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Addition of Rational Number

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Addition of Rational Number:

i) Adding Rational number when the denominator is the same:

While adding rational numbers with the same denominators, we add the numerators keeping the denominators the same.

Add `-7/8 + (5/8)`

On the number line, we have:

The distance between two consecutive points is `1/8`.
So adding `-7/8 "to" 5/8` will mean, moving to the left of `-7/8`, making 5 jumps. We reach at `-2/8`.

ii) Adding Rational number when the denominator is different:

Two rational numbers with different denominators are added by first taking the LCM of the two denominators and then converting both the rational numbers to their equivalent forms having the LCM as the denominator.

For example, let us add `(-7)/5 and (-2)/3`

LCM of 5 and 3 is 15

So, `(-7)/5 = (-21)/15 and (-2)/3 = (-10)/15`.

Thus, `(-7)/5 + (-2)/3 = (-21)/15 + (-10)/15 = (-31)/15`

Here, LCM of 3 and 8 is 24.

Example

Add: `-2/3 + 3/8`

`-2/3 + 3/8 = (-16)/24 + 9/24 = (-16 + 9)/24 = -7/24`.

Example

Add: `5/7 + 9/11`.

`5/7 + 9/11`

`= (55 + 63)/77`

`= 118/77`

Example

Add: `2 1/7 + 3 8/14`.

`2 1/7 + 3 8/14`

`= 15/7 + 50/14`

`= 30/14 + 50/14`

`= 80/14`

`= 40/7`

Example

Satpal walks `2/3 "km from a place P, towards the east and then from there"  1 5/7` km towards west. Where will he be now from P?

Let us denote the distance travelled towards the east by positive sign. So, the distances towards the west would be denoted by a negative sign.

Thus, distance of Satpal from the point P would be

`2/3 + (- 1 5/7)`

`=  2/3 + (-12)/7`

`= (2 xx 7)/(3 xx 7) + ((- 12) xx 3)/(7 xx 3)`

`= (14 - 36)/21`

`= (-22)/21`

`= - 1 1/21`

Since it is negative Satpal is at a distance `1 1/21` km towards west of P.

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