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Multiplying fractions is a straightforward process once you understand the rules that govern it. When you multiply fractions, you simply need to multiply the numerators together to find the new numerator and the denominators together to find the new denominator.

• Numerator: The top number in a fraction.
• Denominator: The bottom number in a fraction.

For example, if you have two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), their product is given by:\[\frac{a \cdot c}{b \cdot d}\]In the problem given, we multiply \( \frac{x}{2} \) by \( \frac{3}{y} \) to get:\[\frac{3x}{2y}\]It's important to remember to always simplify the fraction if possible. Simplification means reducing the fraction to its lowest terms, which makes it easier to understand and use in calculations.

Solving equations involves finding the value of the unknowns that make the equation true. In our problem, we are given the equation:\[\frac{3x}{2y} = \frac{3}{2}\]To solve for the unknown variable "y", you first aim to isolate "y" on one side of the equation. This generally involves several steps which may include:

• Rearranging terms
• Multiplying or dividing both sides by a constant or a variable
• Using inverse operations to simplify

In our solution, we start by noticing that both sides of the equation have the fraction \( \frac{3}{2} \). The focus is to manipulate the terms so that we isolate "y" by reversing operations. Here, you divide both sides by 3x and rearrange, which helps simplify the equation to make "y" the subject.

Variables in algebra are symbols used to represent numbers. They allow us to form equations and express generalities. In our exercise, "x" and "y" are variables, representing unknown values at first.

• Variables can stand for a single number or a range of numbers.
• They are typically denoted by letters such as x, y, z, etc.

Understanding variables is crucial because they are the core components of algebraic expressions and equations. They enable expressions like \( \frac{x}{2} \) or \( \frac{3}{y} \) to be manipulated and solved. Knowing how to handle variables, such as isolating them in an equation, allows us to discover the specific values they represent. This foundational skill is applicable in various math problems and even complex real-world situations.