Write this ratio another way.
120/150
The Correct Answer and Explanation is :
The correct answer is: ( \frac{4}{5} )
The ratio ( \frac{120}{150} ) can be simplified and expressed in several ways.
Simplification
To simplify the ratio ( \frac{120}{150} ), we divide both the numerator (120) and the denominator (150) by their greatest common divisor (GCD). The GCD of 120 and 150 is 30.
- Calculate the GCD:
- The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
- The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
- The common factors are: 1, 2, 3, 5, 6, 10, 15, 30.
- The greatest common factor is 30.
- Divide by the GCD:
[
\frac{120 \div 30}{150 \div 30} = \frac{4}{5}
]
Alternative Representations
- Fraction: As previously shown, ( \frac{120}{150} ) simplifies to ( \frac{4}{5} ).
- Percentage: To express this ratio as a percentage, you can use the formula:
[
\text{Percentage} = \left(\frac{120}{150}\right) \times 100 = 80\%
]
This means that 120 is 80% of 150. - Decimal: By dividing 120 by 150, you get:
[
120 \div 150 = 0.8
]
This decimal representation indicates that 120 is 0.8 times 150.
Conclusion
Thus, the ratio ( \frac{120}{150} ) can be represented in various forms: simplified as ( \frac{4}{5} ), expressed as 80%, or shown as the decimal 0.8. Understanding how to convert ratios into different formats is useful in various applications, such as mathematics, finance, and statistics, where comparisons and proportions are necessary for analysis and decision-making. These representations allow for better communication of quantitative relationships in various contexts.