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`
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`
