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Equation solving is a fundamental aspect of mathematics wherein you need to find the missing value that satisfies a given mathematical statement. In this exercise, the statement involves a percentage, and we're tasked with finding out what number is 78% of a known value, 7.8. To solve problems like this, we begin by translating the problem into an algebraic equation. Here, the problem '7.8 is 78% of what number?' can be written as an equation:

• The problem is represented as: \( 0.78 \times x = 7.8 \)
• Our goal is to find \( x \), the unknown value.

Next comes isolating the variable \( x \) by performing the opposite operation to balance the equation. This involves dividing both sides by 0.78 to solve for \( x \):

• Dividing both sides: \[ x = \frac{7.8}{0.78} \]
• The solution gives: \( x = 10 \).

This process shows that equation solving often involves reversing operations, like multiplication or division, to find the unknown variable.

Understanding how to convert a percentage into a decimal is essential when dealing with percentage problems. Percentages are parts per hundred, which makes them easy to express in decimal form by dividing by 100:

• Take the given percentage (78%)
• Move the decimal point two places to the left or divide by 100 to convert it to a decimal.
• So, 78% becomes 0.78 as a decimal.

This conversion is crucial because many mathematical operations, such as multiplication and forming equations, require the decimal format. For example, in our exercise, converting 78% to 0.78 allows us to easily set up and solve our equation. Without conversion, these calculations would be cumbersome and error-prone.

Prealgebra forms the building blocks for higher-level mathematics, involving basic arithmetic and the foundation of equations, such as understanding variables and operations like addition, subtraction, multiplication, and division. In our exercise:

• The operation is multiplication: \( 0.78 \times x = 7.8 \).
• The variable \( x \) represents the number we aim to find.
• By dividing both sides of the equation by 0.78, we demonstrate a key prealgebra skill: balancing an equation.

It's important to grasp these prealgebra techniques because they develop problem-solving skills and analytical thinking. Prealgebra helps identify patterns, solve real-life problems, and introduces students to logical and structured mathematical thinking necessary for advanced topics.