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A fraction equation is an algebraic equation where at least one term is a fraction. In the exercise, we have \( \frac{35}{y} = 0.07 \). This means that 35 divided by \( y \) equals 0.07. The presence of the fraction might make the equation seem complicated at first, but it's essentially about finding an unknown number (\( y \)) that will satisfy the equation.
A key step in dealing with fraction equations is to first eliminate the fraction to simplify the equation. In our example, multiplying both sides of the equation by \( y \) helps us in this regard, transforming the equation into a more familiar form without fractions. This is crucial because once the fraction is cleared, it's easier to pinpoint the variable and solve for it.

Isolating a variable means manipulating an equation to get the unknown variable by itself on one side of the equation. It's an important skill in algebra that allows you to solve equations systematically. In the context of the problem, after removing the fraction, we are left with \( 35 = 0.07y \). Our goal is to solve for \( y \), so we need to isolate it.
Here’s how you do it:

• You divide both sides of the equation by 0.07 to get \( y \) on one side.
• This process is often referred to as "performing inverse operations", where you do the opposite of the operation currently acting on the variable.

After dividing, you have successfully isolated \( y \), making it possible to calculate its numerical value.

In algebra, division is one of the fundamental operations used to manipulate equations. When solving equations like \( 35 = 0.07y \), you may need to perform division to isolate the variable. Division helps you move numbers across the equal sign to simplify equations.
For instance, to isolate \( y \) in the equation, divide both sides by 0.07. This action cancels out the 0.07 on the side with \( y \), effectively leaving \( y \) on its own. It’s crucial to do the same operation on both sides of the equation to keep it balanced.
Here's a simple division tip for algebra:

• Make sure that you're dividing by the number across from the variable
• Always double-check your division to ensure accuracy in your results

In our exercise, dividing 35 by 0.07 results in \( y = 500 \), successfully solving the equation.