Rational Numbers Class 7 Worksheet — Free PDF Download with Answers

There is a scene that plays out in most Class 7 homes. A student finishes their digital homework in 15 minutes, shows the green tick screen to their parent, and feels they have mastered rational numbers. Then the monthly test comes along and the marks tell a different story. The issue is not effort. It is that learning maths on screens is too smooth. The friction that forces real understanding — pencil slipping on paper, scribbles in the margin, crossed out working — is gone.

Rational numbers introduce negatives into fractions for the first time. A student suddenly has to think about the sign and the fraction at the same time. That dual thinking is exactly what worksheets train. You write the question. You work through it step by step. You look at what you wrote and spot your own error.

Writing by hand also helps students remember steps. A study from the University of Indiana found that children who wrote out maths problems remembered the method far better than those who typed or clicked. The slow movement of pen on paper creates stronger mental traces.

Worksheets also give parents an easy way to help. A printed sheet with an answer key is something any parent can use, even if they have not thought about rational numbers since their own school days. Ten minutes of Mum or Dad sitting with a child and working through a problem is worth an hour of app based practice.

And there is the screen time point. Class 7 students already use devices for online classes, homework submissions and entertainment. A printable worksheet gives the eyes a break.

The worksheet covers every sub topic in the Class 7 rational numbers chapter.

Topics included:

* What is a rational number
* Positive and negative rational numbers
* Equivalent rational numbers
* Representation on a number line
* Comparison of rational numbers
* Addition, subtraction, multiplication and division
* Properties of rational numbers
* Word problems

Level breakdown:

60 questions in total. Question types include MCQ, fill in the blanks, true or false, numerical and word problems. A full answer key is included.

Revise these briefly before picking up the worksheet.

* Rational number — A number of the form $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Examples: $\dfrac{3}{4}$, $-\dfrac{5}{7}$, $0$, $2$.
* Standard form — A rational number is in standard form if the denominator is positive and the HCF of numerator and denominator is $1$.
* Equivalent rational numbers — Multiplying or dividing numerator and denominator by the same non zero integer gives an equivalent rational number.
* Comparison — To compare two rational numbers, write them with a common positive denominator and compare numerators.
* Addition and subtraction — Take LCM of denominators, rewrite fractions, add or subtract numerators.
* Multiplication — Multiply numerators and denominators separately. Apply sign rules.
* Division — Multiply by the reciprocal of the divisor.
* Reciprocal — The reciprocal of $\dfrac{p}{q}$ is $\dfrac{q}{p}$, provided $p \neq 0$. Zero has no reciprocal.

Quick tip: always rewrite rational numbers in standard form before operating on them. It removes many sign errors.

Level 1 — Easy

1. Is $\dfrac{-4}{-6}$ a positive or negative rational number?
Solution: Negative divided by negative is positive. It is positive.

2. Find two rational numbers equivalent to $\dfrac{2}{5}$.
Solution: $\dfrac{4}{10}$ and $\dfrac{6}{15}$.

3. Write $\dfrac{-15}{25}$ in standard form.
Solution: Divide by HCF $5$: $\dfrac{-3}{5}$.

Level 2 — Medium

1. Add: $\dfrac{-3}{4} + \dfrac{5}{6}$.
Solution: LCM is $12$. $\dfrac{-9}{12} + \dfrac{10}{12} = \dfrac{1}{12}$.

2. Multiply: $\dfrac{-2}{7} \times \dfrac{14}{15}$.
Solution: $\dfrac{-28}{105} = \dfrac{-4}{15}$.

3. Divide: $\dfrac{5}{8} \div \dfrac{-25}{16}$.
Solution: $\dfrac{5}{8} \times \dfrac{-16}{25} = \dfrac{-80}{200} = \dfrac{-2}{5}$.

Level 3 — Hard

1. Simplify: $\dfrac{-3}{5} + \dfrac{2}{3} - \dfrac{1}{15}$.
Solution: LCM is $15$. $\dfrac{-9}{15} + \dfrac{10}{15} - \dfrac{1}{15} = \dfrac{0}{15} = 0$.

2. Verify: $\dfrac{2}{3} \times \left(\dfrac{-4}{5} + \dfrac{1}{2}\right) = \dfrac{2}{3} \times \dfrac{-4}{5} + \dfrac{2}{3} \times \dfrac{1}{2}$.
Solution: LHS: $\dfrac{-4}{5} + \dfrac{1}{2} = \dfrac{-8}{10} + \dfrac{5}{10} = \dfrac{-3}{10}$. Then $\dfrac{2}{3} \times \dfrac{-3}{10} = \dfrac{-6}{30} = \dfrac{-1}{5}$. RHS: $\dfrac{-8}{15} + \dfrac{2}{6} = \dfrac{-16}{30} + \dfrac{10}{30} = \dfrac{-6}{30} = \dfrac{-1}{5}$. Verified.

3. The product of two rational numbers is $\dfrac{-15}{28}$. If one of them is $\dfrac{5}{7}$, find the other.
Solution: Other number $= \dfrac{-15}{28} \div \dfrac{5}{7} = \dfrac{-15}{28} \times \dfrac{7}{5} = \dfrac{-105}{140} = \dfrac{-3}{4}$.

1. Print — Sit at a clean desk, not on the sofa.
2. Warm up — Do five quick mental questions on signs and fractions.
3. Time yourself — 15 minutes for Level 1, 25 for Level 2, 30 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redo every wrong answer with full workings.
6. Try again — Redo all wrong questions the next day.

Daily plan: 20 to 25 minutes a day for two weeks finishes the full worksheet with room for revision.

Weekly revision: Every Saturday, pick 10 random questions from the sheet and solve them without peeking at old work. This builds exam ready recall.

1. Sign errors when subtracting — $\dfrac{2}{3} - \dfrac{-1}{4}$ becomes $\dfrac{2}{3} + \dfrac{1}{4}$, not $\dfrac{2}{3} - \dfrac{1}{4}$. Two negatives make a positive.

2. Not using standard form — Operating on rational numbers with negative denominators leads to confusion. Always convert to positive denominator first.

3. Forgetting LCM for addition — Just like regular fractions, rational numbers need a common denominator before adding or subtracting.

4. Reciprocal of zero — Students sometimes write the reciprocal of $0$ as $\dfrac{1}{0}$. Zero has no reciprocal.

5. Comparison errors — Comparing $\dfrac{-3}{5}$ and $\dfrac{-2}{5}$, some students say the first is bigger because $3 > 2$. The opposite is true: $\dfrac{-3}{5} < \dfrac{-2}{5}$.

6. Skipping final simplification — Leaving answers like $\dfrac{10}{20}$ instead of $\dfrac{1}{2}$ loses marks.

CBSE (NCERT)
Rational Numbers is Chapter 9 of Class 7 NCERT maths. Weightage is around 10 marks in the annual exam. Questions focus on operations and simple applications.

ICSE (Selina / ML Aggarwal)
ICSE includes rational numbers early in the syllabus and expects students to verify properties such as closure, commutativity and associativity in detail. Weightage is around 12 marks.

IB MYP
IB MYP introduces rational numbers as a natural extension of fractions and decimals. The emphasis is on real world interpretation, such as temperature change, debt and profit or loss.

Get your free Class 7 Rational Numbers worksheet:

* Rational Numbers CBSE Worksheet
* Rational Numbers ICSE Worksheet
* Rational Numbers IB Worksheet

Practise online:

* Rational Numbers Online — CBSE
* Rational Numbers Online — ICSE

* AI Maths Solver — Upload any problem and get a step by step answer.
* Spark Coach — An AI tutor that gives hints, not full solutions.
* Class 7 Maths Complete Guide — All chapters in one place.
* All Worksheets Hub
* Class 7 Formulas

Week 1: Build the basics

* Day 1: Read the chapter. Note down the standard form rule.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 questions 1 to 10 (addition and subtraction).
* Day 5: Level 2 questions 11 to 20 (multiplication and division).
* Day 6: Redo all wrong answers.
* Day 7: Rest.

Week 2: Application and mastery

* Day 8: Level 3 questions 1 to 10.
* Day 9: Level 3 questions 11 to 20.
* Day 10: Redo wrong Level 3 answers with full steps.
* Day 11: Property verification drill — five questions from the textbook.
* Day 12: Mixed quiz.
* Day 13: Mock test (45 minutes, 30 questions).
* Day 14: Final review.

* Class 7 Integers Worksheet
* Class 7 Fractions and Decimals Worksheet
* Class 7 Algebraic Expressions Worksheet
* Class 7 Simple Equations Worksheet
* Class 7 Maths Complete Guide