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Chapter 2: Problem 19

Translate from algebraic notation to words. \(2 \leq 18 \div 6\)

Short Answer

Expert verified
Two is less than or equal to three.

Step by step solution

01

Understand the Symbols

Identify the symbols in the algebraic notation. The symbols used here are '2', '鈮�' (less than or equal to), '18', '梅' (division), and '6'.
02

Perform the Division

Calculate the value of the division expression. Divide 18 by 6: \[18 \div 6 = 3\]
03

Compare the Results

Now compare the two values with the less than or equal to sign: \[2 \leq 3\]
04

Translate to Words

Translate the entire expression to words: 'Two is less than or equal to three.'

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Key Concepts

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

algebraic notation
Algebraic notation is a method of writing mathematical expressions using symbols and numbers. It allows complex ideas to be conveyed succinctly. For instance, in the exercise, the expression \(2 \leq 18 \div 6\) uses specific algebraic symbols to represent a comparison and a division operation. Here, the '鈮�' symbol is used to represent 'less than or equal to', while '梅' denotes division.
  • The numbers in the expression are: 2, 18, and 6.
  • '鈮�' stands for 'less than or equal to'.
  • '梅' indicates the division operation between 18 and 6.
Understanding these symbols is the first step in translating algebraic notation into words.
inequality
An inequality is a mathematical statement that asserts that two values are not necessarily equal, often by stating that one is greater or less than the other. In our example, the inequality is represented by the less than or equal to symbol (鈮�). This symbol tells us that the value on the left side can either be less than or exactly equal to the value on the right side.Here鈥檚 how to interpret it:
  • '鈮�': means 'less than or equal to'.
When it comes to our example, once the division is performed, the inequality becomes:2 鈮� 3This translates to: 'Two is less than or equal to three.' Inequalities are useful in expressing ranges and comparing values.
division in algebra
Division in algebra follows the same rules as basic arithmetic but is often used in conjunction with other operations and symbols. In our exercise, we divide 18 by 6. This calculation is straightforward:
  • 18 梅 6 = 3
Once the division is complete, the result (3) is compared to the number on the left of the inequality (2). Division is a critical operation in algebra because it simplifies complex expressions and allows for comparison and equation solving. By understanding how to perform division, you can easily simplify and interpret algebraic expressions just as we did in the example.

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