Ratios, Proportions, and Percentages

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:
  1. Identify the ratio or proportion.
  2. Set up an equation based on the ratio or proportion.
  3. 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.

Test your understanding of ratios, proportions, and percentages, including how to express them, equivalent ratios, and calculating percentage increases/decreases.