Problem 153 Translate to an equation and the... [FREE SOLUTION]

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Chapter 2: Problem 153

Translate to an equation and then solve. The quotient \(k\) and 22 is -66.

Short Answer

Expert verified

k = -1452

Step by step solution

Identify the terms

The problem mentions a quotient, which indicates division. It also involves the numbers 22 and -66.

Translate the problem to an equation

To express 'The quotient of k and 22 is -66' as an equation, remember that quotient means division. Thus, the equation can be written as:

Solve for k

To solve for k, multiply both sides of the equation by 22 to isolate k: \( \frac{k}{22} = -66 \) \( k = -66 \times 22 \)

Calculate the value of k

Now, perform the multiplication to find the value of k: \( k = -1452 \)

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Key Concepts

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

Solving Equations

Solving equations is an essential skill in elementary algebra. In this context, an equation is a statement that two expressions are equal. The goal is to find the value of the variable that makes this statement true.

For example, consider the problem: 'The quotient of k and 22 is -66.' Here, the equation is written as: \( \frac{k}{22} = -66 \)
To solve for k, we need to isolate the variable k. This involves performing the same mathematical operation on both sides of the equation.

Since k is divided by 22, we can multiply both sides by 22 to get: \[ k = -66 \times 22 \]
Hence, \( k = -1452 \).

Quotient

In mathematics, a quotient is the result of division. When dividing one number by another, the number you get is called the quotient.

For example, in the exercise: 'The quotient of k and 22 is -66,' the term 'quotient' indicates that an operation of division has occurred.

To express this as an equation, you write it as: \( \frac{k}{22} = -66 \)
Here, k is called the numerator, 22 is the divisor, and -66 is the quotient.

Understanding this terminology helps in translating word problems into mathematical equations accurately.

Translation of Word Problems

Translation of word problems into mathematical equations can sometimes be tricky, but breaking it down step by step helps.

Let's take the problem: 'The quotient of k and 22 is -66.' To translate this, identify the key terms:

'Quotient' - this indicates division.
'k and 22' - the numbers involved in the division.
'is' - translates to the equal sign (=).
'-66' - the result or quotient of the division operation.

Thus, we can write: \( \frac{k}{22} = -66 \)
By understanding each term and its mathematical equivalent, we can convert word problems into equations that are easier to solve.

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91影视

Translate to an equation and then solve. The quotient \(k\) and 22 is -66.

Short Answer

Step by step solution

Identify the terms

Translate the problem to an equation

Solve for k

Calculate the value of k

Key Concepts

Solving Equations

Quotient

Translation of Word Problems

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