Percentages are just another way of expressing a fraction over 100. So, if 75 percent of students who took a test passed the test, you could also say that 75 out of every 100 students passed or -- more simply -- just write it as 75/100. Every ratio that can be expressed as a fraction -- just like this one -- also has a number called its multiplicative inverse, or the number you'd multiply it by to get a total of 1. All you have to do to find that inverse for a percentage is express the percentage as a fraction, then swap the numerator and denominator of the fraction.

## Work an Example

If 23 percent of students do their homework every night, find the inverse of that percentage. First you express the percentage as a fraction over 100: 23/100. Then you swap the numerator and denominator to get the multiplicative inverse: 100/23. This works because when you multiply across you get 23/100 x 100/23 = 23(100)/23(100) which cancels out to 1/1 or 1. The same is true for any numerator and denominator, as long as neither one is equal to zero. So, the inverse of 23 percent is 100/23 or, if you must write it out as a decimal, 4.35, when rounded to the nearest hundredth.

References

Photo Credits

Comstock Images/Stockbyte/Getty Images