Ratios and Proportions

Click on the flashcard to see the answer

What is a ratio?

A ratio is a comparison of two quantities by division.

How can a ratio be expressed?

A ratio can be expressed in three ways: using the colon (a:b), as a fraction (a/b), or in words (a to b).

What is a proportion?

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

If the ratio of apples to oranges is 3:4, how many apples are there if there are 8 oranges?

There are 6 apples because 3/4 = x/8, so x=6.

How do you solve a proportion like 2/3 = x/9?

Cross-multiply to get 2×9 = 3x, then solve for x to get x = 6.

What is the concept of equivalent ratios?

Equivalent ratios are different ratios that represent the same relationship.

How can you create an equivalent ratio to 5:10?

By multiplying or dividing both terms by the same number. For example, multiply both by 2 to get 10:20.

What is a real-life example of using ratios?

Mixing paint colors in a specific ratio to achieve a desired shade.

Describe the role of proportions in cooking recipes.

Proportions are used to scale recipes up or down while maintaining the same ratio of ingredients.

What are the four terms in a proportion called?

First term, second term (antecedents), third term, and fourth term (consequents).

How do you determine if two ratios form a proportion?

Check if the cross products of the ratios are equal.

What is an aspect of scaling in art that involves ratios?

Aspect ratio in image resizing, where the ratio of width to height is maintained.

How can errors in proportion affect real-world structures?

Incorrect proportions can lead to structural failures, such as in architecture or engineering.

What is the ratio of the sides of a triangle with sides measuring 3 cm, 4 cm, and 5 cm?

The ratio is 3:4:5.

How is understanding proportions useful in business?

Proportions are used in financial analysis, such as calculating profit margins and cost ratios.