Express 37 1/2% as a fraction in its lowest terms.
To express 37 1/2% as a fraction in its lowest terms, we first convert the percentage to a decimal by dividing it by 100.
37 1/2% = 37.5 / 100
Next, we simplify the fraction 37.5/100 by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 12.
37.5 / 100 = (37.5 ÷ 12) / (100 ÷ 12)
= 3.125 / 8.3333
Since the decimal is recurring in the denominator, we can multiply both the numerator and the denominator by 10000 to eliminate the decimal.
3.125 / 8.3333 = (3.125 × 10000) / (8.3333 × 10000)
= 31250 / 83333
The resulting fraction, 31250 / 83333, is already in its lowest terms since its numerator and denominator do not have any common factors other than 1.
To express a percentage as a fraction, you can follow these steps:
1. Rewrite the percentage as a fraction by putting it over 100.
In this case, 37 1/2% can be written as 37 1/2/100.
2. Simplify the fraction if possible by finding the greatest common divisor (GCD) between the numerator and denominator.
To simplify a fraction, you need to find the greatest common divisor (GCD) between the numerator and denominator. In this case, the numerator is 37 1/2 and the denominator is 100. Let's simplify it:
GCD(37 1/2, 100)
To simplify the mixed number, we convert it to an improper fraction:
37 1/2 = (37 * 2 + 1)/2 = 75/2
Now we have:
GCD(75/2, 100)
To proceed, we need to simplify both the numerator and denominator:
Numerator (75/2):
The GCD of 75 and 2 is 1, so we cannot simplify the numerator any further.
Denominator (100):
The GCD of 100 is 25, which can be simplified.
3. Divide both the numerator and denominator by the GCD obtained in step 2 to simplify the fraction further.
The GCD we obtained was 25.
Numerator (75/2):
Divide the numerator by 25: 75 ÷ 25 = 3.
Denominator (100):
Divide the denominator by 25: 100 ÷ 25 = 4.
The simplified fraction is 3/4.
Therefore, expressing 37 1/2% as a fraction in its lowest terms is 3/4.
37 1/2 % = 37.5 % = 37.5 / 100 = 375 / 1000 = 125 ∙ 3 / 125 ∙ 8 = 3 / 8
37 1/2 % = 3 / 8