What is 45 of 120? Understanding Fractions, Percentages, and Ratios
The question "What is 45 of 120?" can be interpreted in several ways, depending on what you're trying to find out. Let's explore the different mathematical interpretations and how to solve them.
1. 45 as a Fraction of 120:
This interpretation asks what fraction 45 represents when compared to the whole, 120. To calculate this, we simply express 45 as the numerator and 120 as the denominator:
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 denominator by 15 gives us:
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 first calculate the fraction as shown above (45/120 = 3/8). Then, we convert the fraction to a decimal by dividing the numerator by the denominator:
3 รท 8 = 0.375
Finally, we multiply the decimal by 100 to express it as a percentage:
0.375 x 100 = 37.5%
So, 45 is 37.5% of 120.
3. 45 as a Ratio to 120:
A ratio expresses the quantitative relationship between two or more amounts. In this case, the ratio of 45 to 120 is written as:
45:120
Similar to the fraction, this ratio can be simplified by dividing both numbers by their GCD (15):
3:8
The simplified ratio is 3:8.
In Summary:
The answer to "What is 45 of 120?" depends on the context. It can be expressed as a fraction (3/8), a percentage (37.5%), or a ratio (3:8). Understanding these different mathematical representations allows for a more comprehensive understanding of the relationship between the two numbers.
