91Ó°ÊÓ

Algebraic formulas are equations that relate different quantities using algebraic expressions. They are used to describe mathematical relationships and can include variables, constants, and arithmetic operations. Understanding these formulas is essential because they help us solve real-world problems more easily.

For example, the formula \(I = p r t\) is often used in finance to calculate simple interest, where:

• \(I\) is the interest earned
• \(p\) is the principal amount
• \(r\) is the rate of interest
• \(t\) is the time period

By manipulating this formula algebraically, you can solve it for any variable you need. This is especially helpful when you have all other values and require only one unknown.

Isolating variables is a crucial skill in algebra. It involves getting the variable you are interested in by itself on one side of the equation. This makes it easier to solve the equation and find the value of that variable.

In the exercise, we need to isolate the variable \(r\) from the formula \(I = p r t\). To do this, we perform algebraic operations to both sides of the equation until \(r\) is alone on one side. Here's how:

• First, identify the term that contains the variable you need to solve for. In this case, it’s \(r\) in the term \( p r t \).


• Next, divide both sides of the equation by the other terms. So, divide both sides by \( p t \). When you divide \( p r t \) by \( p t \), the \( p \) and \( t \) cancel out, leaving \( r \) by itself. This is a general principle in algebra to perform the same operation on both sides of the equation to maintain equality.

Now, the equation becomes \( \frac{I}{p t} = r \). You have successfully isolated \( r \).

Division in algebra is used to split expressions into smaller parts, just like in regular arithmetic. It is particularly useful when isolating variables in an equation.

To isolate a variable, you can divide both sides of an equation by a number or an expression that is multiplying the variable you want to isolate. This works because dividing by something undoes multiplication, which effectively 'removes' that term from the variable.
In the exercise, we had the equation \( I = p r t \) and we needed to solve for \( r \). We divided both sides of the equation by \( p t \) to get:

\ r = \frac{I}{p t} \,
where we divided each side of the original equation \( I = p r t \) by the product \( p t \). This action split the term \( p r t \) into \( r \) and ensures every part of the equation is balanced and correct.

Remember these key points about division in algebra:

• Division is the opposite of multiplication.
• Always perform the same operation on both sides of the equation to keep it balanced.
• Be mindful of dividing by zero; it's undefined in mathematics.

Understanding division in algebra helps you simplify and solve equations more efficiently!