write each percent as a fraction in simplest form

write each percent as a fraction in simplest form: 45% 62% 68% 2%

The correct answer and explanation is:

Here are the given percentages converted into fractions in simplest form:

1. 45%
   45% means 45 out of 100, so it is written as the fraction 45/100. To simplify, find the greatest common divisor (GCD) of 45 and 100, which is 5. Divide both numerator and denominator by 5:
   45 ÷ 5 = 9
   100 ÷ 5 = 20
   So, 45% as a simplified fraction is 9/20.
2. 62%
   62% is 62 out of 100, written as 62/100. The GCD of 62 and 100 is 2. Divide numerator and denominator by 2:
   62 ÷ 2 = 31
   100 ÷ 2 = 50
   Therefore, 62% as a simplified fraction is 31/50.
3. 68%
   68% means 68 out of 100, or 68/100. The GCD of 68 and 100 is 4. Divide both numerator and denominator by 4:
   68 ÷ 4 = 17
   100 ÷ 4 = 25
   So, 68% as a simplified fraction is 17/25.
4. 2%
   2% means 2 out of 100, written as 2/100. The GCD of 2 and 100 is 2. Divide numerator and denominator by 2:
   2 ÷ 2 = 1
   100 ÷ 2 = 50
   Thus, 2% as a simplified fraction is 1/50.

Explanation

Percent means “per hundred,” so to convert a percent to a fraction, the percent number is written over 100. For example, 45% means 45 out of 100, which is written as 45/100. This fraction can often be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is the largest number that divides both evenly.

Finding the GCD simplifies the fraction to its lowest terms, which makes it easier to understand and work with. For example, 45/100 simplifies to 9/20 because 9/20 is an equivalent fraction that uses smaller numbers. It represents the same value but is simpler.

Simplification is important because it shows the fraction in its most basic form, making calculations easier and the number easier to interpret. When simplifying, always check for the highest number that can divide both parts of the fraction without leaving a remainder.

This process applies to all percentages converted to fractions: write over 100, then simplify by dividing numerator and denominator by the GCD. For smaller percentages like 2%, the fraction reduces to 1/50, which means one part out of fifty.

Using fractions instead of percentages or decimals can sometimes make mathematical operations easier, especially when comparing ratios or working with parts of whole numbers.