What is 45 of 120? Understanding Fractions, Percentages, and Ratios
The question "What is 45 of 120?" can be interpreted in a few ways, depending on what you want to know. Let's explore the different mathematical relationships:
1. 45 as a Fraction of 120:
This is the most straightforward interpretation. We express 45 out of 120 as a fraction: 45/120. This fraction can be simplified by finding the greatest common divisor (GCD) of 45 and 120, which is 15. Dividing both the numerator and the denominator by 15 gives us the simplified fraction:
3/8
Therefore, 45 is 3/8 of 120.
2. 45 as a Percentage of 120:
To express 45 as a percentage of 120, we divide 45 by 120 and multiply by 100:
(45/120) * 100 = 37.5%
So, 45 is 37.5% of 120.
3. The Ratio of 45 to 120:
The ratio of 45 to 120 is written as 45:120. Similar to the fraction, we can simplify this ratio by dividing both numbers by their GCD (15):
3:8
Thus, the simplified ratio is 3:8.
In summary: The relationship between 45 and 120 can be represented as a fraction (3/8), a percentage (37.5%), or a ratio (3:8). The best representation depends on the context of your problem. Understanding these different mathematical expressions helps to analyze and interpret data effectively in various situations.
