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Chapter 1: Problem 22

In each term, give the numerical coefficient of the variable(s). $$ \frac{x}{6} $$

Short Answer

Expert verified
The numerical coefficient of \(x\) is \(\frac{1}{6}\).

Step by step solution

01

- Understand the Term

The term given is \(\frac{x}{6}\). Here, \(x\) is the variable, and it is important to identify its coefficient.
02

- Identify the Coefficient

For any term in the form of \(\frac{a}{b} \times c \), the coefficient of \(c\) can be seen directly. In \(\frac{x}{6}\), the coefficient of \(x\) is \(\frac{1}{6}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coefficient
A coefficient is a number that is multiplied by a variable in an algebraic term. In simpler terms, it tells you how many times the variable is being counted. For example, in the term \(3x\), the number 3 is the coefficient. It means that \(x\) is being multiplied by 3. Coefficients can be positive, negative, fractions, or even decimals. Identifying coefficients correctly is crucial for solving algebraic expressions. In the provided exercise, the coefficient of the term \( \frac{x}{6} \) is \( \frac{1}{6} \), indicating that \( x \) is being multiplied by \( \frac{1}{6} \).
Variable
A variable is a symbol that represents an unknown value in an algebraic expression. Typically, variables are denoted using letters like \(x\), \(y\), and \(z\). They can take on different values depending on the context of the problem. For example, in the term \( \frac{x}{6} \), \(x\) is the variable. It represents an unknown quantity that we may eventually solve for. Understanding variables is fundamental because they are the building blocks of algebraic equations and functions.
Algebraic Term
An algebraic term is a mathematical expression that can include numbers, variables, and coefficients, all multiplied together. Terms can be simple, like \(5x\), or more complex, like \(2a^2b\). In each term, the combination of numbers and variables plays a different role. The number part is the coefficient, while the letter part is the variable or variables. In our example, \( \frac{x}{6} \) is an algebraic term where \(x\) is the variable and \( \frac{1}{6} \) is the coefficient. The term itself implies multiplication between these components.
Fractions in Algebra
Fractions in algebra function similarly to regular fractions but involve variables. They can seem complicated but are often simpler than they appear. For example, in the term \( \frac{x}{6} \), \( \frac{1}{6} \) is a fraction. This fraction is our coefficient when multiplied by \(x\). It's crucial to handle fractions carefully. When dividing by a number in algebra, it鈥檚 helpful to remember that this is the same as multiplying by the reciprocal of that number. In this case, dividing by 6 is the same as multiplying by \( \frac{1}{6} \). Recognizing this can help simplify solving algebraic expressions with fractions.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. The product of 4 and \(-7,\) added to \(-12\)

Simplify each expression. $$ 5 y^{3}+6 y^{3}-3 y^{2}-4 y^{2} $$

Simplify each expression. $$ 2 p^{2}+3 p^{2}-8 p^{3}-6 p^{3} $$

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. Show that (a) \(4,249,474\) is not divisible by 12 (b) \(4,253,520\) is divisible by 12 and

Write a numerical expression for each phrase and simplify. \(20 \%\) of the product of \(-5\) and 6
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