Problem 5 - Prealgebra

Question

Write each of the following in words. $$-10<-3$$

Step-by-Step Solution

Answer

Negative ten is less than negative three.

Step 1: Understand the Symbols

Identify the meaning of each symbol in the expression. The symbol '-' before a number indicates it is negative. The symbol '<' is the less than sign, meaning the number on the left is smaller than the number on the right.

Step 2: Identify the Numbers

The numbers in the given inequality are -10 and -3. We need to describe the relationship between these numbers using words.

Step 3: Write the Expression in Words

Combine the meanings of the symbols and numbers to write the entire expression in words. The expression '-10 < -3' is read as 'negative ten is less than negative three.'

Key Concepts

Understanding Negative Numbers

When dealing with negative numbers, it's crucial to understand what the negative sign represents. The negative sign, indicated by '-' in front of a number, signifies that the number is below zero on the number line. Negative numbers are the opposite of positive numbers and indicate quantities that are less than nothing, often measured in terms of debt or directions below a starting point.

Think of the number line:

• To the left of zero, you have negative numbers: -1, -2, -3, and so forth.
• To the right of zero, you have positive numbers: 1, 2, 3, and so on.

Negative numbers can be a bit tricky because a larger number with a negative sign represents a smaller value. For example,

• -10 is less than -3, even though 10 is greater than 3.

Understanding this reversed order is key when comparing negative numbers.

Grasping the Less Than Symbol

The '<' symbol is known as the "less than" symbol in mathematics. Its primary purpose is to compare two values, showing that the value on the left is smaller than the value on the right.

In the inequality

• -10 < -3, the symbol indicates that -10 is a lesser value compared to -3.

Think of it as a mouth, always open towards the larger of the two numbers because it wants to "eat" the bigger number. This visual can help remember the direction and meaning of the symbol.

Using the less than symbol is fundamental when writing inequalities, which is how mathematicians express relationships between different numbers.

Expressing Mathematical Expressions in Words

Mathematical expressions, like

• -10 < -3, can be written in words to make them more understandable, especially for beginners.

Converting symbols and numbers into words involves interpreting each part separately and then putting it together. For the expression

• -10 < -3, it's read as "negative ten is less than negative three."

Describing mathematical expressions in words helps to cement comprehension by translating complex symbols into human language, making the concept accessible to everyone. This approach can be particularly useful in learning environments where understanding is prioritized over memorization.