**Add and subtract rational numbers :**

The number which is in the form of "p/q" is known as rational number. In which q is not equal to zero.

Whenever we want add or subtract any two or three rational numbers, first we have to consider the denominator.

- If the denominator are same, we can easily combine the numerators by writing one common denominator.
- If the denominators are not same, we have to convert the denominators same, by taking L.C.M.
- Once we change the fractions with the common denominator, we can combine them.

**Example 1 :**

Add : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Since the denominators are same, we can put only one common denominator and combine the numerators.

= (3 + 4)/7

= 7/7

= 1

Hence the answer is 1.

**Example 2 :**

Subtract : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Since the denominators are same, we can put only one common denominator and combine the numerators.

= (12 - 4)/13

= 8/13

Hence the answer is 8/13.

**Example 3 :**

Add : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Since the denominators are not same, we need to take L.C.M in order to convert the denominators same.

L.C.M (4, 3) = 12

= (3/4) x (3/3) + (2/3) x (4/4)

= (9/12) + (8/12)

= (9 + 8)/12

= 17/12

The numerator is grater than the denominator, we have to convert it into mixed fraction.

(12 + 5)/12 = 1 5/12

Hence the answer is 1 5/12.

**Example 4:**

Subtract : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Since the denominators are not same, we need to take L.C.M in order to convert the denominators same.

L.C.M (3, 4) = 12

= (2/3) x (4/4) - (1/4) x (3/3)

= (8/12) - (3/12)

= (8 - 3)/12

= 5/12

Hence the answer is 5/12.

**Example 5 :**

Subtract : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Now we need to consider the given question as two parts.

First we have to simplify the fractions inside the parenthesis.

Subtract 2/9 from the simplified answer.

= {(8/9) - (1/9)} - (2/9)

= (8- 1)/9 - (2/9)

= (7/9) - (2/9)

= (7 - 2)/9

= 5/9

Hence the answer is 5/9.

**Example 6 :**

Add : Simplify your answer and write it as a proper fraction or as a whole or mixed number.

**Solution :**

Since the denominators are not same, we have to L.C.M in order to convert the denominators same.

L.C.M (4, 5, 8) = 40

= (3/4) x (10/10) + (2/5) x (8/8) + (4/8) x (5/5)

= (30 + 16 + 20)/40

= 66/20

= 33/10

Since the numerator is greater than the denominator, we have to convert into mixed fraction.

Hence the answer is 3 3/10.

After having gone through the stuff given above, we hope that the students would have understood "Add and subtract rational numbers".

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