What's the difference between adding two rational number and get a negative number

Comparing two rational numbers

Make the denominators the same and compare the numerators. The number with the smaller numerator is smaller. For example, to compare a/b and c/d, we rewrite

a/b=a*d/b*d

  = ad/bd and c/d = c*b/d*b=bc/bd

Now just compare the numerators : "ad" and "bc"

Multiplying and Dividing Rational Numbers 

Multiplying and dividing rational numbers in decimal form is the same as multiplying and dividing integers. The decimal place of the product is the same of all decimals of all multiplied numbers. For example, 3.12*2.4.

Solution => 3.12*2.4=7.488

When multiplying or dividing rational numbers in fractional form, you multiply the numerators (N*N) and then multiply the denominators (D*D).

When dividing rational numbers in fractional form, first take the reciprocal of the divisor, and then multiply the numerators and the denominators.

Example => 5/9 divided by 2/7 .

Solution => 5/9 * 7/2 =  35/18

Adding Rational numbers

Adding and Subtracting rational numbers in decimal form is the same as adding and subtracting integers.

Example => -3.54+2.79=-0.75

When adding or subtracting rational numbers in fractional form, first make the denominator equal, and then add or subtract the numerators. 

Step-by-step explanation:

Given system of equations,

12x + 15y= 34  ------(1)

-6x + 5y = 3 ------(2),

Equiation (1) + 2 × equation (2),

We get,

15y + 10y = 34 + 6

25y = 40

⇒

From equation (2),

⇒