CBSE Class 7 Rational Numbers Worksheet with Answers

The chapter on Rational Numbers in CBSE Class 7 teaches students about rational numbers, their properties, and operations like addition, subtraction, multiplication, and division. The chapter is critical according to the CBSE syllabus and NCERT textbook and the foundation of some other basic concepts of math. A rational numbers class 7 worksheet helps students practice these concepts. It includes various problems and exercises that match what is taught in the chapter. 

By solving these problems, students can better understand rational numbers and improve their math skills. The class 7 rational numbers worksheet provides examples and challenges to apply the knowledge in different ways. 

Having a rational numbers class 7 worksheet with answers is very useful. It allows students to check their work and learn from their mistakes, helping them understand the topic more deeply. A rational numbers class 7 worksheet with answers pdf is also available, making it easy for students to download and practice anytime. 

These worksheets are helpful for both students and teachers. They allow students to practice at their own pace and help teachers monitor progress and provide extra support.

Consistent practice on a class 7 rational numbers worksheet will keep students on schedule with the CBSE syllabus and ready to take exams. These work sheets complement the lessons taught in the NCERT textbook and provide additional practice to reinforce the knowledge on rational numbers among students.

Overview of Rational Numbers Class 7 Maths

• A rational number is any number which can be represented as the ratio of two integers and where the denominator is not equal to zero.
• Rational numbers include all whole numbers, fractions, and integers.
• Rational numbers can be positive, negative, or zero.
• Examples of rational numbers: 3/4, -2/5, 0, 7, 1/2.

Properties of Rational Numbers

• Closure Property: The sum, the difference and the product of two rational numbers are also a rational number.
• Commutative Property: a + b = b + a and a × b = b × a, where a and b are rational numbers.
• Associative Property: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c), where a, b, and c are rational numbers.
• Distributive Property: a × (b + c) = (a × b) + (a × c), where a, b, and c are rational numbers.
• Identity Property: a + 0 = a and a × 1 = a, where a is a rational number.
• Inverse Property: Given any rational number a, there is an additive inverse -a, and a multiplicative inverse 1/a, where a + (-a) = 0 and a × (1/a) = 1.

Also Check: CBSE Class 7 Maths MCQs | NCERT Solutions for Class 7 Maths

Representation of Rational Numbers on the Number Line

• Rational numbers can be represented on the number line by identifying the point corresponding to the ratio p/q, where p and q are integers and q ≠ 0.
• There are infinitely many rational numbers between any two given rational numbers.

Operations with Rational Numbers

• Addition and Subtraction: To add or subtract rational numbers with different denominators, we need to find the least common denominator (LCD) and then perform the operation.
• Multiplication: To multiply two rational numbers, we multiply the numerators and then multiply the denominators.
• Division: To divide one rational number by another, we multiply the first rational number by the reciprocal of the second rational number.

By understanding the properties and operations of rational numbers, students can effectively work with them in various mathematical contexts.

Also Check: Class 7 Maths Sample Papers | Class 7 Maths Important Questions

Rational Numbers Class 7 Worksheet with Answers Downlaod PDF

Download the Rational numbers Worksheet Class 7 PDF from the given Link and start solving the questions right away to build strong foundations. Mark the questions that confuse you, revise those concepts, and re-attempt similar problems until you feel confident. Aim for regular short practice sessions (20–30 minutes daily) and check your answers carefully to spot patterns in mistakes. Doing this will improve your speed, accuracy, and conceptual understanding.

Rational Numbers Class 7 Worksheet with Answers

Here are the Rational Numbers exercise worksheet class 6 with answers:

Rational Numbers Class 7 Worksheet Questions

Fill in the Blanks:

a) A rational number is a number that can be expressed as a fraction p⁄q where p and q are __________ and q ≠ 0.

b) The additive inverse of 5⁄7 is __________.

c) The rational number -8⁄10 in simplest form is __________.

d) The product of two rational numbers is always a __________ number.

True or False:

a) 3⁄4 and 6⁄8 are equivalent rational numbers.

b) The sum of 6⁄3 and 2⁄5 is 12/5.

c) 7⁄-9 is the same as -7⁄9.

d) The rational number 0⁄1 is zero.

Multiple Choice Questions (MCQs):

a) Which of the following is not a rational number?

1. 5⁄2
2. -3⁄7
3. 4⁄0
4. 0⁄5

b) What is the sum of 3/2 and 2⁄3?

1. 3⁄5
2. 7⁄6
3. 13/6
4. 4⁄6

c) What is the reciprocal of 3⁄4?

