Ratios - Ratio and Proportion, Mathematics Class 6

What is a Ratio?
A ratio is a way to compare two or more quantities using division. It is a relationship between two numbers that shows how many times one value is contained within the other. Ratios are usually expressed in the form of a fraction, with a colon or with the word "to" between the two numbers.

Understanding Ratios and Proportions
Ratios and proportions are closely related concepts. A proportion is an equation that states that two ratios are equal. In other words, a proportion is created when two ratios are set equal to each other. Ratios help us compare quantities, while proportions help us solve problems involving ratios.

Example Questions:

1. What is the ratio of apples to oranges?
- Let's say we have 4 apples and 6 oranges. The ratio of apples to oranges would be 4:6 or 4/6. This ratio can be simplified to 2:3 or 2/3.

2. If a recipe calls for 2 cups of flour and 3 cups of sugar, what is the ratio of flour to sugar?
- The ratio of flour to sugar would be 2:3 or 2/3. This means that for every 2 cups of flour, we need 3 cups of sugar.

3. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the ratio of red marbles to the total number of marbles?
- The total number of marbles is 5 + 3 + 2 = 10. The ratio of red marbles to the total number of marbles would be 5:10 or 5/10. This ratio can be simplified to 1:2 or 1/2.

4. Suppose a car travels 180 miles in 3 hours. What is the ratio of miles to hours?
- The ratio of miles to hours would be 180:3 or 180/3. This ratio can be simplified to 60:1 or 60/1. This means that the car is traveling at an average speed of 60 miles per hour.

5. In a class of 30 students, 18 are girls. What is the ratio of boys to girls?
- The number of boys is 30 - 18 = 12. The ratio of boys to girls would be 12:18 or 12/18. This ratio can be simplified to 2:3 or 2/3.

6. If a rectangle has a length of 8 cm and a width of 4 cm, what is the ratio of the length to the width?
- The ratio of the length to the width would be 8:4 or 8/4. This ratio can be simplified to 2:1 or 2/1.

7. A bag contains 3 red balls, 2 blue balls, and 5 green balls. What is the ratio of blue balls to the total number of balls?
- The total number of balls is 3 + 2 + 5 = 10. The ratio of blue balls

A is 11.5 :216 B is 101:115 C is 101:216