Basics of Ratios
What is a ratio?
A ratio is a comparison of two quantities that shows the relative size of one quantity to another.
What is a unit rate?
A unit rate is a rate with a denominator of 1.
What defines a proportional relationship?
Two quantities are in a proportional relationship if their ratio is constant.
What is a tape diagram and when is it used?
A tape diagram visually represents part-to-part or part-to-whole relationships and is used when quantities have the same units.
How might you use ratios when cooking?
Ratios are used in recipes to maintain consistent flavors.
How can a ratio be expressed in words?
A ratio can be expressed in words like “3 to 2,” “3 for every 2,” or “3 out of 5.”
Calculate the unit rate from a ratio of 3 cups of flour to 2 cups of sugar.
Divide the numerator (3 cups of flour) by the denominator (2 cups of sugar) to get 1.5 cups of flour per cup of sugar.
How can you tell if two quantities are in a proportional relationship using a table?
Check if the ratio between quantities in all table entries is the same.
Explain what a double number line diagram represents.
A tape diagram visually represents part-to-part or part-to-whole relationships and is used when quantities have the same units.
Give an example of how ratios are used in financial calculations.
Ratios help calculate interest rates, currency exchange, or discounts.
What is an example of a ratio involving different units?
An example is “3 meters in 2 seconds.”
If a car travels 150 miles in 3 hours, what is the unit rate in miles per hour?
150 miles ÷ 3 hours = 50 miles per hour.
Write an equation for a proportional relationship where the constant of proportionality is 4.
y = 4x.
How can visual representations help solve problems involving ratios?
They clarify relationships by showing patterns and equivalent ratios visually.
In a school, the ratio of boys to girls is 3:5. If there are 120 students, how many are boys?
Boys = (3/8) × 120 = 45 boys.
How do you find equivalent ratios?
Multiply both terms of the ratio by the same positive number.
Why are unit rates useful in real-life situations?
Unit rates simplify comparisons, such as price per unit, to make decisions easier.
Describe a real-world scenario illustrating a proportional relationship.
For example, the amount of paint needed to color a wall is proportional to the wall’s area.
What are the benefits of using visual aids for ratios and proportions?
They help identify relationships and improve understanding of abstract concepts.
How can understanding ratios help with speed and distance calculations?
Ratios calculate average speed, like miles per hour.
Explain the difference between a ratio and a rate.
A ratio compares two quantities, while a rate compares two quantities with different units.
If a recipe calls for 4 cups of water for every 3 cups of rice, how many cups of water are needed for 9 cups of rice?
4/3 = x/9; solving gives x = 12 cups of water.
How can you represent a proportional relationship on a graph?
A proportional relationship appears as a straight line passing through the origin on a graph.
Create a tape diagram for the ratio 5:3.
[Insert a simple drawing of a tape diagram with 5 segments labeled as one quantity and 3 segments labeled as another.]
Explain how ratios and proportions are used in making predictions from data statistics.
Ratios are used in sampling data to predict trends or outcomes for larger populations.