How To Add / Subtract Fractions When You Have A Negative Denominator Or Numerator?

A fraction can only be in two states, positive or negative, so there is no such thing as a negative numerator or denominator, there is simply either a positive or negative fraction as any negative top or bottom of the fraction makes the entire fraction negative. Adding and subtracting them involves some basic rules of mathematics that anyone can learn and these concepts are taught in most schools when a student enters the 5th or 6th grade. Learning these rules and applying them are the foundation necessary to move on to more advanced mathematical topics such as algebra and calculus that most schools now require for a student to gain a high school diploma.

In the addition of two fractions where one of them is positive, and the other is negative, subtract the larger fraction from the smaller and give it the sign of the larger fraction. In the subtraction of negative fraction from a positive number you will add the the negative number to the positive as the minus sign in front of the negative sign turns it positive. There are also very specific rules that must be followed in the multiplication and division of fractions that must be learned in order to get the right result from the operation.

The best way to add and subtract any sort of fraction from another fraction or an integer is to visualize the problem as a pie chart or as a percentage. To work fractions a student must first have a strong grasp of the mathematical foundations of adding, subtracting, multiplying, and dividing. Once the adding, subtracting, multiplication, and division of fractions is mastered, a student is ready to take on a high school class in pre-algebra where the topics will be built upon with statistics, probabilities, and more advanced concepts.
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A negative denom. Or numerator means that the whole fraction is negative because a neg. Into a pos. Or pos. Into a neg. Results in a negative quotient.
So if you are adding two fractions and one is neg. You subtract the larger fraction from the smaller and give it the sign of the larger fraction.
If you are subtracting a neg. Fraction from a pos., you will add because the minus of a minus number changes the sign to pos.
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Oddman commented
A fraction that has both a negative numerator and a negative denominator has a positive overall value (the negative signs "cancel"). A fraction having either a negative numerator or a negative denominator (but not both) has a negative overall value.

When doing signed arithmetic involving one positive and one negative number, you actually subtract the smaller number from the larger and give the sign of the larger to the result. 