91Ó°ÊÓ

Algebra is like the language of mathematics. It lets us describe mathematical relationships using symbols and letters. This makes it easier to work with numbers in a flexible way. In algebra, we use letters to represent numbers. These unknown numbers are called variables.
Algebra is important because it helps us find missing values in equations. For example, if the equation is given as \( p = mv \), it contains a relationship between three variables: \( p \) (momentum), \( m \) (mass), and \( v \) (velocity). Algebra lets us rearrange and solve such equations to find unknown values.

• Algebraic expressions consist of numbers, variables, and operations.
• Equations are statements indicating that two algebraic expressions are equal.

This understanding helps us solve practical problems by finding the value of an unknown variable, as we did in the example equation \(p = mv\).

Isolation of variables means getting a variable by itself on one side of an equation. This is a fundamental step when solving for a specific variable. It allows us to clearly understand how other variables affect this one variable.
For example, to solve the equation \( p = mv \) for \( m \), we need to isolate \( m \). Here's how we can do it:

• Start with the original equation: \( p = mv \).
• We need \( m \) alone, so we divide both sides by \( v \): \( \frac{p}{v} = m \).

By isolating \( m \), we now have \( m \) on one side of the equation. This isolation helps to easily substitute known values into the equation to find the unknown value of \( m \). This technique is useful because it can be used for any variable in an equation.

The substitution method is a powerful tool that involves replacing a variable with its known value. This method is often used after isolating the variable we are interested in. It simplifies equations so that they can be solved directly.
In the exercise, once we isolated \( m \) to get \( m = \frac{p}{v} \), we substituted the given values \( p = 4240 \) and \( v = 260 \):

• Substitute these values into the equation \( m = \frac{4240}{260} \).
• This gives us the simple arithmetic calculation: \( m = 16.3 \).

The substitution method is useful not only in solving equations but also in making complicated expressions simpler. It provides an uncomplicated path to reach a solution by using known values to find unknowns efficiently.