How To Add Fractions With Negative Numbers

A fraction is a numeric value that defines as role of a whole. It is derived from the word 'fractio' means to break. Information technology is used to solve daily life issues like dividing food, supplies, currency, etc. A number that is in the form of a/b tin can be called a fraction. Where a, b are whatever numbers. For example 2/3, 12/4, etc. Rational, Irrational numbers which are of form a/b can be considered as fractions.

Part of Fraction

Fraction consist of two parts:

Denominator: The lowest part of the fraction is known as the denominator. It represents in which how many parts the given whole number will be divided. For instance, 2/iii, here 3 is known as denominator.
Numerator: The upper role of the fraction is known equally the numerator. It represents in which how many sections of the fraction. For example, ii/iii, here 3 is known as numerator

Type of Fraction

Following are the type of fractions:

Proper Fraction: Proper fractions are those fractions in which the numerator is always less than its denominator. For example, v/16, 1/4, etc.
Improper Fraction: Improper fractions are those fractions in which the numerator is e'er more than than or equal to its denominator. For case, 5/2, xi/4, etc.
Unit of measurement Fraction: Unit fractions are those fractions that accept simply 1 at the numerator. For case, 1/2, i/14, etc.
Mixed Fraction: Mixed fractions are those fractions that contain the mixture of whole and proper fractions. For example, $4\frac{1}{2}, 7\frac{2}{3}$ , etc.
Equivalent Fraction: Equivalent fractions are those fractions that contain the same values. For example, 2/9 x ii/2 = four/18.
Like Fraction: Similar fractions are those fractions that contain the aforementioned denominators. For case, 2/8, 4/viii, etc.
Unlike Fraction: Unlike fractions are those fractions that comprise dissimilar denominators. For case, 2/9, 8/13, etc.

Add fractions with Negative Numbers

Equally we know addition is the basic operation of mathematics. Information technology is used to notice the sum of two positive or negative numbers. We can as well add fractions with the same or different denominators. We are allowed also allowed to add fractions with negative numbers. Some rules nosotros demand to call back when nosotros perform addition or subtraction between whatever positive or negative numbers. Those are mentioned beneath-

Rule 1: When two positive numbers are multiplied we get positive result.

(+) 10 (+) = +

Example: 5×two=x

Rule 2: When two negative numbers/symbols are multiplied we become positive consequence.

(-) 10 (-) = +

Case: (-7)×(-2)= xiv

Here two negative symbols are cancelled to each other.

Dominion 3: When a positive and negative integers are multiplied and so resultant number will be negative.

(-) x (+) = –

Example: (-vii) x 2 = -xiv

So nosotros need to consider these rules while performing the improver between fractions and negative numbers.

Steps to add fractions with negative numbers:

We accept a fraction a/b and a negative number -c. Now we add together them using the post-obit steps:

Step one: Catechumen their symbols according to the above rule. Here, a/b + (-c) = a/b – c

Stride 2: a/b – c can also written equally a/b -c/one

Pace 3: Now accept the LCM on b and ane

Step four: Now the last equation is (a – c)/b and solve this equation to become the final outcome.

Sample Questions

Question i: (1/2) + (-1) = ?

Solution:

Here nosotros have + performance before a negative number. Co-ordinate to dominion-3 when we multiply + with – we get negative symbol.

(1/two) + (-1) will exist converted to (i/ii) – 1

This (i/2) – one can be rewritten into (i/two) – (ane/1)

LCM of two denominators two,1 is 2.

(1/two) – (i/1) = (1 – 2)/2

= -i/2

= -0.5

Question two: -(1/2) + (-1) = ?

Solution:

Hither we have + performance before a negative number. According to rule-3 when we multiply + with – we get negative symbol.

-(1/two) + (-1) will be converted to -(1/2) – 1

This -(1/two) – one can exist rewritten into (-1/2) – (one/i)

LCM of 2 denominators 2,i is 2.

(-1/2) – (1/i) = (-1 – 2)/2

= -3/2

= -i.five

Question 3: -(i/iii) + (iii/6) = ?

Solution:

LCM of 2 denominators 3, 6 is 6.

(-1/iii) + (3/6) = (-2 + 3)/vi

= 1/6

Question iv: -(one/3) + (3/eight) = ?

Solution:

LCM of 2 denominators three,8 is 24.

(-ane/3) + (three/8) = ( (-1 x 8) + (3 x iii) )/24

=(-viii + 9) /24

= 1/24

Question 5: -(1/3) + (-2) = ?

Solution:

Here nosotros accept + functioning earlier a negative number. According to rule-3 when nosotros multiply + with – we get negative symbol.

(-1/3) + (-2) will exist converted to (-1/3)-(two)

This -(ane/3) – ii can be rewritten into (-1/3) – (two/1)

LCM of 2 denominators 3, 1 is 3.

(-i/3) – (two/i) = (-one – 2)/3

= -three/three

= -i