

Q: What is the common denominator?

A: The common denominator is the least common multiple of the denominators of the coefficients.

Q: How do I find the common denominator?

A: You can find the common denominator by listing the multiples of each denominator and finding the smallest number that appears in both lists.

Final Answer

The final answer is:

\boxed{-\frac{33}{10} z - 11}$<br/> # Simplify the Expression: A Step-by-Step Guide to Combining Like Terms ===========================================================

Introduction

The Given Expression

The given expression is:

Introduction

The Given Expression

Step 1: Identify Like Terms

Step 2: Combine Like Terms

Combining the Coefficients of zzz

Combining the Constants

Step 3: Simplify the Expression

Conclusion

Frequently Asked Questions

Q: What are like terms?

Q: How do I combine like terms?

Q: What is the common denominator?

Q: How do I find the common denominator?

Final Answer

Introduction

The Given Expression

Combining the Coefficients of $z$