What is a ratio?

A ratio is a relationship between two quantities, showing how many times one value contains or is contained within the other. It can be expressed in various forms, such as 'a to b', a:b, or a/b.

How do you simplify a ratio?

To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For example, to simplify the ratio 20:30, find the GCD (which is 10), and divide both terms by 10, resulting in 2:3.

If the ratio of boys to girls in a class is 3:4 and there are 28 girls, how many boys are in the class?

Hint: Use the concept of equivalent ratios.

Let the number of boys be 3x and the number of girls be 4x. Since there are 28 girls, we set up the equation 4x = 28. Solving for x gives x = 7. Therefore, the number of boys is 3x = 3*7 = 21.

A recipe requires 3 parts of oil to 5 parts of vinegar. If you want to make a total of 32 parts of the mixture, how much oil and vinegar do you need?

Hint: Find the total parts and use ratios to divide accordingly.

The total parts of the mixture is 3 + 5 = 8 parts. To find the amount of each ingredient, divide the total parts (32) by the number of parts (8) to find 1 part = 4. Therefore, oil = 3 parts * 4 = 12 and vinegar = 5 parts * 4 = 20.

What is a proportion?

A proportion is an equation that states that two ratios are equal. For example, if a:b = c:d, then a, b, c, and d are in proportion.

A fruit seller sold apples and oranges in the ratio 5:3. If he sold 40 apples, how many oranges did he sell?

Hint: Set up the ratio equation.

Let the number of oranges sold be 3x. According to the ratio, 5x = 40. Solving for x gives x = 8. Therefore, the number of oranges sold is 3x = 3*8 = 24.

Two numbers are in the ratio 7:9. If their sum is 128, what are the numbers?

Hint: Use the concept of part-to-whole relationships.

Let the numbers be 7x and 9x. Their sum is 7x + 9x = 16x. Setting this equal to 128 gives 16x = 128, so x = 8. Therefore, the numbers are 56 and 72.

If 3 parts of a mixture contain 6 liters of water, how much water is in 8 parts of the mixture?

Hint: Find the water per part first.

If 3 parts contain 6 liters, then each part contains 6/3 = 2 liters. Therefore, in 8 parts, the amount of water is 8 * 2 = 16 liters.

In a group of students, the ratio of boys to girls is 2:3. If there are 30 boys, how many girls are there in the group?

Hint: Set up the ratio to find girls.

Let the number of girls be 3x. Since the ratio is 2:3 and there are 30 boys, we can set 2x = 30. Solving gives x = 15. Therefore, the number of girls is 3x = 3*15 = 45.

If 5 pens cost 200 rupees, how much will 8 pens cost? Hint: Set up a proportion based on the given information.

Let the cost of 8 pens be x. The proportion is 5/200 = 8/x. Cross-multiplying gives 5x = 1600. Thus, x = 320. The cost of 8 pens is 320 rupees.

How do you convert a ratio into a fraction?

To convert a ratio a:b into a fraction, simply express it as a/b. For instance, the ratio 3:4 can be written as the fraction 3/4.