Question

Simplify by combining like terms. $$7 k-18 k$$

Short answer

Question: Simplify the expression $$7k - 18k$$. Answer: $$-11k$$.

Step-by-step solution

Identify the like terms

In the given expression, we have two terms with the same variable k: $$7k$$ and $$-18k$$.

Combine the like terms

To combine the like terms, we simply add or subtract the coefficients (the numbers that are multiplied by the variable k): $$7k - 18k$$.

Apply the arithmetic

Perform the subtraction of the coefficients: $$7 - 18 = -11$$. So, the simplified expression is $$-11k$$. So, the simplified expression is $$-11k$$.

Key concepts

Simplifying Expressions

When we talk about simplifying expressions, we are trying to make mathematical expressions easier to understand and work with. Simplification often involves combining like terms, which are terms that have the same variable raised to the same power. In the expression \(7k - 18k\), we are dealing with two terms that both contain the variable \(k\). This variable similarity allows us to combine these terms into one.
Combining like terms means taking all the coefficients (the numbers in front of the variables) and performing arithmetic operations on them. The goal is to reduce the expression to its most compact form. In this example, we group \(7k\) and \(-18k\), focusing on the coefficients \(7\) and \(-18\). Simplifying helps in achieving the simplest form of the expression, which is \(-11k\). By understanding and simplifying expressions, you can handle more complex mathematical problems more easily.

Arithmetic Operations

Arithmetic operations are fundamental in mathematics and include addition, subtraction, multiplication, and division. When simplifying expressions, these operations help us combine like terms effectively. Considering the expression \(7k - 18k\), subtraction is the arithmetic operation used here.
To simplify \(7k - 18k\), we focus on subtracting the coefficients: \(7\) and \(18\). Subtraction is calculated by finding the difference between two numbers, which in this case, results in \(-11\). This operation transforms the expression into \(-11k\).
Understanding arithmetic operations allows you to manipulate and simplify expressions correctly. It's also the key to solving equations and other arithmetic problems in mathematics.

Coefficients

In algebraic expressions, coefficients are the numbers that multiply the variable part of the term. They play a crucial role in determining the value of the expression. In the example \(7k - 18k\), the coefficients are \(7\) and \(-18\).
To combine these terms, we perform arithmetic operations on the coefficients. By subtracting \(18\) from \(7\), we get \(-11\). This resulting number becomes the new coefficient of \(k\) in the simplified expression, which is \(-11k\).
Recognizing the role of coefficients in expressions is vital. They tell you how much of the variable you have and help in the simplification process by enabling the combination of like terms. Through coefficients, you can quickly identify and simplify parts of an expression to its simplest form.