MathsRatio And Proportion

Ratio And Proportion

Ratio And Proportion

  • A ratio is a comparison between two numbers. The two numbers can be anything, such as two lengths, two weights, two amounts of money, or two percentages. The two numbers are usually written in a line with a colon (:) between them. For example, 5:7 is a ratio.
  • A proportion is an equation that states that two ratios are equal. The two ratios are usually written as fractions. For example, if the ratio of the length of two lines is 5:7, then the proportion is 5/7 = 1/1.5. This equation states that the length of the two lines are in the same proportion.

Formula and of Ratio and Proportion

The formula for calculating a ratio is:

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    • (Quantity A divided by Quantity B) multiplied by 100
    • This formula will give you a percentage that reflects the ratio between Quantity A and Quantity B.
    • (Quantity A divided by Quantity B) equals (Quantity C divided by Quantity D)
    • This formula will tell you whether or not Quantity A and Quantity B are equal to Quantity C and Quantity D.

    Ratio And Proportion

    Ratio and Proportion in Daily Life

    • A ratio is a comparison of two quantities, typically expressed as a fraction. For example, if there are ten students in a classroom and twenty desks, the ratio of students to desks is two to one, or 2:1.
    • A proportion is an equation that states that two ratios are equal. For example, if the ratio of students to desks is 2:1 and the ratio of teachers to students is 1:10, then the proportion of teachers to desks is 10:1, or 10:20.

    Real-life Example of Ratio Analysis

    • Ratio analysis is a technique that is used to evaluate the financial performance of a company over a period of time. This analysis is done by taking ratios of different aspects of the company’s financial statement, and then comparing the ratios from different time periods. This can give the company’s management an idea of how well the company is doing financially, and where it might need to make changes.
    • One real-life example of how ratio analysis can be used is the case of a company that is trying to decide whether or not to expand its business. The company can use ratio analysis to compare its current financial performance with what it would be like if the company were to expand. This can help the company to make a decision about whether or not to expand.
    • Another real-life example of how ratio analysis can be used is in the case of a company that is trying to decide whether or not to purchase another company. The company can use ratio analysis to compare the financial performance of the two companies to see if there is a difference in the performance. This can help the company to make a decision about whether or not to purchase the other company.

    Ratio and Proportion

    • A ratio is a comparison of two numbers. The two numbers can be the same, like 2:2, or different, like 2:3. When the two numbers are the same, the ratio is called a “simple ratio.” When the two numbers are different, the ratio is called a “compound ratio.”
    • A proportion is an equation that states that two ratios are equal.

    What are Ratio and Proportion?

    • A ratio is a comparison between two numbers. The ratio of boys to girls in a classroom is 4 to 3. This means that for every four boys in the room, there are three girls.
    • A proportion is a comparison between two ratios. In the classroom example, the proportion of boys to girls is 4 to 3. This means that the ratio of boys to girls is the same as the ratio of girls to boys.

    Definition of Ratio

    A ratio is a comparison of two quantities. The first quantity is usually called the numerator, and the second quantity is called the denominator. The ratio is written as a fraction, with the numerator above the denominator.

    Definition of Proportion

    A proportion is a mathematical statement that two ratios are equal. The two ratios are usually written as a fraction, with the first number above the line and the second number below the line.

    Direct Proportion

    • A proportion is a statement of equality between two ratios.
    • \(\frac{A}{B} = \frac{C}{D}\)
    • In this proportion, A is to B as C is to D.

    Inverse Proportion

    Inverse proportion is a mathematical relation between two variables such that as one variable increases, the other decreases and vice versa.

    Ratio and Proportion Formula

    • The following is the formula for ratio and proportion:
    • \(\frac{A}{B} = \frac{C}{D}\)
    • In this formula, A and B are the numerators, while C and D are the denominators.

    Tricks for Ratio and Proportion

    There are a few tricks you can use to help you with ratio and proportion problems.

    • First, remember that the ratio of two numbers is just the comparison of the two numbers. So, if you are given a ratio, all you have to do is divide the two numbers to find the answer.
    • For example, if you are given the ratio 2:5, you would divide 2 by 5 to get the answer 0.4.
    • For example, if you are given the ratio 2:5, you would convert it to a fraction by using the formula above. This would give you the fraction 2/5.

    Few Solved Examples

    Example 1

    A triangular prism is shown. Find the surface area.

    The surface area is the sum of the surface areas of the six faces.

    There are three sides of length 6 and three sides of length 4.

    The surface area is 36 + 12 + 12 = 60.

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