Question

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

Answer 1

Percentages are really just fractions out of 100. So 45% is really just 45/100. If you want to find the lowest fractions, you have to break each number up into prime factors and see which overlap. So:

45 = 9x5
     = 3 x 3 x 5
100 = 2 x 50
       = 2 x 5 x 10
       = 2 x 5 x 2 x 5

So 45/100 = 3x3x5/2x2x5x5

Now because there's a 5 on both sides, we can cancel down. If we do, that leaves us with

3x3/2x2x5

Which is 9/20

Answer 2

To make a percent into a fraction you:

1. Set the percentage up as a fraction by putting it over 100 (represents 100 percent).

2. Simplify the fraction by dividing both the numerator and denominator by the greatest common factor of each. 

45%
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 100: 1, 2, 3, 4, 5, 10, 20, 25, 50, 100

GCF = 5

$\frac{45}{100} = \frac{9}{20}$

62%
Factors of 62: 1, 2, 62
Factors of 100: 1, 2, 3, 4, 5, 10, 20, 25, 50, 100

GCF = 2
$\frac{62}{100} = \frac{31}{50}$

68%
Factors of 68: 1, 2, 4, 68
Factors of 100: 1, 2, 3, 4, 5, 10, 20, 25, 50, 100

GCF = 4

$\frac{68}{100} = \frac{17}{25}$

2%
Factors of 2: 1, 2
Factors of 100: 1, 2, 3, 4, 5, 10, 20, 25, 50, 100
GCF = 2

$\frac{2}{100} = \frac{1}{50}$