Problem 6 - Prealgebra

Question

Write each of the following in words. $$-20<-5$$

Step-by-Step Solution

Answer

"Negative twenty is less than negative five."

Step 1: Identify Numbers in the Inequality

We are given the inequality \(-20 < -5\). Start by identifying the numbers involved in the expression. Here, we have \(-20\) and \(-5\).

Step 2: Identify the Inequality Symbol

Next, note the inequality symbol used in the expression, which is \(<\). This symbol indicates that the number on the left is smaller than the number on the right.

Step 3: Translate the Inequality

Based on the inequality \(-20 < -5\), we translate it to: "Negative twenty is less than negative five." This expresses the mathematical relationship described by the inequality in words.

Key Concepts

Understanding the Number Line

The number line is a fundamental concept in mathematics that helps us visualize numbers in a linear format. It acts as a visual representation of numerical order and allows us to easily compare numbers.
Imagine a straight horizontal line:

• The center of the number line is usually zero.
• To the right of zero are positive numbers.
• To the left of zero, you'll find negative numbers.

When working with inequalities, such as oindent egin{equation} -20 < -5, oindent ext{we can use the number line to visualize this relationship.} egin{itemize} ulleteven though -20 has a larger absolute value (ignoring the negative sign) than -5, it is further to the left on the number line. nBy identifying positions, we confirm -20 is less than -5. egin{equation}

Exploring Negative Numbers

Negative numbers are those that appear on the left side of the zero on a number line. These numbers represent values less than zero.
Understanding negative numbers is essential, as they appear frequently in various contexts, such as debts or below-freezing temperatures. Here are some key aspects of negative numbers:

• Opposites of positive numbers: Each negative number can be seen as the opposite of a positive number of the same absolute value.
• Smaller than zero: Negative numbers are always smaller than zero and any positive number.
• In Inequalities: When comparing two negative numbers, the number with the smaller absolute value is actually greater. For example, -5 is greater than -20, even though |-5| < |-20|.

Working with negatives can be tricky, but once you get the hang of their properties, they become easier to manage.

Interpreting Mathematical Symbols

Mathematical symbols are vital in communicating complex ideas succinctly. In inequalities, these symbols help define relationships between numbers.
Let's focus on the symbols in the given inequality: -20 < -5.

• Inequality Symbol - "<": This symbol means "less than." When seeing \(-20 < -5\), it tells us that -20 is less than -5 on the number line.

Understanding these symbols can clarify expressions and equations quickly. They are the mathematical language that allows us to express relationships efficiently.
Next time you spot these symbols, remember:

• "<" indicates smaller value
• ">" indicates larger value
• "=" means both sides are equal

These are shortcuts that make interpreting mathematical relationships effortless.