Ratio - Proportion - Rate of change

What is a rate of change?

The rate of change refers to how much a quantity changes over a period of time.

What is a proportion?

A proportion is an equation that states two ratios are equivalent.

What is a ratio?

A ratio is a relationship between two quantities, showing how many times the first quantity contains the second.

How do you calculate a rate of change?

Rate of change is calculated by the formula: (Change in value) / (Change in time).

What is a direct proportion?

Direct proportion occurs when two variables increase or decrease together at a constant rate.

What is an inverse proportion?

Inverse proportion occurs when one variable increases as the other decreases.

What is an example of a ratio?

An example of a ratio is 3:4, indicating a relationship between two quantities.

How can you express a proportion?

A proportion can be expressed as a fraction, such as a/b = c/d.

What is a unit rate?

A unit rate is a comparison of two different quantities, where one of the quantities is 1.

How do you find the unit rate?

To find the unit rate, divide the first quantity by the second quantity.

What are equivalent ratios?

Equivalent ratios are ratios that have the same value when simplified.

What is the cross-multiplication method?

The cross-multiplication method is a technique used to solve proportions by multiplying the means and the extremes.

What role does the rate of change play in calculus?

In calculus, the rate of change is crucial for understanding derivatives and slopes of curves.

What is a constant rate of change?

A constant rate of change means that the quantity changes at a fixed rate over time.

How is a percentage related to ratios?

Percentages are a type of ratio that expresses a number as a fraction of 100.

What is the difference between ratio and rate?

A ratio compares two quantities, while a rate compares a quantity to a unit of time or another measure.

How do you represent a ratio visually?

A ratio can be represented visually using diagrams, such as pie charts or bar graphs.

What is the importance of rates in real-world applications?

Rates are important in various fields such as finance, science, and economics for analyzing changes.

What is a scale factor?

A scale factor is a number that scales, or multiplies, some quantity.

How does a percentage change relate to rate of change?

Percentage change is a specific calculation of the rate of change expressed as a percentage.

What is a gradient in relation to rates of change?

Gradient refers to the slope of a line, indicating the rate of change between points.

When are ratios used in recipes?

Ratios are used in recipes to compare the proportions of ingredients.

What is proportional reasoning?

Proportional reasoning is the ability to recognize and use the multiplicative relationships between quantities.

What is the formula for calculating percentage change?

Percentage change = [(New Value - Old Value) / Old Value] x 100.

How does knowing rates help in budgeting?

Knowing rates helps in budgeting by analyzing costs over time and making informed financial decisions.

What is the relationship between distance, speed, and time?

The relationship is described by the formula: Speed = Distance / Time.

What is an example of an inverse relationship in real life?

An example is the relationship between supply and price, where increased supply typically leads to lower prices.

What does 'proportionally increased' mean?

'Proportionally increased' means that a quantity is increased by the same ratio as another quantity.

How can ratios be simplified?

Ratios can be simplified by dividing both terms by their greatest common divisor.

What is a conversion factor in relation to rates?

A conversion factor is a numeric ratio used to convert one unit of measurement to another.

What is dynamic change?

Dynamic change refers to a rate of change that constantly shifts over time.

What influences rates of change in a business context?

Factors influencing rates include market demand, costs, and competition.

How is rate of change visually represented in graphs?

Rate of change is visually represented by the slope of a line on a graph.