Problem 11 - Prealgebra

Question

Write each of the following in symbols. 10 is less than \(0 .\)

Step-by-Step Solution

Answer

\( 10 < 0 \)

Step 1: Identify the Numbers

The numbers given in the sentence are '10' and '0'. We need to identify these correctly to form the inequality.

Step 2: Determine the Relation

The phrase '10 is less than 0' suggests a comparison where 10 is smaller or less than 0. In mathematical symbols, the word 'less than' typically translates to the symbol '<'.

Step 3: Write the Inequality

Combine the numbers with the correct relation symbol. In this case, we write the inequality as: \( 10 < 0 \).

Key Concepts

Mathematical Symbols

Mathematical symbols are like a universal language. They help communicate complex ideas more simply. Let's take the symbol '<', for example. It stands for "less than." When you see this symbol, it indicates that a number on the left side is smaller than the number on the right side.

Symbols save time and space in writing mathematical expressions. They turn words into concise expressions. Think of it as a shorthand for math. When someone writes "10 < 0," you don't need to read any extra words, you immediately know that 10 is less than 0. Other examples include '=' for equal and '>' for greater than. Understanding these symbols is crucial. It helps in reading and solving mathematical problems effectively.

Number Comparison

Number comparison is the process of evaluating two numbers to see how they relate to each other. When comparing numbers, you might want to check if one number is greater than, less than, or equal to another. This exercise focuses on recognizing when a number is less than another.

Here are some terms you often encounter in comparisons:

• Greater than (>)
• Less than (<)
• Equal to (=)

Understanding these terms makes it easier to figure out which number is larger or smaller. For example, if you have the numbers 10 and 0, deciding which is smaller involves using '<' or 'greater than' would involve '>'. This comparison is fundamental in mathematics. It's used in everything from basic arithmetic to complex theories.

Expression Writing

Writing expressions in math is about turning words into equations. When writing expressions, the goal is to accurately represent a mathematical situation. Here, you transform a sentence like "10 is less than 0" into the expression: 10 < 0. It requires recognizing the mathematical terms and numbers, and then selecting the right symbols for those terms.

The steps involved in writing a mathematical expression include:

• Identifying the numbers and their order.
• Understanding the relationship between the numbers, often given by keywords like 'less than'.
• Selecting the appropriate mathematical symbols.
• Assembling the expression using all these elements.

Practice is key to getting better at writing precise and correct expressions. It becomes second nature the more you do it!