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Chapter 2: Problem 16

Translate from algebraic notation to words. \(6 n=36\)

Short Answer

Expert verified
Six times a number n is equal to thirty-six.

Step by step solution

01

Identify the Components

The equation given is 6n = 36. First, identify the components: the coefficient 6, the variable n, and the constant 36.
02

Translate the Equation

Translate each part of the equation into words. The coefficient 6 multiplying the variable n can be stated as 'six times a number n'. The equals sign translates to 'is equal to'. The constant 36 remains 'thirty-six'.
03

Put It All Together

Combine the translated parts into a complete sentence. 'Six times a number n is equal to thirty-six.'

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Key Concepts

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

Algebraic Notation
Algebraic notation is a concise way of representing mathematical relationships using symbols. In the given equation, we see that algebraic notation allows us to convey complex ideas in a simpler form.
For example, the equation 6n = 36 is an instance of algebraic notation. Here, 6n means '6 multiplied by n', making it easier to understand mathematical relationships quickly.
By translating algebraic notation into words, we make the underlying relationships clearer, aiding in comprehension and problem-solving.
Coefficients
The term 'coefficient' refers to a number used to multiply a variable.
In the equation 6n = 36, the coefficient is 6.
This coefficient tells us how many times the variable n is to be taken.
Coefficients serve as multipliers and are essential for quantifying relationships between variables in algebraic expressions and equations.
Understanding coefficients helps in decoding the meaning of algebraic expressions and grasping the scale of the numbers involved.
Variables
Variables are symbols used to represent unknown numbers or values.
In the equation 6n = 36, the letter n is the variable.
Variables can stand for any number and are crucial in solving algebraic equations.
They allow us to create generalized formulas and solve problems that depend on unknown values.
By solving for the variable, we can find specific values that satisfy the equation.
Constants
Constants are fixed values that don't change.
In the equation 6n = 36, the constant is 36.
Unlike variables, constants always represent the same number.
They provide a reference point in algebraic equations, allowing us to find the value of variables.
Understanding constants is important because they often represent known quantities in real-world problems.
Equations
An equation is a mathematical statement that asserts the equality of two expressions.
Equations use the equals sign (=) to show this relationship.
In the given example, 6n = 36 is an equation stating that '6 times a number n is equal to 36'.
Solving equations involves finding the value of the variable that makes the equation true.
Mastering equations is fundamental in algebra, as it helps solve many types of mathematical and real-world problems.

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Most popular questions from this chapter

In the following exercises, find all the factors of each number. $$ 378 $$

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Grocery shopping Hot dogs are sold in packages of ten, but hot dog buns come in packs of eight. What is the smallest number of hot dogs and buns that can be purchased if you want to have the same number of hot dogs and buns? (Hint: it is the LCM!)

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