Illustrative Math Alignment: Grade 7 Unit 9

Topic

Ratios, Proportions, and Percents

Definition

Calculating tax involves determining the percentage amount to be added to the base price of a product or service.

Description

Calculating tax is a fundamental application of percentages in real-world scenarios. When purchasing goods or services, the total cost is often the sum of the base price and the tax applied. Understanding how to calculate tax is essential for budgeting and financial literacy.

For example, if a product costs $50 and the tax rate is 8%, the tax amount is calculated as 

50 × 0.08 = 4

Therefore, the total cost is 

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Calculating tips involves determining the amount of money to give as a gratuity based on a percentage of the total bill.

Description

Calculating tips is a common use of percentages in everyday life, particularly in service industries such as dining. Tips are usually calculated as a percentage of the total bill, and understanding how to compute this is important for both customers and service providers. 

For instance, if a meal costs $80 and you want to leave a 15% tip, the tip amount is calculated as 

80 × 0.15 = 12

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Converting units involves changing a measurement from one unit to another using a conversion factor.

Description

Converting units is essential in various fields such as science, engineering, and everyday life. It involves using ratios and proportions to switch between different measurement systems, such as converting inches to centimeters or gallons to liters.

For example, to convert 5 miles to kilometers, knowing that 1 mile is approximately 1.60934 kilometers, you multiply 

5 × 1.60934 = 8.0467 kilometers

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Dimensional analysis is a method used to convert one unit of measurement to another using conversion factors.

Description

Dimensional analysis is a powerful tool in mathematics and science for converting units and solving problems involving measurements. It uses the principle of multiplying by conversion factors to ensure that units cancel out appropriately, leading to the desired unit.

For example, to convert 50 meters per second to kilometers per hour, you use the conversion factors  1 meter = 0.001 kilometers and 1 hour = 3600 seconds: 

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Equivalent ratios are ratios that express the same relationship between quantities.

Description

Equivalent ratios are fundamental in understanding proportions and scaling in mathematics. They represent the same relationship between quantities, even though the numbers themselves may differ. This concept is crucial in various applications, such as cooking, map reading, and creating models.

For instance, the ratios 2:3 and 4:6 are equivalent because they both simplify to the same ratio when reduced.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-part ratios compare different parts of a whole to each other.

Description

Part-to-part ratios are used to compare different parts of a whole, providing a way to understand the relationship between different components. This type of ratio is essential in fields such as statistics, biology, and economics.

For example, if a class has 10 boys and 15 girls, the part-to-part ratio of boys to girls is 10:15, which simplifies to 2:3.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

Part-to-whole ratios compare one part of a whole to the entire whole. These ratios are more commonly known as fractions.

Description

Part-to-whole ratios are used to compare a part of a whole to the entire whole, providing insights into the composition of a dataset or population. This type of ratio, more commonly referred to as fractions, is widely used in statistics, finance, and everyday decision-making.

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates.

For example, if you score 45 out of 50 on a test, your percentage score is 

(45/50) × 100 = 90%

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent decrease measures the reduction in value expressed as a percentage of the original value.

Description

Percent decrease is used to quantify the reduction in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as price reductions and weight loss.

For example, if the price of a jacket drops from $80 to $60, the percent decrease is calculated as 

(80 − 60)/80 × 100 = 25%.

Topic

Ratios, Proportions, and Percents

Definition

Percent increase measures the growth in value expressed as a percentage of the original value.

Description

Percent increase is used to quantify the growth in value over time, expressed as a percentage of the original value. It is commonly used in finance, economics, and everyday scenarios such as salary increases and population growth.

For example, if the price of a stock rises from \$50 to \$75, the percent increase is calculated as 

(75 − 50)/50 × 100 = 50%