Problem 67 - Elementary Algebra

Question

Translate each statement into an English sentence. $$ 10<20 $$

Step-by-Step Solution

Answer

10 is less than 20.

Step 1: Understanding the Symbols

The statement involves the symbol `<`, which means 'less than'. So any number presented on the left of this symbol is less than any number presented on the right.

Step 2: Identifying the Numbers

In the given statement, the numbers involved are 10 and 20. The number 10 is on the left side and the number 20 is on the right side of the less than symbol.

Step 3: Formulating the Sentence

Combine the understanding of the symbols and the numbers to form an English sentence. The sentence becomes: '10 is less than 20.'

Key Concepts

Mathematical Symbols

Mathematical symbols are like a universal language used to convey mathematical ideas quickly and clearly. Understanding these symbols is key to working with mathematical expressions.
In the expression \(10 < 20\), the symbol **<** represents 'less than'. This means any number on the left side of this symbol is smaller than the number on the right side.
Here's a quick rundown of common symbols and their meanings:

• **<** : Less than
• **>** : Greater than
• **=** : Equal to
• **≤** : Less than or equal to
• **≥** : Greater than or equal to

Knowing these symbols helps you read and write mathematical expressions easily.

Number Comparison

Comparing numbers involves understanding their relative size or value. In math, this is often done using symbols like **<** or **>** to show which number is bigger or smaller.
When comparing numbers, place them on either side of a symbol:

• If a number is to the left of **<**, it is smaller. E.g., \(10 < 20\).
• If a number is to the left of **>**, it is bigger. E.g., \(30 > 20\).

By using these symbols, we can quickly understand the relationship between any two numbers without lengthy explanations.

Translating Mathematical Expressions to English

Turning mathematical expressions into understandable English sentences helps in grasping what the math actually means and in explaining math to others who might not be familiar with the symbols.
To translate \(10 < 20\) into English:1. Identify the numbers and their position relative to the symbol.2. Recognize the meaning of the symbol **<**.3. Formulate the sentence: '10 is less than 20.'
This process is crucial when starting with math, as it builds the bridge between abstract numbers and real-world understanding.