Ratios and proportions are fundamental concepts in mathematics that are used to compare quantities. A ratio is a comparison of two or more quantities in terms of their sizes or values. It is usually written in the form of a fraction, using a colon (:) or a division symbol (/) to separate the two values being compared.

For example, let's consider a bag of marbles that contains 5 red marbles and 3 blue marbles. The ratio of red marbles to blue marbles can be expressed as 5:3 or 5/3. This means that for every 5 red marbles, there are 3 blue marbles.

Proportions, on the other hand, are equations that state two ratios are equal. In other words, if two ratios are proportional, their values are in a consistent relationship with each other. Proportions can be used to solve problems involving unknown quantities.

For example, if we have a proportion equation such as 5/3 = x/9, we can solve for the unknown value of x. By cross-multiplying, we get 3x = 45, and dividing both sides by 3, we find that x = 15.




The unitary method is a problem-solving technique that involves finding the value of a single unit and using it to determine the value of a given quantity. It is often used to solve problems related to ratios, proportions, and rates.

For example, let's say we want to find the cost of 4 pens if the cost of 6 pens is $30. In this case, we can use the unitary method to find the cost of a single pen.

To do this, we divide the total cost ($30) by the number of pens (6). This gives us the cost of one pen, which is $5.

Once we know the cost of one pen, we can easily find the cost of 4 pens by multiplying the cost of one pen by 4. Therefore, the cost of 4 pens would be $20.

The unitary method allows us to find the value of a single unit and apply it to solve problems involving multiple units. It is a useful technique for solving real-world problems that involve ratios and proportions.

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