In elementary school, students are introduced to the world of fractions at a very basic level--adding, subtracting, multiplying and dividing. As you advance in your math studies, you learn more complicated use of fractions in subjects, such as algebra and trigonometry. An understanding of the basic fraction fundamentals can lay the groundwork for future math studies.

## Common Denominators

Add fractions that have common denominators by adding the two numerators together and placing that sum over the common denominator. For example, in the equation 1/4 + 2/4, there is a common denominator of 4. Adding the two numerators together equals 3. Place the 3 over the common denominator of 4 to equal 3/4.

Subtract fractions with common denominators by subtracting the two numerators and placing them over the common denominator. For example, in the equation 15/8 - 4/8, you subtract 4 from 15 to get 11; place the result over the common denominator to get 11/8.

Simplify the fraction to its lowest form by dividing the denominator into the numerator. The numerator, 11, divided by 8 equals 1 3/8.

## Different Denominators

Multiply the denominators when you are adding or subtracting fractions that have different denominators. For example, in the equation 2/6 + 4/18, you multiply 6 x 18 to get 108.

Divide the new common denominator, 108, by the old denominator in the first fraction, 6, to get 18. Multiply the first numerator, 2, by 18. Your first fraction is now 36/108. Do the same for the second fraction; 108 divided by 18 equals 6. Multiply 6 x 4. Your second fraction is now 24/108.

Add the two fractions together; 36/108 + 24/108 = 60/108.

Simplify the result to the smallest form. The numerator and the denominator both can be divided by 12, so 60/108 becomes 5/9.

## Multiplying and Dividing

Whether adding, subtracting, multiplying or dividing, always remember to simplify a fraction to its lowest form.

Multiply fractions by multiplying the two numerators together.

Multiply the two denominators together.

Place the product of the two numerators over the product of the two denominators. For example, in the equation 2/5 x 1/2, multiply 2 x 1 and get 2. Then multiply 5 x 2 and get 10. Place the numerator over the denominator to get 2/10.

Simplify the fraction by finding the lowest number that can be divided into both the numerator and the denominator. In this case, 2 divided into the numerator (2) equals 1, and 2 into the denominator (10) equals 5. Your final simplified answer is 1/5.

Divide fractions by multiplying the numerator of the first fraction times the denominator of the second fraction. This answer is your new numerator.

Multiply the denominator of the first fraction times the numerator of the second fraction to get your new denominator.

Place your new numerator over your new denominator. For example, in the equation 2/3 divided by 1/5, multiply 2 x 5 to get 10. Multiply 3 x 1 to get 3. Your new answer is 10/3. Because the answer contains a numerator that is larger than the denominator, simplify the fraction by dividing the denominator into the numerator to get 3 1/3.