Write 45% as a fraction or mixed number in simplest form.
The Correct Answer and Explanation is:
To convert 45% to a fraction or mixed number in simplest form, we start by understanding what the percentage represents. A percentage is a way of expressing a number as a fraction of 100. Thus, 45% can be written as:
[
45\% = \frac{45}{100}
]
The next step is to simplify the fraction (\frac{45}{100}). To do this, we need to find the greatest common divisor (GCD) of the numerator (45) and the denominator (100). The GCD is the largest number that divides both numbers without leaving a remainder.
Finding the GCD:
- Prime Factorization:
- The prime factorization of 45 is:
[
45 = 3^2 \times 5^1
] - The prime factorization of 100 is:
[
100 = 2^2 \times 5^2
]
- Identify Common Factors:
- The common prime factor is (5). The lowest power of (5) common to both factorizations is (5^1). Therefore, the GCD of 45 and 100 is (5).
Simplifying the Fraction:
Now, we divide both the numerator and the denominator by their GCD:
[
\frac{45 \div 5}{100 \div 5} = \frac{9}{20}
]
Thus, (45\%) in fraction form is (\frac{9}{20}).
Mixed Number Conversion:
Since (\frac{9}{20}) is already a proper fraction (the numerator is less than the denominator), it cannot be expressed as a mixed number. Therefore, the simplest form of (45\%) as a fraction is (\frac{9}{20}).
In conclusion, (45\%) is equivalent to the fraction (\frac{9}{20}). This fraction cannot be simplified further as 9 and 20 have no common factors other than 1, confirming that (\frac{9}{20}) is indeed in its simplest form.