Unit 4

Question

Unit ratios & proportions

Answer 1

In mathematics, ratios and proportions are important concepts that are used to compare quantities and solve problems involving fractions.

A ratio is a comparison of two quantities or numbers. It is often written as "a:b" or "a to b." For example, if there are 10 boys and 20 girls in a class, the ratio of boys to girls is 10:20 or 1:2.

Proportions, on the other hand, are equations that state that two ratios are equal. If two ratios are proportional, it means that they have the same value. Proportions are often used to solve problems involving unknown quantities.

For example, suppose you know that the ratio of the length of a rectangle to its width is 3:2. If the width of the rectangle is 4, you can set up a proportion:

(length of rectangle) / (width of rectangle) = 3/2

Let x be the length of the rectangle. The proportion becomes:

x / 4 = 3/2

To solve for x, you can cross-multiply and solve for x:

2x = 12

x = 6

So the length of the rectangle is 6 units.

Ratios and proportions are used in various real-life situations such as cooking, finance, and geometry. They allow us to compare and understand relationships between quantities and make calculations based on those relationships.