Short Answer 
Ratios compare two quantities, expressed as a/b or a:b, indicating their relative size, while proportions are equations stating that two ratios are equal, expressed as a/b = c/d. Both concepts are essential in real-life applications such as measurements and budgeting, allowing for effective problem-solving.
Step 1: Understanding Ratios
A ratio is a comparison between two quantities that shows the relative size of one quantity to another. It is typically expressed as an ordered pair of numbers, written as a/b or a:b, where b cannot be zero. For instance, if a student scores 2 out of 5 in a test, the ratio of marks received to total marks is 2:5. This helps to evaluate how one number compares to another.
Step 2: Defining Proportion
A proportion is an equation that states that two ratios are equal. It is represented as a/b = c/d, where a and d are called the extreme terms and b and c are the mean terms. Proportions help us understand relationships between ratios, allowing us to find unknown values by cross-multiplying. For example, if you know that 2:4 is equal to x:8, you can find x by setting up the proportion.
Step 3: Practical Applications
Ratios and proportions are widely used in various contexts like measurements, comparisons, and scaling. They can represent quantities such as lengths, weights, or counts of objects. Understanding how to work with these concepts enables problem-solving in real-life situations, such as cooking recipes or budget calculations. Remember, always ensure that the quantities being compared are of the same unit to maintain accuracy in your calculations.