Adding Fractions with Negative Numbers

Introduction for Adding Fractions with Negative numbers:

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator.

Source – Wikipedia.

Adding Fractions with Negative Numbers – Method 1:
The examples show the adding the fractions with negative numbers.

This is the formula to calculate the algebraic fractions for addition is ` a/b + c/d` = `(ad + bc) / (bd)` .

Adding the fractions: `-3/5 + 2/8 `

Solution:

Multiply the numerator and denominator

= `(-3xx8 + 2xx5) / (5xx8)`

Then adding the numerator

= `(-24 + 10) / 40`

= `-14/40` .
By reducing this fraction we get `-7/20` .

Adding the fractions: `4/6 + (-3)/7`

Solution:

Multiply the numerator and denominator

= `(4xx7 + 6xx-3)/(6xx7)`

Then adding the numerator

= `(28 - 18)/42`

= `10/42`

By reducing this fraction we get `5/21` .

Adding the fractions: `15/-6 + 10/-2`

Solution:

Multiply the numerator and denominator

= `(15xx-2 + (-6)xx10)/(-6xx-2)`

Then adding the numerator

= ` (-30 - 60)/-12`

= `-90/-12`

By reducing this fraction we get `15/2` .

I am planning to write more post on rational numbers definition, rounding to the nearest tenth. Keep checking my blog.

Adding Fractions with Negative Numbers – Method 2:
The examples show the adding the fractions with negative numbers.

Adding the algebra fractions: `-3/4 + 9/-7` .

Solution:

LCM for the denominators in the fractions are

The LCM of 4, -7 = -28

So `(-3xx-7)/(4xx-7)` = `-21/-28`

`(9xx4)/(-7xx4)` = `36/-28`

Denominators are equal and adding the numerator in the fractions.

= `-21/-28+36/-28`

= `(-21+36)/-28`

= `15/-28` is the solution.

Adding the algebra fractions: `(-8x)/11 + (-10x)/4` .

Solution:

The given fractions are

= `(-8x)/11 + (-10x)/4`

LCD for the denominators 11 and 4 is 44.

= `(-8xxx4)/44+((-10x)xx11)/44`

To express the denominators in the LCD form as

= `(-32x)/44+(-110x)/44`

We can simplify the numerators.

=` (-32x-110x)/44`

We can add the numerators.

= `(-142x)/44`