Calculating ratios in Grade 10 involves expressing the relationship between two or more quantities. You generally aim to simplify these ratios to their simplest form. Here's a breakdown of how to do it:
1. Understanding Ratios
A ratio compares two or more quantities of the same kind. It can be written in several ways:
- Using a colon: a : b (e.g., 3 : 4)
- As a fraction: a/b (e.g., 3/4)
- Using the word "to": a to b (e.g., 3 to 4)
2. Simplifying Ratios
The goal is to find the simplest whole number ratio that represents the same relationship. This is done by dividing all parts of the ratio by their greatest common factor (GCF).
Steps for Simplifying Ratios:
- Identify the parts of the ratio: For example, in the ratio 20 : 15 : 5, the parts are 20, 15, and 5.
- Find the Greatest Common Factor (GCF) of all the parts: The GCF is the largest number that divides evenly into all parts of the ratio. In the example of 20 : 15 : 5, the GCF is 5.
- Divide each part of the ratio by the GCF:
- 20 / 5 = 4
- 15 / 5 = 3
- 5 / 5 = 1
- Write the simplified ratio: The simplified ratio is 4 : 3 : 1.
Example 1:
Simplify the ratio 12 : 18
- The GCF of 12 and 18 is 6.
- Divide both parts by 6:
- 12 / 6 = 2
- 18 / 6 = 3
- Simplified ratio: 2 : 3
Example 2:
Simplify the ratio 36 : 24 : 12
- The GCF of 36, 24, and 12 is 12.
- Divide all parts by 12:
- 36 / 12 = 3
- 24 / 12 = 2
- 12 / 12 = 1
- Simplified ratio: 3 : 2 : 1
3. Ratios in Word Problems
Grade 10 problems often present ratios within word problems. You will need to extract the relevant quantities and express them as a ratio, then simplify if necessary.
Example:
In a class, there are 28 boys and 35 girls. What is the ratio of boys to girls in its simplest form?
- Ratio of boys to girls: 28 : 35
- The GCF of 28 and 35 is 7.
- Divide both parts by 7:
- 28 / 7 = 4
- 35 / 7 = 5
- Simplified ratio: 4 : 5
Key Takeaways:
- Ratios compare quantities.
- Simplifying ratios makes them easier to understand and use.
- Finding the GCF is crucial for simplifying ratios.
- Word problems require you to identify the quantities to be compared.
