Class 7 - Addition and Subtraction of Rational numbers: Worksheet

Addition and subtraction of rational numbers are fundamental arithmetic operations. A rational number is any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. These operations are fundamental for solving problems in algebra, number systems, data analysis, etc. 

Table of Contents

• What are Addition and Subtraction of Rational Numbers?

• Section A: Basic Addition of Rational Numbers

• Section B: Basic Subtraction of Rational Numbers

• Section C: Addition and Subtraction of Rational Numbers with Unlike Denominators

• Section D: Addition and Subtraction of Rational Numbers and Integers

• Section E: Mixed Operations

• Section F: Word Problems on Addition and Subtraction of Rational Numbers

• Section G: Fill in the Blanks Addition and Subtraction of Rational Numbers

• Answer Key

What are Addition and Subtraction of Rational Numbers?

The addition and subtraction of rational numbers involve combining or finding the difference between the rational numbers.

Addition of Rational Numbers

Let two rational numbers be p/q and r/s.

• When denominators are the same (q = s):

pq+rq=p+rq

• When denominators are different (q ≠ s):

pq+rs=ps+rqqs

​Subtraction of Rational Numbers

Let two rational numbers be p/q and r/s.

• When denominators are the same (q = s):

pq−rq=p−rq

• When denominators are different (q ≠ s):

pq−rs=ps−rqqs

Section A: Basic Addition of Rational Numbers

1.  35+25 = ______

2.  78+18 = ______

3.  −49+29 = ______

4.  56+16 = ______

5.  −37+−27 = ______

Section B: Basic Subtraction of Rational Numbers

6.  910−310 = ______

7.  56−16 = ______

8.  −78−18 = ______

9.  1112−512 = ______

10.  −45−(−25)= ______
    
    

Section C: Addition and Subtraction of Rational Numbers with Unlike Denominators

11.  23+14= ______

12.  56−13 = ______

13.  35+27 = ______

14.  78−34 = ______

15.  910+35= ______
    
    

Section D: Addition and Subtraction of  Rational Numbers with Integers

16.  3+25 = ______

17.  −4−37 = ______

18.  5−94 = ______

19.  −2+73 = ______

20.  112−3= ______
    
    

Section E: Mixed Operations

21.  34+12−18 = ______

22.  2−35+110 = ______

23.  −56+23−16 = ______

24.  79−23+19 = ______

25.  −3+54+34= ______
    
    

Section F: Word Problems on Addition and Subtraction of Rational Numbers

26. A student walked 34km in the morning and  12 km in the evening. What is the total distance travelled by the student?

27. A tank had 78 litre of water. 38 litre of water was used. How much water is left?

28. A rope is 56 m long.  13m of rope is cut. What is the length of the remaining rope?

29. A person spent  25of their salary on rent and  15 on food. What fraction of salary is spent in total?
    
    

Section G: Fill in the Blanks on Addition and Subtraction of Rational Numbers

30.  35 + ___ = 1

31. ___ −  27=57

32.  49 + ___ =  79

33. ___ − 14=34

34.  512+718 = ______

35.  1−58−14= ______

36.  116−73+52= ______

 

Answer Key

Section A

1. 1

2. 1

3. −29

4. 1

5. −57

Section B

6. 35

7. 23

8. -1

9. 12

10. −25

Section C

11. 1112

12. 12

13. 3135

14. 18

15. 32

Section D

16. 175

17. −317

18. 114

19. 13

20. 52

Section E

21. 98

22. 32

23. −13

24. 29

25. -1

Section F

26. 54

27. 12

28. 12

29. 35

Section G

30. 25

31. 1

32. 13

33. 1

34. 2936

35. 18

36. 2