10 Questions
What is the simplified ratio of 75:45:30:60?
5:3:2:4
Which of the following is the correct way to simplify the ratio 16:4?
Divide both terms by 4 to get 4:1
What is the simplified ratio of $6:10$?
$2:3$
Ratios are useful in mathematics because they:
Can be used to compare costs, weights, or sizes
Which of the following is the correct way to simplify a ratio?
Divide all parts of the ratio by their highest common factor
What is the greatest common factor of 8 and 36?
4
When simplifying the ratio 8:36, what should be the new ratio after dividing both terms by 4?
2:9
What is the greatest common factor of 6 and 10?
1
After simplifying the ratio 3:8 by dividing both terms by their greatest common factor, what should be the new ratio?
3:8
If a ratio is given as 5:15, what would be the simplest form after dividing both terms by their greatest common factor?
1:3
Study Notes
Comparing and Simplifying Quantities: Understanding Ratios
In mathematics, ratios are used to compare two or more quantities. Whether you are comparing costs, weights, or sizes, ratios provide valuable insights into the relationship between different values. They do not have units, making them useful for comparison across different contexts. Like fractions, ratios can often be simplified to make comparisons even easier to understand.
Simplifying Ratios
To simplify a ratio, divide all parts of the ratio by their highest common factor. For example, consider the ratio 4:2. The highest common factor of both parts is 2, so 4:2 simplifies to 2:1. Similarly, if we want to simplify the complex ratio 75:45:30:60, we first identify that each component ends with a digit that could potentially be a common factor. In this case, we find the greatest common factor of 5. Dividing through by 5 gives 15:9:6:12. We then notice that 15 and 9 share another common factor of 3, further simplifying the ratio to 5:3:2:4.
Let's look at how to simplify the ratio 16:4 using the same method. First, we determine that the highest common factor of 16 and 4 is 4. By dividing both terms by 4, we obtain the simplified ratio 4:1.
For a more visual explanation of the process, consider the following examples:
Example 1: Simplify the ratio 6:10.
- Identify the factors of
6: 1, 2, 3, 6. - Identify the factors of
10: 1, 2, 5, 10. - Determine the greatest common factor of
6and10: 2. - Divide both terms by
2: 6 ÷ 2 = 3, 10 ÷ 2 = 5. - Rewrite the ratio in simplest form:
3:5.
Example 2: Simplify the ratio 8:36.
- Identify the factors of
8: 1, 2, 4, 8. - Identify the factors of
36: 1, 2, 3, 4, 6, 9, 12, 18, 36. - Determine the greatest common factor of
8and36: 4. - Divide both terms by
4: 8 ÷ 4 = 2, 36 ÷ 4 = 9. - Rewrite the ratio in simplest form:
2:9.
Example 3: Simplify the ratio 3:8.
- Identify the factors of
3: 1, 3. - Identify the factors of
8: 1, 2, 4, 8. - Determine the greatest common factor of
3and8: 1. - Divide both terms by
1: 3 ÷ 1 = 3, 8 ÷ 1 = 8. - Since the greatest common factor is already 1, no further division is necessary. The ratio
3:8is already in simplest form.
Learn how to simplify ratios to compare quantities more effectively. Discover the process of identifying and dividing by the highest common factor to express ratios in simplest form. Practice with examples like 6:10, 8:36, and 3:8 to master the art of ratio simplification.
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