1. 4⁄3
2. 3⁄4
3. -3⁄4
4. -4⁄3

Simplify:

a) 2⁄5 + 3⁄10

b) 7⁄8 - 1⁄4

c) 3⁄7 × 4⁄9

d) 5⁄6 ÷ 2⁄3

Word Problems:

a) A rope is 7⁄4 meters long. If it is cut into pieces of 1⁄2 meter each, how many pieces are there?

b) A tank is 5⁄6 full. If 10 liters of water are added to it, it becomes full. What is the capacity of the tank?

Rational Numbers Class 7 Worksheet Answers

Fill in the Blanks:

a) A rational number is a number that can be expressed as a fraction p⁄q where p and q are integers and q ≠ 0.

b) The additive inverse of 5⁄7 is -5⁄7.

c) The rational number -8⁄10 in simplest form is -4⁄5.

d) The product of two rational numbers is always a rational number.

True or False:

a) True

b) True

c) True

d) True

Multiple Choice Questions (MCQs):

a) -3/7

b) 13/6

c) 4⁄3

Simplify:

a) 2⁄5 + 3⁄10 = 4⁄10 + 3⁄10 = 7⁄10

b) 7⁄8 - 1⁄4 = 7⁄8 - 2⁄8 = 5⁄8

c) 3⁄7 × 4⁄9 = 12⁄63 = 4⁄21

d) 5⁄6 ÷ 2⁄3 = 5⁄6 × 3⁄2 = 15⁄12 = 5⁄4

Word Problems:

a) Number of pieces = 7⁄4 / 1⁄2 = 7⁄4 × 2⁄1 = 14⁄4 = 3.5. Therefore, there are 3 full pieces and one half-piece.

b) Let the capacity of the tank be x. Then 5⁄6x + 10 = x → x - 5⁄6x = 10 → 1⁄6x = 10 → x = 60. The capacity of the tank is 60 liters.

Rational Numbers Class 7 Worksheet 2

Questions

Section A: Multiple Choice Questions

1. Which of the following is a rational number?

a) √2
b) π
c) 3/4
d) e

2. What is the decimal representation of 7/8?

a) 0.875
b) 0.78
c) 0.87
d) 0.88

3. Which of the following fractions are in their simplest form?

a) 4/8
b) 9/12
c) 15/20
d) 7/11

4. Which of the following is the reciprocal of 5/6?

a) 6/5
b) 5/6
c) 1/6
d) 1/5

5. What is the result of 2/3 + 4/5?

a) 6/8
b) 22/15
c) 8/5
d) 2/15

Section B: Short Answer Questions

1. Express 24/36 in simplest form.
2. Convert 0.75 to a fraction and simplify.
3. Subtract 3/4 from 5/6.
4. Multiply 7/9 by 3/4.
5. Divide 8/15 by 2/5.

Section C: Long Answer Questions

1. In one cake recipe, one needs 2/3 cup of sugar. How much sugar would you put in the recipe half?
2. Simplify the following expression: 3/4 + 1/6 - 1/3.
3. Find the value of 5/8 ÷ 2/3 × 4/5.
4. If 4/8 of a number is 20, what is the number?
5. Ravi has 7/12 of a liter of paint. He uses 1/3 of it to paint a wall. How much paint is left?

Answer Key

Section A: Multiple Choice Questions

1. c) 3/4
2. a) 0.875
3. d) 7/11
4. a) 6/5
5. b) 22/15

Section B: Short Answer Questions

1. 24/36 = 2/3 (by dividing both numerator and denominator by 12)
2. 0.75 = 3/4 (since 0.75 = 75/100 and simplified by dividing both by 25)
3. 5/6 - 3/4 = 10/12 - 9/12 = 1/12
4. 7/9 × 3/4 = 21/36 = 7/12 (by simplifying 21/36)
5. 8/15 ÷ 2/5 = 8/15 × 5/2 = 40/30 = 4/3 (by simplifying 40/30)

Section C: Long Answer Questions

1. 2/3 × 1/2 = 2/6 = 1/3 cup of sugar
2. 3/4 + 1/6 - 1/3 = 3/4 + 1/6 - 2/6 = 3/4 - 1/6 = 9/12 - 2/12 = 7/12 (by finding a common denominator and simplifying)
3. 5/8 ÷ 2/3 × 4/5 = 5/8 × 3/2 × 4/5 = 5 × 3 × 4 / 8 × 2 × 5 = 60/80 = 3/4 (by simplifying 60/80)
4. If 4/5 of a number is 20, the number is 20 ÷ 4/8 = 20 × 8/4 = 40
5. Ravi has 7/12 liters of paint. He uses 1/3 of it, which is 7/12 × 1/3 = 7/36. The paint left is 7/12 - 7/36 = 21/36 - 7/36 = 14/36 = 7/18