Which Ratio Is The Smallest: $32:24$ Or $30:22$?
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Introduction
When comparing ratios, it's essential to understand that a ratio is a way of expressing the relationship between two quantities. In this article, we will explore how to compare two ratios, specifically the ratios of 32:24 and 30:22, to determine which one is the smallest.
Understanding Ratios
A ratio is a comparison of two numbers, often expressed as a fraction. For example, the ratio of 3:4 can be written as 3/4. Ratios can be used to compare quantities, such as the number of boys to girls in a class or the number of apples to oranges in a basket.
Comparing Ratios
To compare two ratios, we need to find a common multiple or a common divisor. A common multiple is the smallest number that both numbers can divide into evenly. A common divisor is the largest number that both numbers can divide into evenly.
Finding a Common Multiple
To find a common multiple, we can list the multiples of each number and find the smallest number that appears in both lists.
- Multiples of 32: 32, 64, 96, 128, 160, ...
- Multiples of 24: 24, 48, 72, 96, 120, ...
As we can see, the smallest number that appears in both lists is 96. Therefore, we can rewrite the ratios as follows:
- 32:24 = 32/24 = 4/3
- 30:22 = 30/22 = 15/11
Finding a Common Divisor
To find a common divisor, we can list the divisors of each number and find the largest number that appears in both lists.
- Divisors of 32: 1, 2, 4, 8, 16, 32
- Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24
As we can see, the largest number that appears in both lists is 4. Therefore, we can rewrite the ratios as follows:
- 32:24 = 32/24 = 8/6
- 30:22 = 30/22 = 15/11
Comparing the Ratios
Now that we have rewritten the ratios, we can compare them to determine which one is the smallest.
- 4/3 = 1.33
- 8/6 = 1.33
- 15/11 = 1.36
As we can see, the ratio 4/3 is equal to 1.33, which is the smallest of the three ratios.
Conclusion
In conclusion, when comparing ratios, it's essential to find a common multiple or a common divisor. By rewriting the ratios and comparing them, we can determine which one is the smallest. In this article, we compared the ratios 32:24 and 30:22 and found that the ratio 4/3 is the smallest.
Final Answer
The final answer is: