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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

  • Frequently Asked Questions on Addition and Subtraction of Rational Numbers
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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\frac{p}{q} + \frac{r}{q} = \frac{p + r}{q}

  • When denominators are different (q ≠ s):

pq+rs=ps+rqqs\frac{p}{q} + \frac{r}{s} = \frac{ps + rq}{qs}

​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\frac{p}{q} - \frac{r}{q} = \frac{p - r}{q}

  • When denominators are different (q ≠ s):

pq−rs=ps−rqqs\frac{p}{q} - \frac{r}{s} = \frac{ps - rq}{qs}

Know more about related topics:

Section A: Basic Addition of Rational Numbers

  1.  35+25\frac{3}{5} + \frac{2}{5} = ______

  2.  78+18\frac{7}{8} + \frac{1}{8} = ______

  3.  −49+29-\frac{4}{9} + \frac{2}{9} = ______

  4.  56+16\frac{5}{6} + \frac{1}{6} = ______

  5.  −37+−27-\frac{3}{7} + -\frac{2}{7} = ______


Section B: Basic Subtraction of Rational Numbers

  1.  910−310\frac{9}{10} − \frac{3}{10} = ______

  2.  56−16\frac{5}{6} − \frac{1}{6} = ______

  3.  −78−18-\frac{7}{8} − \frac{1}{8} = ______

  4.  1112−512\frac{11}{12} − \frac{5}{12} = ______

  5.  −45−(−25)-\frac{4}{5} − (-\frac{2}{5}) = ______

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

  1.  23+14\frac{2}{3} + \frac{1}{4} = ______

  2.  56−13\frac{5}{6} − \frac{1}{3} = ______

  3.  35+27\frac{3}{5} + \frac{2}{7} = ______

  4.  78−34\frac{7}{8} − \frac{3}{4} = ______

  5.  910+35\frac{9}{10} + \frac{3}{5} = ______

Section D: Addition and Subtraction of  Rational Numbers with Integers

  1.  3+253 + \frac{2}{5} = ______

  2.  −4−37−4 − \frac{3}{7} = ______

  3.  5−945 − \frac{9}{4} = ______

  4.  −2+73−2 + \frac{7}{3} = ______

  5.  112−3\frac{11}{2} − 3 = ______

Section E: Mixed Operations

  1.  34+12−18\frac{3}{4} + \frac{1}{2} − \frac{1}{8} = ______

  2.  2−35+1102 − \frac{3}{5} + \frac{1}{10} = ______

  3.  −56+23−16-\frac{5}{6} + \frac{2}{3} − \frac{1}{6} = ______

  4.  79−23+19\frac{7}{9} − \frac{2}{3} + \frac{1}{9} = ______

  5.  −3+54+34−3 + \frac{5}{4} + \frac{3}{4} = ______

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

  1. A student walked 34 \frac{3}{4} km in the morning and  12\frac{1}{2} km in the evening. What is the total distance travelled by the student?

  2. A tank had 78 \frac{7}{8} litre of water. 38 \frac{3}{8} litre of water was used. How much water is left?

  3. A rope is 56 \frac{5}{6} m long.  13 \frac{1}{3} m of rope is cut. What is the length of the remaining rope?

  4. A person spent  25 \frac{2}{5} of their salary on rent and  15\frac{1}{5} on food. What fraction of salary is spent in total?

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

  1.  35\frac{3}{5} + ___ = 1

  2. ___ −  27=57\frac{2}{7} = \frac{5}{7}

  3.  49\frac{4}{9} + ___ =  79\frac{7}{9}

  4. ___ − 14=34 \frac{1}{4} = \frac{3}{4}

  1.  512+718\frac{5}{12} + \frac{7}{18} = ______

  2.  1−58−141 − \frac{5}{8} − \frac{1}{4} = ______

  3.  116−73+52\frac{11}{6} − \frac{7}{3} + \frac{5}{2} = ______

 

Answer Key

Section A

  1. 1

  2. 1

  3. −29-\frac{2}{9}

  4. 1

  5. −57-\frac{5}{7}

Section B

  1. 35\frac{3}{5}

  2. 23\frac{2}{3}

  3. -1

  4. 12\frac{1}{2}

  5. −25-\frac{2}{5}

Section C

  1. 1112\frac{11}{12}

  2. 12\frac{1}{2}

  3. 3135\frac{31}{35}

  4. 18\frac{1}{8}

  5. 32\frac{3}{2}

Section D

  1. 175\frac{17}{5}

  2. −317-\frac{31}{7}

  3. 114\frac{11}{4}

  4. 13\frac{1}{3}

  5. 52\frac{5}{2}

Section E

  1. 98\frac{9}{8}

  2. 32\frac{3}{2}

  3. −13-\frac{1}{3}

  4. 29\frac{2}{9}

  5. -1

Section F

  1. 54\frac{5}{4}

  2. 12\frac{1}{2}

  3. 12\frac{1}{2}

  4. 35\frac{3}{5}

Section G

  1. 25\frac{2}{5}

  2. 1

  3. 13\frac{1}{3}

  4. 1

  1. 2936\frac{29}{36}

  2. 18\frac{1}{8}

  3. 2

Numbers make sense when they're taught right. To see how Orchids The International School turns Maths from intimidating to intuitive, reach out to our admissions team.

Frequently Asked Questions on Addition and Subtraction of Rational Numbers

1. How do I add rational numbers with the same denominator?

Let two rational numbers be p/q and r/s.When denominators are the same (q = s): pq+rq=p+rq \frac{p}{q} + \frac{r}{q} = \frac{p + r}{q}

2. How do I subtract rational numbers with the same denominator?

Let two rational numbers be p/q and r/s.When denominators are the same (q = s): pq−rq=p−rq \frac{p}{q} - \frac{r}{q} = \frac{p - r}{q}

3. How do I subtract rational numbers with the different denominator?

Let two rational numbers be p/q and r/s.When denominators are different (q ≠ s):  pq−rs=ps−rqqs\frac{p}{q} - \frac{r}{s} = \frac{ps - rq}{qs}

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