Let's explain the concepts of ratio and proportion to a class of 6th graders.
Ratio:
A ratio is a way to compare two or more quantities or numbers. It shows the relationship between the quantities or numbers in terms of their relative sizes or amounts. Ratios are often expressed in the form of a fraction, using a colon (:), or using the word "to."
For example, let's consider a class of 20 students, with 12 boys and 8 girls. The ratio of boys to girls in the class can be written as:
12 boys : 8 girls
or
12 boys / 8 girls
or
12 boys to 8 girls
The ratio tells us that for every 12 boys, there are 8 girls in the class.
Proportion:
Proportion is a special type of ratio that shows the equality of two ratios. When two ratios are proportional, it means that the corresponding fractions are equal.
For example, let's consider two different fruit baskets. In the first basket, there are 5 apples and 3 oranges, and in the second basket, there are 10 apples and 6 oranges. We can compare the ratio of apples to oranges in both baskets:
Basket 1: 5 apples : 3 oranges
Basket 2: 10 apples : 6 oranges
To check if the two ratios are proportional, we can cross-multiply and see if the fractions are equal:
5/3 = 10/6
Simplifying both sides of the equation, we get:
10/6 = 10/6
Since both fractions are equal, we can say that the ratios are proportional. This means that for every 5 apples, there are 3 oranges in both baskets.
In summary, ratio is a way to compare quantities or numbers, while proportion is a special type of ratio that shows the equality of two ratios. Ratios help us understand the relationship between different quantities or amounts, while proportions allow us to compare different ratios and determine if they are equal.