Question

Write each statement using symbols. The quotient 2 divided by \(x\) is 6 .

Short answer

\( \frac{2}{x} = 6 \)

Step-by-step solution

Identify the components

First, recognize the components of the statement: the quotient, the divisor, and the result. Here, the quotient is 2, the divisor is represented by the variable x, and the result is 6.

Set up the equation

Write the statement 'The quotient 2 divided by x is 6' in the form of an equation. The word 'quotient' indicates division, and 'is' suggests equality. Therefore, the equation is \( \frac{2}{x} = 6 \).

Key concepts

Quotient

Let's start with understanding the term 'quotient'. In mathematics, the quotient is the result you get when you divide one number by another. For instance, when you divide 10 by 2, the quotient is 5. In our exercise, when the problem states 'The quotient 2 divided by x', it means we need to divide 2 by a variable, x. The quotient in this statement is a key part of forming our equation, as it represents the outcome of the division.

Division

The process of division plays a crucial role in solving algebraic equations. Division is the operation of determining how many times one number (the divisor) is contained within another number (the dividend). In our exercise, 2 is the dividend, and the variable x is the divisor. Understanding division helps you translate word problems into mathematical equations. So for 'The quotient 2 divided by x', we use the division operation this way: \(\frac{2}{x}\), representing the division of 2 by x.

Equality

Equality is an essential concept in algebra, signified by the equal sign (=). It shows that two expressions are equivalent. In our problem, 'The quotient 2 divided by x is 6' translates into an equation. The term 'is' hints at equality, meaning the quotient \(\frac{2}{x}\) is equal to 6. Writing it as \(\frac{2}{x} = 6\) indicates that whatever value x takes, the division 2 by that x must result in 6. This forms the basis of solving our algebraic equation.

Variable

A variable in algebra is a symbol that represents an unknown number. It can be any letter, commonly x, y, or z. In the statement 'The quotient 2 divided by x is 6', the variable is x. This variable stands in place of a number that we need to find. By setting up the equation \(\frac{2}{x} = 6\), we express that 2 divided by whatever number x stands for must equal 6. Understanding variables allows you to solve for unknowns in equations effectively.