How to add and subtract negative and positive fractions

Calculator Use

Add and subtract proper and improper fractions with this calculator and see the work involved in the solution.

Select the number of fractions in your equation and then input numerators and denominators in the available fields. Click the Calculate button to solve the equation and show the work.

You can add and subtract 3 fractions, 4 fractions, 5 fractions and up to 9 fractions at a time.

How to Add and Subtract Fractions

When the Denominators are the Same

When fractions have the same denominators we simply add or subtract the numerators as indicated and place the result over the common denominator. If necessary we can simplify the fraction to lowest terms or a mixed number.

When the Denominators are Unlike or Different

When fractions have unlike denominators the first step is to find equivalent fractions so that all of the denominators are the same. We find the Least Common Denominator (LCD) then rewrite all fractions in the equation as equivalent fractions using the LCD as the denominator. When all denominators are alike, simply add or subtract the numerators and place the result over the common denominator. The resulting fraction can be simplified to lowest terms or written as a mixed number.

How to Work With Negative Fractions

When an equation calls for adding a negative fraction, we can rewrite the equation as subtracting a positive fraction. Likewise, if the equation calls for subtracting a negative fraction, this is the same as adding a positive fraction and can be rewritten this way. This calculator rewrites negative fractions when it shows the work involved in finding the answer.

Simplifying Operations on Negative Numbers

Whether you are working with fractions, whole numbers or decimals, use these guidelines when adding and subtracting positive and negative numbers.

Original

Adding a Positive Number

+

+

Adding a Negative Number

+

-

Subtracting a Positive Number

−

+

Subtracting a Negative Number

−

-

Changes to

+

+

Adding a Positive Number

−

+

Subtracting a Positive Number

−

+

Subtracting a Positive Number

+

+

Adding a Positive Number

For similar and more basic methods of working with fractions you can also visit Help With Fractions.

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Negative fractions are like any other fraction, except that they have a preceding negative (-) sign. The process of adding and subtracting negative fractions can be straightforward, if you keep in mind two things. A negative fraction added to another negative fraction will result in a negative fraction as result. A negative fraction subtracted from another is the same thing as adding the positive complement of that fraction.

Make the denominators (the bottom of the fraction) the same, if they are not already. You can only add halves to halves or quarters to quarters or tenths to tenths and so on. Subtraction of negative fractions follows the same method.

Thus, if the negative fractions you are adding do not have the same denominator, you can make it so.

-1/2, for example, can be written as -2/4, -3/6, -4/8, et cetera. In each case, the number at the top is always half the number at the bottom. These fractions all mean half of a quantity.

Consider the adding and subtracting of the following negative fractions.

• 1/4 + (-3/10) - 1/4 - (-3/10)

The first example is the addition of negative three-tenths to negative one-fourth. The second is the subtraction of negative three-tenths from negative one-fourth.

Method: You cannot add one-fourths to three-tenths until you express both of them to a uniform standard, so that you have a common point of reference with which you can work. You can only add like to like, or subtract like from like. More like being able to compare apples to oranges only when you at least call them both pieces of fruit.

You need a common denominator. This will be the lowest number that the two denominators 4 and 10 will divide into. This will be 20.

Keep the fraction equivalent using this common denominator: 20.

(- 1/4) becomes (- 5/20), because 5 is a quarter of 20.

(- 3/10) becomes (- 6/20). The denominator increased 2 times, so the numerator, the top part, has to double also, to keep the fraction the same.

Now that a common denominator has been found, and the negative fractions expressed in terms of this new denominator, the negative fractions can then be added or subtracted.

When adding negative fractions, add as per normal. Then stick the negative sign to your answer.

When subtracting negative fractions, you are, in effect, adding the positive complement of the negative fraction you are subtracting, because subtracting a negative number or fraction is the same as adding the positive of that negative fraction or number. The two consecutive negative signs "cancel out" to give a positive sign.

Adding the negative fractions: (- 1/4) + (- 3/10) = - 5/20 + - 6/20 = - (11/20)

When subtracting: (- 1/4) - (- 3/10) = - 5/20 - (- 6/20) \= - 5/20 + 6/20 (two consecutive minus signs become a + sign) \= 1/20.

What are the rules for adding and subtracting negative fractions?