**Add and subtract rational numbers word problems :**

Here we are going to see, how to solve word problems on fractions through some examples.

**Example 1 :**

The sum of two rational numbers is 17/4 . If one of the numbers is 5/2 , find the other number.

**Solution :**

The sum of two rational numbers = 17/4

One of the numbers = 5/2

Let "x" be the other rational number

x + (5/2) = 17/4

In order to solve for "x", we have to subtract 5/2 on both sides

x + (5/2) - (5/2) = (17/4) - (5/2)

x = (17/4) - (5/2)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (4, 2) = 4

= (17/4) - (5/2) x (2/2)

= (17/4) - (10/4)

= (17 - 10)/4

= 7/4

Hence the required other number is 7/4.

**Example 2 :**

What number should be added to 5/6 so as to get 49/30

**Solution :**

Let "x" be the required number

x + (5/6) = 49/30

In order to solve for "x", we have to subtract 5/6 on both sides

x + (5/6) - (5/6) = (49/30) - (5/6)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (30, 6) = 30

x = (49/30) - (5/6) x (5/5)

x = (49/30) - (25/30)

= (49 - 25)/30

= 24/30

Dividing both numerator and denominator by 6

= 4/5

Hence the required fraction is 4/5.

**Example 3 :**

A shop keeper sold 7 3/4 kg, 2 1/2 kg and 3 3/5 kg of sugar to three customers in a day.Find the total weight of sugar on that day?

**Solution :**

To find the total weight of sugar on that day, we have to add the above quantities.

Total weight of sugar = 7 3/4 + 2 1/2 + 3 3/5

Converting the above mixed fractions as improper fractions, we get

= (31/4) + (5/2) + (18/5)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (4, 2, 5) = 20

= (31/4) x (5/5) + (5/2) x (10/10) + (18/5) x (4/4)

= (155/20) + (50/20) + (72/20)

= (155 + 50 + 72)/20

= 277/20

= 13 17/20

Hence the total weight of sugar sold = 13 17/20 kg.

**Example 4 :**

John bought 25 kg of Rice and he used 1 3/4 kg on the first day, 4 1/2 kg on the second day. Find the remaining quantity of rice left.

**Solution :**

Rice used on first day = 1 3/4 kg

Rice used on second day = 4 1/2 kg

Quantity of rice used on first and second day

= (1 3/4) + (4 1/2)

Converting the above mixed fraction in to improper fraction, we get

= 7/4 + 9/2

= 7/4 + (9/2) x (2/2)

= 7/4 + 18/4

= (7 + 18)/4

= 25/4

Remaining quantity of rice left = 25 - (25/4)

= (100 - 25)/4

= 75/4

= 18 3/4 kg

Remaining quantity of rice = 18 3/4 kg.

After having gone through the examples explained above, we hope that students would have understood "Add and subtract rational numbers word problems".

Apart from the examples, if you want to know more about "Add and subtract rational numbers word problems", please click here.

**Please click the below links to know "How to solve word problems in each of the given topics"**

**1. Solving Word Problems on Simple Equations**

**2. Solving Word Problems on Simultaneous Equations**

**3. Solving Word Problems on Quadratic Equations**

**4. Solving Word Problems on Permutations and Combinations**

**5. Solving Word Problems on HCF and LCM**

**6. Solving Word Problems on Numbers**

**7. Solving Word Problems on Time and Work**

**8. Solving Word Problems on Trains**

**9. Solving Word Problems on Time and Work.**

**10. Solving Word Problems on Ages.**

**11.Solving Word Problems on Ratio and Proportion**

**12.Solving Word Problems on Allegation and Mixtures.**

**13. Solving Word Problems on Percentage**

**14. Solving Word Problems on Profit and Loss**

**15. Solving Word Problems Partnership**

**16. Solving Word Problems on Simple Interest**

**17. Solving Word Problems on Compound Interest**

**18. Solving Word Problems on Calendar**

**19. Solving Word Problems on Clock**

**20. Solving Word Problems on Pipes and Cisterns**

**21. Solving Word Problems on Modular Arithmetic**

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