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# How to Simplify Negative Fractions

How to Simplify Negative Fractions?

In Mathematics, we know that whole numbers can be negative or positive. Similarly, fractions can also be positive or negative.

Negative Fractions
The negative fractions are handled in the same way as we handle negative whole numbers.
The rules for mathematical operations on negative whole numbers such as addition, subtraction, multiplication and division also apply to fractions.
The negative fractions can also be calculated using number line.

Points to be noted in a Negative Fraction

•    A negative sign in front of a fraction implies that either the numerator or the denominator is negative.
•    The fraction that has negative numbers in both the numerator and the denominator can be simplified.
After simplifying this negative fraction, the two minus signs will get cancelled and we get the same numbers as a positive fraction.

Simplifications of Negative Fractions

The negative fractions can be simplified using the mathematical operators. Let us see some methods of simplification of negative fractions using mathematical operations:

CASE 1:

1               5           4               2
-   __    +    __   =     __  =      __

6               6              6             3

In the above example, as the signs of the fractions are different, the two fractions are subtracted and the sign of the highest number is applied in the result.
As 5 is greater than 1 and the difference of 5 and 1 is 4, we get +4 divided by the denominator 6 as the result.

CASE 2:
If both the numbers to be added are negative, then the result will be the total of the two fractions preceded by a negative sign.

CASE 3:
In a mathematical problem where a negative fraction is to be subtracted from a positive fraction, minus of a negative fraction will become positive and so the two numbers will be added and the result will be a positive fraction being the sum of the two fractions given.

CASE 4:
In case of subtraction of two fractions in which the first fraction is a negative fraction and the second is a positive fraction, then the result will be the addition of two fractions preceded by a negative sign.

CASE 5:
In case of multiplication, product of one positive fraction and one negative fraction will result in a negative fraction. But the product of two negative fractions results in a positive fraction as “minus into minus is plus”.

CASE 6:
In case of division of fractions, if one fraction is positive and the other fraction is negative, then the resultant fraction will be negative. A negative fraction divided by another negative fraction results in a positive fraction.

An important point to be considered in simplifying negative fractions is that once the result is obtained, the numerator and the denominator should be reduced in its value by dividing it with a common factor, as we saw in CASE 1.
This should be repeated until there is no common factor between the numerator and the denominator.

Question:I really don't get it. I thought I would because its basically the same as adding positive and negative numbers together right? Well I had to do a problem that was -2/5 - 1and3/4. the answer turned out to be -2and3/20. how did that happen??? can someone explain this to me?

Answers:It really is just the same, only with a bit more work. -2/5 -1 3/4 is the same as -2/5 + -1 3/4 Then you add: -1 3/4 + -2/5 --------- ?? K, so then when you add, you need to find a common denominator. What is a common denominator for 3/4 and 2/5?? How about 20? Change ur fractions..... -1 3/4 = -1 15/20 -2/5 = -8/20 Now you can add... -1 15/20 + -8/20 ---------- -2 3/20 Because..... 15+8 = 23. so it would be -1 23/20. Then u simplify it to -2 3/20 Do you get it now??

Question:How are complex fractions simplified? Give an example of a simplifying a complex fraction.

Answers:They are simplified by "rationalizing" the denominator...I use quotes because usually rationalizing is use to refer to taking out square roots...but it's the same idea. You may have seen this with square roots: 1/(1 + sqrt(2)) Multiply by conjugate: (1 - sqrt(2)) / (1 + 2) = (1 - sqrt(2))/3 The conjugate works because of differences of squares: (x + y) * (x - y) = x^2 - y^2 So comlex numbers work the same way: You can "rationalize" the complex number by multiplying by it's complex conjugate (just negate the imaginary part): (a + bi) * (a - bi) = a^2 - (ib)^2 = a^2 - (i^2)(b^2) = a^2 - (-1)b^2 = a^2 + b^2 So...that's how you get rid of the imaginary part in the denominator...someone else already gave you an example.

Question:my homework says: simplify each expression. and there's lots that are adding negatives. i.e. -6+(-8) -15+(-11) -8+(-17) so how do you simplify adding two negatives??!!! pleez and thank you.

Answers:rules for division and multiplying: negative times a negative is a positive negative times a positive is a negative positive times a positive is a positive rules for adding and subtracting: negative plus a negative is a negative positive plus a positive is a positive

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