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Chapter 2: Problem 95

In the following exercises, identify the coefficient of the given term. $$5 r^{2}$$

Short Answer

Expert verified
The coefficient is 5.

Step by step solution

01

Identify the term

The given term is displaying text version of the term inside \[5r^2\].
02

Identify the coefficient

The coefficient of the term \(5r^2\) is the numerical factor that is multiplied by the variable part. In this case, the numerical factor is \(5\).

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Key Concepts

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

Numerical Factor
In prealgebra, the numerical factor is known as the numerical coefficient. It is the number that multiplies the variable term in an algebraic expression.

For instance, in the term \[5r^2\], the numerical factor is the number \(5\). This number is the coefficient because it is directly multiplying the variable term \(r^2\).

Identifying the numerical factor is essential because it tells you how many times the variable term is being multiplied. Breaking down expressions by their numerical factors can make solving algebraic equations easier.

Here are a few more examples to help you understand better:
  • In the term \(3x\), the numerical factor is \(3\).
  • For \(-7y\), the numerical factor is \(-7\).
  • In \[12a^3\], the numerical factor is \(12\).
Remember, the numerical factor can be positive, negative, or even a fraction!
Variable Term
A variable term consists of a variable and may include an exponent that indicates how many times the variable is multiplied by itself.

In the term \[5r^2\], \(r\) is the variable, and \(2\) is its exponent. Together, they form the variable term \(r^2\).

Variable terms can vary in complexity. They might include just one variable, such as \(x\) or \(y^3\), or they could be part of more complicated expressions involving multiple variables.
  • In \(7x\), the variable term is \(x\).
  • For \(-2y^2\), the variable term is \(y^2\).
  • In \[4x^2y^3\], the variable terms are \(x^2\) and \(y^3\).
Understanding what a variable term is helps you quickly identify and work with different parts of algebraic expressions.
Prealgebra
Prealgebra is the foundation of algebra, including basic mathematical concepts that prepare students for higher-level math.

It involves arithmetic operations, fractions, decimals, percentages, and basic properties of numbers. Introducing variables and simple algebraic expressions hones understanding.

For example, in prealgebra, you learn to deal with equations like \(5 + 2x = 15\).

The focus is often on simple operations and understanding how to manipulate variables and constants. Skills acquired include:
  • Identifying coefficients and variables.
  • Performing arithmetic on polynomials.
  • Solving simple equations.
Mastering prealgebra concepts such as numerical factors and variable terms forms a crucial base for more advanced topics in algebra and beyond.

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Most popular questions from this chapter

In the following exercises, translate from an algebraic equation to English phrases. $$ 6 \cdot 4 $$

Insurance Vince's car insurance has a \(\$ 500\) deductible. Find the amount the insurance company will pay, \(p,\) for an \(\$ 1800\) claim by solving the equation \(500+p=1800\)

Sale purchase Arthur bought a suit that was on sale for \(\$ 120\) off. He paid \(\$ 340\) for the suit. Find the original price, \(p,\) of the suit by solving the equation \(p-120=340\)

In the following exercises, identify each number as prime or composite. $$ 51 $$

In the following exercises, solve each equation using the subtraction property of equality. $$ 116=q+79 $$
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