Ratios are crucial in mathematics for comparing quantities. Simplifying ratios and dividing quantities according to ratios are essential skills for a variety of real-world applications.
![Ratio](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Ff5827db8-cb2e-4b8f-8349-d8e783b092c2-file.png&w=1080&q=75)
Simplifying Ratios
Reducing ratios to their simplest form involves finding the greatest common divisor (GCD) of the numbers and dividing them by it.
Simplify the ratio 20:30:40
1. GCD of 20, 30, 40 is 10.
2. Simplified Ratio:
Simplify the ratio 45:60:90
1. GCD of 45, 60, 90 is 15.
2. Simplified Ratio:
Dividing Quantities in a Ratio
This involves calculating the value of a single part in the ratio and then distributing the total quantity accordingly.
Divide £120 in the ratio 2:3:4
1. Total Parts:
2. Value per Part:
3. Distribution:
- Person 1:
- Person 2:
- Person 3:
Divide £180 in the ratio 3:2:5
- Total Parts:
- Value per Part:
- Distribution:
- Part 1:
- Part 2:
- Part 3:
Worked Problems
Problem 1: Ratio Application in Recipes
Suppose a recipe for a cake requires ingredients in the ratio 2:3:4. If you have 900g of the first ingredient, how much of the other two ingredients do you need?
Solution:
- Given Ratio: 2:3:4.
- Total parts of the given ingredient: per part.
- Required quantities:
- Second ingredient: .
- Third ingredient: .
Problem 2: Mixing Paints
To get a particular shade of green, a painter mixes yellow and blue paint in the ratio 3:2. If the painter needs 500ml of green paint, how much of each colour does he use?
Solution:
- Total Ratio Parts: .
- Total Paint: 500 ml
- Value per Part:
- Quantities:
- Yellow paint:
- Blue paint: