Ratio and Proportion

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The relationship between two quantities expressed as a fraction or a proportion.

Introduction to Ratio and Proportion: This topic provides an overview of what ratio and proportion are, including definitions, properties, and basic operations.
Simplifying Ratios: A skill that helps simplify complex or larger ratios by expressing them in their simplest form. It involves dividing both the numerator and the denominator by the common factor until we can no longer do so.
Types of Ratios: This topic covers different types of ratios, including simple ratios, compound ratios, direct ratios, inverse ratios, and joint proportions.
Proportion: Proportion refers to the equality of two ratios. This topic covers how to solve proportion problems, such as finding unknown quantity given the other three values.
Applications of Ratio and Proportion: This topic is about real-life problems that can be solved using ratio and proportion, such as distance problems, mixture problems, and percentage problems among others.
Ratio Problems Involving Fractions: Some ratios might come with fractions, which can add complexity since fractions are incredibly hard to work with in arithmetic. Learn how to solve problems involving ratios that have fractions.
Variation: Variation refers to the different ways two variables can affect each other. This topic covers direct and inverse proportion and how variables are related in each.
Ratios and Proportions in Geometry: This topic focuses on the application of ratios and proportions in geometry used in real-world problems.
Algebra and Ratio: This branch of algebra lets you use ratios to solve for unknowns by using algebraic techniques to manipulate the ratios.
Solving Problems with Ratios: In this topic, you learn how to solve problems involving ratios; this includes setting up ratios, cross-multiplying, and simplifying the ratio before solving.
Simple Ratio: It is a comparison of two quantities that are of the same unit.
Compound Ratio: It is a comparison of multiple ratios.
Inverse Ratio: It is a proportion where one variable increases while the other decreases or vice versa.
Direct Proportion: It is a proportion where both variables increase or decrease together.
Inverse Proportion: It is a proportion where an increase in one variable causes the other variable to decrease and vice versa.
Mixed Proportion: It is a combination of direct and inverse proportion.
Continued Proportion: It is a proportion where the first term is to the second term as the second term is to the third term and so on.
Duplicate Ratio: It is a proportion where the first quantity is the square of the second quantity.
Triplicate Ratio: It is a proportion where the first quantity is equal to the cube of the second quantity.
Partition Ratio: It is a ratio used to divide a quantity into certain parts in a specific ratio.
Ratio of Divisions: It is a proportion used to find the length of segments when a line is divided in a given ratio.
Componendo and Dividendo: It is a rule used for solving problems based on proportionality.
Cross Multiplication Method: It is a method used for finding the value of an unknown variable in a proportion.
Proportionality Theorem: It states that if a line is parallel to one side of a triangle, then the other two sides are divided proportionally.
Similarity of Triangles: It is a proportionality theorem where two triangles are said to be similar if their corresponding angles are equal, and their corresponding sides are in proportion.
Harmonic Mean: It is a ratio of the number of values to the sum of their reciprocals.
Geometric Mean: It is a mean calculated by multiplying the values together and then taking the nth root of the result.
Arithmetic Mean: It is a mean calculated by adding all the values together and dividing the sum by the number of values.
Apparent Simple Interest: It is a ratio of the simple interest earned to the principal amount.
True Simple Interest: It is a ratio of the interest earned to the principal amount, calculated using the exact number of days in a year.
Compound Interest: It is a ratio of the amount of money earned over a period of time to the principal amount invested.
Discount: It is a price reduction given to a buyer in exchange for early payment of a debt or purchase.
Profit and Loss: It is a ratio that compares the amount earned or lost to the cost of a product or investment.
Gross Profit Margin: It is a ratio calculated by dividing the gross profit by net sales.
Net Profit Margin: It is a ratio calculated by dividing the net profit by net sales.
Return on Investment: It is a ratio of the amount earned or lost on an investment to the amount invested.
Debt-to-Equity Ratio: It is a ratio of the company's total liabilities to its total equity.
Current Ratio: It is a ratio of the company's current assets to its current liabilities.
Quick Ratio: It is a ratio of the company's cash and cash equivalents, short-term investments, and accounts receivable to its current liabilities.
Inventory Turnover Ratio: It is a ratio of the cost of goods sold to the average inventory held during a specific period.
"In mathematics, a ratio () shows how many times one number contains another."
"The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc."
"In most contexts, both numbers are restricted to be positive."
"A ratio may be specified either by giving both constituting numbers, written as 'a to b' or 'a:b', or by giving just the value of their quotient a/b."
"A statement expressing the equality of two ratios is called a proportion."
"A ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction."
"Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers."
"A more specific definition adopted in physical sciences (especially in metrology) for a ratio is the dimensionless quotient between two physical quantities measured with the same unit."
"A quotient of two quantities that are measured with different units may be called a rate."
"For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3)."
"The ratio of lemons to oranges is 6:8 (or 3:4)."
"The ratio of oranges to the total amount of fruit is 8:14 (or 4:7)."
"The numbers in a ratio may be quantities of any kind."
"A ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator."
"Equal quotients correspond to equal ratios."
"A statement expressing the equality of two ratios is called a proportion."
"Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers."
"A more specific definition adopted in physical sciences (especially in metrology) for a ratio is the dimensionless quotient between two physical quantities measured with the same unit."
"A quotient of two quantities that are measured with different units may be called a rate."
"The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc."