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Understanding the properties of equality is essential when dealing with algebraic equations. These properties allow us to manipulate and solve equations correctly. There are several key properties, including:

• Addition Property: Adding the same number to both sides of an equation keeps it equal.
• Subtraction Property: Subtracting the same number from both sides also maintains equality.
• Multiplicative Property: Multiplying both sides by the same nonzero number keeps the equation balanced.
• Division Property: Dividing both sides by the same nonzero number preserves equality.

Each of these properties helps maintain the balance of an equation while simplifying or solving it. In the exercise example, the multiplicative property of equality is used to solve for the variable 't.' It's important to correctly apply these properties to reach a solution while ensuring the solution remains valid.

Solving equations involves finding the value of the unknown variable that makes the equation true. This process follows a series of logical steps, where each step uses mathematical properties to simplify the equation. Here's a simple guide to follow:

• Identify the equation and unknown variable.
• Use algebraic properties, like those of equality, to simplify and isolate the variable.
• Perform operations equally on both sides to maintain balance.
• Check your solution by substituting it back into the original equation.

In the given problem, the equation \( \frac{t}{9} = 16 \) is solved by eliminating the fraction through multiplication. This strategy isolates the variable and makes it easier to calculate its value. By multiplying both sides by 9, balance is preserved while the variable is isolated.

The multiplicative property of equality is a powerful tool in algebra. It states that when you multiply both sides of an equation by the same nonzero number, the equation remains balanced. This property is particularly useful for eliminating fractions in equations.
In the exercise, the equation \( \frac{t}{9} = 16 \) shows 't' divided by 9. To solve for 't', multiply both sides by 9:\[9 \times \frac{t}{9} = 9 \times 16\]Simplifying the left side cancels the 9s, leaving \( t = 144 \).
The multiplicative property helps transform equations into simpler forms that are more convenient to solve. It's crucial to apply this property correctly, ensuring that each side of the equation is balanced throughout the process.