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Questions and Answers
What is the fundamental principle of proportion?
What is the formula to calculate percentage increase?
What is the formula to calculate profit percentage?
What is the average of a set of numbers?
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What is the purpose of the unitary method?
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What is the median of a set of numbers?
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What is the formula to calculate loss percentage?
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What is the mode of a set of numbers?
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Study Notes
Ratio and Proportion
- A ratio is a comparison of two quantities of the same kind.
- It is expressed as a fraction, colon(:), or division sign(/).
- Equivalent ratios have the same value.
- Proportion is an equality of two ratios.
- If a:b = c:d, then a, b, c, and d are in proportion.
Percentage
- Percentage is a fraction with a denominator of 100.
- It is expressed as a percentage sign (%).
- Percentage increase/decrease:
((new value - original value) / original value) * 100 - Percentage change:
((new value - original value) / original value) * 100
Profit and Loss
- Profit: Selling price - Cost price
- Loss: Cost price - Selling price
- Profit percentage:
(Profit / Cost price) * 100 - Loss percentage:
(Loss / Cost price) * 100
Average
- Average: Sum of values / Number of values
- Types of averages:
- Mean: Average of a set of numbers
- Median: Middle value of a set of numbers when arranged in order
- Mode: Most frequent value in a set of numbers
Unitary Method
- A method to solve problems involving ratios and proportions.
- Steps:
- Identify the ratio or proportion.
- Set up an equation based on the ratio or proportion.
- Solve the equation to find the unknown value.
- Used to solve problems involving:
- Cost and selling price
- Ratio of quantities
- Percentage increase/decrease
Ratio and Proportion
- A ratio compares two quantities of the same kind and is expressed as a fraction, colon, or division sign.
- Equivalent ratios have the same value and can be written in different forms.
- Proportion is an equality of two ratios, denoted as a:b = c:d, where a, b, c, and d are in proportion.
Percentage
- A percentage is a fraction with a denominator of 100, expressed with a percentage sign (%).
- Percentage increase or decrease is calculated as ((new value - original value) / original value) * 100.
- Percentage change is also calculated using the same formula.
Profit and Loss
- Profit is the difference between selling price and cost price.
- Loss is the difference between cost price and selling price.
- Profit percentage is calculated as (Profit / Cost price) * 100.
- Loss percentage is calculated as (Loss / Cost price) * 100.
Average
- Average is the sum of values divided by the number of values.
- There are three types of averages:
- Mean: the average of a set of numbers.
- Median: the middle value of a set of numbers when arranged in order.
- Mode: the most frequent value in a set of numbers.
Unitary Method
- The unitary method is used to solve problems involving ratios and proportions.
- It involves identifying the ratio or proportion, setting up an equation, and solving for the unknown value.
- This method is applied to solve problems involving cost and selling price, ratio of quantities, and percentage increase/decrease.
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Description
Test your understanding of ratios, proportions, and percentages, including how to express them, equivalent ratios, and calculating percentage increases/decreases.
