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CBSE Class 7 Rational Numbers Worksheet
The chapter on Rational Numbers in CBSE Class 7 teaches students about rational numbers, their properties, and operations like addition, subtraction, multiplication, and division. This chapter is essential as per the CBSE syllabus and the NCERT textbook and forms the foundation for many advanced math concepts.
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. Regular practice with a class 7 rational numbers worksheet ensures that students stay on track with the CBSE syllabus and are well-prepared for exams. These worksheets support the lessons in the NCERT textbook and offer extra practice to strengthen students’ understanding of rational numbers.
Overview of Rational Numbers Class 7 Maths
- A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not 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, difference, and product of two rational numbers is 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: For every rational number a, there exists an additive inverse -a and a multiplicative inverse 1/a, such that a + (-a) = 0 and a × (1/a) = 1.
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.
Rational Numbers Class 7 Worksheet with Answers
Here are the Rational Numbers exercise worksheet class 6 with answers:
Rational Numbers Class 7 Worksheet 1
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 2⁄3 and 4⁄5 is 6⁄8.
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 1⁄2 and 2⁄3?
- 1. 3⁄5
- 2. 7⁄6
- 3. 5⁄6
- 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?
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) False (The sum is 22⁄15)
c) True
d) True
Multiple Choice Questions (MCQs):
a) 3. 4⁄0
b) 2. 7⁄6
c) 1. 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
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 is in its 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. A cake recipe calls for 2/3 cup of sugar. If you want to make 1/2 of the recipe, how much sugar do you need?
2. Simplify the following expression: 3/4 + 1/6 – 1/3.
3. Find the value of 5/8 ÷ 2/3 × 4/5.
4. If 4/5 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 ÷ 4/5 = 20 × 5/4 = 25
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
Rational Numbers Class 7 Worksheet with Answers PDF
Here is the downloadable Rational Numbers class 6 worksheet pdf:
