NCERT Exemplar Class 7 Maths Chapter 1: Integers. NCERT Exemplar Solutions for Class 7 Maths Chapter 1 Integers prepare students for their Class 7 exams thoroughly.
Maths problems and solutions for the Class 7 pdf are provided here which are similar to the questions being asked in the previous year's board.
NCERT Exemplar Class 7 Maths Chapter 1: Integers
Class 7: Maths Chapter 1 solutions. Complete Class 7 Maths Chapter 1 Notes.
Main Concepts and Results
Representation of integers on the number line and their addition and subtraction.
Properties of integers:
- Integers are closed under addition, subtraction and multiplication.
- Addition and multiplication are commutative for integers, i.e., a + b = b + a and a × b = b × a for any two integers a and b.
- Addition and multiplication are associative for integers, i.e., (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) for any three integers a, b and c.
- Zero (0) is an additive identity for integers, i.e., a + 0 = 0 + a = a for any integer a.
- 1 is multiplicative identity for integers, i.e., a × 1 = 1 × a = a for any integer a.
- Integers show distributive property of multiplication over addition, i.e., a × (b + c) = a × b + a × c for any three integers a, b and c.
Product of a positive integer and a negative integer is a negative integer, i.e, a × (–b) = – ab, where a and b are positive integers.
Product of two negative integers is a positive integer, i.e., (–a) × (–b) = ab, where a and b are positive integers.
Product of even number of negative integers is positive, where as the product of odd number of negative integers is negative, i.e.,
Solved Examples
Adding Integers
| If the signs are the same | If the signs are different |
| Find the sum of the values of integers without sign, and then use the same sign as the integers have. | Find the difference of the values of integers without sign (subtract lower value integer from greater value integer) and then use the sign of the integer with the greater value. |
Subtracting Integers:
| Words | Numbers | Formula |
| To subtract an integer, add its inverse | 3 – 7 = 3 + (–7) 5 – (–8) = 5 + 8 | a – b = a + (–b) a – (– b) = a + b |
Multiplying and Dividing Two Integers:
- If the signs are the same, the sign of the answer is positive.
- If the signs are different, the sign of the answer is negative.
Multiple Choice Questions
Fill in the Blanks Type Questions
True False Type Questions
Other Important Type Questions
Application
Answers
