What is 12 out of 15 written as a decimal, fraction, and a percent?
The Correct Answer and Explanation is :
To express ( \frac{12}{15} ) as a decimal, fraction, and percent, we can break down the conversions as follows:
Fraction
The fraction ( \frac{12}{15} ) can be simplified by finding the greatest common divisor (GCD) of the numerator (12) and the denominator (15). The GCD of 12 and 15 is 3.
Dividing both the numerator and denominator by their GCD:
- ( 12 \div 3 = 4 )
- ( 15 \div 3 = 5 )
Thus, ( \frac{12}{15} ) simplifies to ( \frac{4}{5} ).
Decimal
To convert the fraction ( \frac{12}{15} ) into a decimal, you can divide the numerator by the denominator:
[
12 \div 15 = 0.8
]
So, ( \frac{12}{15} ) as a decimal is 0.8.
Percent
To convert the decimal to a percentage, multiply the decimal by 100:
[
0.8 \times 100 = 80\%
]
So, ( \frac{12}{15} ) expressed as a percent is 80%.
Summary
- As a fraction: ( \frac{12}{15} ) simplifies to ( \frac{4}{5} ).
- As a decimal: ( 0.8 ).
- As a percent: ( 80\% ).
Explanation
Understanding these conversions is essential in various fields, including mathematics, finance, and science. Fractions represent parts of a whole, where the numerator signifies how many parts we have, and the denominator signifies how many equal parts make up the whole. Converting fractions to decimals and percentages provides different perspectives on the same value. For example, a score of ( \frac{12}{15} ) on a test indicates a solid understanding of the material, which translates to 80% success, a common measure in educational assessments. Understanding these representations enhances numerical literacy and helps in making informed decisions based on quantitative data.