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Percentages are a way of expressing numbers as parts of a whole divided into 100 parts. This makes them particularly useful when comparing quantities and expressing proportions.
In mathematics, especially when dealing with word problems, understanding how to calculate percentages is vital. It involves understanding the conversion between percentages and decimals. To convert a percentage to a decimal, you simply divide by 100. For example, 5% becomes 0.05.
When calculating a percentage of a number, you multiply the base number by the decimal form of the percentage. This principle is expressed in the equation from the exercise:

• The base is 10.56.
• The percentage in decimal form is 0.05 (since 5% = 5/100 = 0.05).
• The equation becomes: \[ x = 0.05 \times 10.56 \] This equation yields the number that represents 5% of 10.56.

Understanding this concept allows you to tackle more complex percentage-related problems as you encounter them in various contexts.

Mathematical symbols provide a universal language that simplifies complex ideas into easy-to-understand expressions. In the context of the given exercise, there are critical symbols that you should be familiar with:

• Percent Sign (%): Represents a part per hundred. Understanding this symbol is crucial as it's used to denote a percentage.
• Multiplication Symbol (\(\times\)): Indicates that the numbers it separates are to be multiplied together. It's often written as \(\times\) or in some cases simply with parentheses or an asterisk (*) in digital formats.
• Equals Sign (=): Shows that the values on either side of it are equivalent.

Interpreting these symbols correctly is essential for solving math problems, as they tell us how to transform words into calculations. They turn verbal questions into clear mathematical operations, making complex scenarios more manageable.

An expression in mathematics is a combination of numbers, symbols, and operators (like addition or multiplication) that represent a specific value. A mathematical expression does not have an equals sign. For example, in the problem, "0.05 \(\times\) 10.56" is an expression.
An equation, however, is a statement that shows that two expressions are equal, marked by an equals sign (=). Using the earlier example, when we write \[ x = 0.05 \times 10.56 \] this becomes an equation because it shows that the expression on one side equals the unknown quantity on the other side, represented by \(x\).
Equations are powerful tools because they allow us to solve for unknown values and establish relationships between different quantities. In the exercise, writing the equation was the solution as per the requirement, even without solving for \(x\). Understanding both expressions and equations is fundamental in algebra and helps to simplify and clarify complex problems.