Glossary
Constant Speed
Movement at a consistent rate, meaning the distance covered per unit of time remains unchanged. This relationship is often described by the formula d = rt.
Example:
A train traveling at 80 mph maintains a constant speed, covering 80 miles every hour.
Cross Multiplication
A method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other, and setting the products equal. This creates a linear equation to solve for the unknown.
Example:
To solve 3/x = 9/15, you would use cross multiplication to get 3 * 15 = 9 * x, leading to 45 = 9x.
Currency Exchange
The process of converting one country's currency into another's, based on a specific exchange rate. This is a real-world application of rates and proportions.
Example:
If the currency exchange rate is 1 USD = 0.92 EUR, then 50 USD would convert to 46 EUR.
Percentages
A way to express a part of a whole as a fraction of 100. They are widely used for discounts, taxes, and representing proportional parts.
Example:
If a shirt is 25% off its original price of 10, illustrating the application of percentages.
Population Growth
The increase in the number of individuals in a population over time. It can often be modeled using proportional relationships or rates.
Example:
A town's population growth rate of 2% per year means its population increases by 2% annually.
Proportion
An equation stating that two ratios are equivalent. It is used to solve for an unknown quantity when a relationship between two ratios is known.
Example:
To scale a recipe, you might set up a proportion like 2 cups of flour for 8 cookies equals 'x' cups of flour for 24 cookies.
Proportional Relationships
Relationships between two quantities where their ratio is constant. As one quantity changes, the other changes by a consistent multiplier.
Example:
The cost of apples is directly proportional to their weight; if 1 pound costs 4, showing a proportional relationship.
Rate
A comparison of two quantities with different units, indicating how one quantity changes in relation to another. Speed (miles per hour) is a common example.
Example:
A runner completes 10 kilometers in 50 minutes, so their rate is 0.2 kilometers per minute.
Ratio
A comparison of two quantities, often expressed as a fraction or with a colon (a:b). Ratios should always be simplified to their lowest terms.
Example:
If a class has 10 boys and 15 girls, the ratio of boys to girls is 2:3 after simplification.
Recipe Scaling
Adjusting the quantities of ingredients in a recipe proportionally to yield a different number of servings. This involves using ratios and proportions.
Example:
If a recipe for 12 cookies calls for 1 cup of flour, recipe scaling to make 36 cookies would require 3 cups of flour.
Scale Drawings
Representations of real-world objects or areas where dimensions are reduced or enlarged proportionally. They use a specific scale to relate drawing measurements to actual measurements.
Example:
On a map with a scale of 1 inch = 50 miles, a distance of 3 inches on the map represents an actual distance of 150 miles, demonstrating the concept of scale drawings.
Solution Concentrations
A measure of the amount of solute dissolved in a given amount of solvent or solution, often expressed as a ratio or percentage.
Example:
A saline solution might have a 0.9% sodium chloride solution concentration, meaning 0.9 grams of salt per 100 mL of solution.
Unit Conversion
The process of changing a measurement from one unit to another (e.g., feet to inches, kilometers to miles) using conversion factors. It's essential for ensuring consistent units in calculations.
Example:
To convert 5 feet to inches, you perform a unit conversion by multiplying 5 by 12, resulting in 60 inches.
Unit Rate
A rate where the denominator is 1 unit, making it easy to compare different rates. It shows the amount of one quantity per single unit of another quantity.
Example:
If a 12-ounce soda costs 0.15 per ounce.
d = rt (Distance = Rate * Time)
A fundamental formula used to calculate distance, rate, or time when two of the three variables are known. It is crucial for solving problems involving constant speed.
Example:
If a car travels at a rate of 60 mph for 2.5 hours, you can use d = rt to find the distance traveled: 60 * 2.5 = 150 miles.