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Chapter 3: Problem 21

Translate to a variable expression. negative twelve divided by \(k\)

Short Answer

Expert verified
Question: Translate the phrase "negative twelve divided by k" into a variable expression. Answer: $$\frac{-12}{k}$$

Step by step solution

01

Identify the numbers and variable involved

The phrase mentions negative twelve (-12) and the variable \(k\). We are dividing negative twelve by the variable \(k\).
02

Write the division operation using the numbers and variable

To write a variable expression, we will use the division symbol (梅) to divide negative twelve (-12) by the variable \(k\).
03

Replace the division symbol with a fraction notation

In mathematics, we can represent a division operation using a fraction notation. To do this, we will replace the division symbol (梅) with a fraction line, where the numerator will be -12 and the denominator will be \(k\).
04

Write the final variable expression

Now that we have represented the division operation using the fraction notation, we can write the final variable expression. The variable expression is: $$\frac{-12}{k}$$

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Key Concepts

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

Understanding the Division Operation
Division is a basic arithmetic operation used to split a number into equal parts. Think of it as sharing or distributing something equally. For example, if you have 12 apples and you want to divide them among 4 friends, you want each friend to get an equal number of apples. We can write this action as a division equation:
  • The total number of apples (12)
  • The number of parts you want to divide them into (4)
When performing division, the first number (12) is divided by the second number (4).
This process is denoted using the division symbol, ":" or "\( \div \)".
In our exercise, negative twelve is divided by the variable \( k \). Therefore, the expression starts as "-12 \( \div \) k".
Using Fraction Notation
In mathematics, we often replace the division symbol with a fraction. This is known as fraction notation.
A fraction is a way to represent numbers using two parts: the numerator and the denominator, which makes it an efficient way to express division.
  • Fraction notation is especially used in algebra to simplify expressions and solve equations.
  • It becomes particularly handy later in more complex mathematics.
When we use a fraction to represent division, the result is much clearer and easier to work with for further calculations.
Instead of writing "-12 \( \div \) k", the division is represented in fraction notation as \( \frac{-12}{k} \).
Numerator and Denominator Explained
A fraction is composed of two main parts: the numerator and the denominator.
  • The numerator is the number on the top, representing how many parts you have.
  • The denominator is the number on the bottom, indicating the total number of equal parts something is divided into.
So, in our given expression \( \frac{-12}{k} \):
  • \(-12\) is the numerator, which is being divided.
  • \(k\) is the denominator, showing into how many parts or how the quantity (\(-12\)) is being distributed.
Understanding the role of numerators and denominators is crucial in handling fractions, simplifying expressions, and solving mathematical problems effectively. Equally, mastering these helps greatly in manipulating variables and expressions in algebra.

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