How to Understand Fractions and Percentages

By eHow Education Editor

A fraction is a number that expresses part of a group. A percentage is a number that expresses part of a group of 100. Here is some introductory material about both.

Fractions

Remember that the number above the line is the numerator, and the number below the line is the denominator. In the fraction, ½, the 1 is the numerator, and the 2 is the denominator.

Add two fractions whose denominators are the same by adding their numerators. For example, 3/5 + 1/5 = 4/5.

Subtract two fractions whose denominators are the same by subtracting their numerators: 3/5 - 1/5 = 2/5.

To add or subtract two fractions whose denominators are different, first convert one or both fractions so that they have the same, or "common," denominator.

Convert a fraction by multiplying both its numerator and denominator by the same non-zero number. If you want to add 1/5 and 1/10 together, then convert 1/5 by multiplying both the 1 and the 5 by 2: 1/5 X 2/2 = 2/10. Next, you can add 2/10 + 1/10 = 3/10.

Multiply two fractions by first multiplying the numerators, then multiplying the denominators: 1/3 X 2/5 = 2/15. (When multiplying or dividing fractions, the denominators do not have to be the same!)

Divide two fractions by first inverting (or turning upside down) the fraction you are using to divide into the other fraction. Then multiply the two fractions. For example, 3/7 divided by 9/10: Invert to 3/7 x 10/9 = (3 x 10)/(7 x 9) = 30/63.

Reduce a fraction to its "lowest term" by dividing the numerator and the denominator by a number that can go into both (a "common factor"). For 5/10, for example, you can divide both the 5 and the 10 by 5 to reduce 5/10 to ½.

Keep dividing until there are no more common factors. You will then have reached the fraction's 'lowest terms."

Understand improper fractions. They have numerators that are larger than or equal to their denominators. For example, 15/2 is an improper fraction. Convert an improper fraction to a mixed number by dividing the numerator by the denominator. A mixed number has a whole number and a fraction part. When you convert 15/2, you end up with 7½, which is a mixed number.

Percentages

Understand that a percent is the same as a fraction that has a denominator of 100. For example, 6% of something is the same as 6/100 of that thing.

Make sure you know that percent and hundredths are basically equivalent. This makes conversion between percent and decimals very easy.

To convert from a decimal to a percent, just move the decimal 2 places to the right. Example: 0.15 = 15 hundredths = 15%.

To convert a fraction to a percentage, divide the numerator by the denominator. Then move the decimal point two places to the right (which is the same as multiplying by 100) and add a percent sign. Example: 5/8 = .625; .625 x 100 = 62.5 or 62.5%.