In the class 7 Maths Chapter 1 Integers, various properties and operations carried out on integers are discussed. Before we delve deeper into the chapter let us look at a few points studied about integers in our previous classes.
What are Integers?
Integers are a collection of numbers formed by whole numbers and their negatives. Integers can be represented on a number line as follows:
In the given number line, the ascending order of the listed numbers is -16, -9, -4, 0, 3, 8, 14.
The descending order is 14, 8, 3, 0, -4, -9, -16.
Properties of Integers Under Addition And Subtraction
- The addition and subtraction of two integers give an integer. In other words, a+band a-b are again integers, where a and b are integers
- For all integers, Addition is commutative which means that a+b=b+a
- For all integers, addition is associative, i.e., (a+b)+c=a+(b+c)
- The additive identity in integers is 0, for every integer a,a+0=0+a=a.
Properties of Integers Under Multiplication
- The product of two integers is always an integer.
- Multiplication is commutative for integers, i.e.,ab=ba, where a and b are integers.
- The multiplicative identity for integers is 1, For any integer a, 1 x a = a x 1.
- For integers, multiplication is associative, i.e., (ab)c=a(bc), where a and b are integers.
The distributive property is exhibited under addition and multiplication of integers, i.e.,a(b+c) = ab+ ac, for any three integers a, b and c.
Integers manifest the following properties under division:
- The quotient obtained when a positive integer divided by a negative integer is negative.
- When a negative integer is divided by another negative integer, the obtained quotient is positive.
- For any integer a,
- a ÷ 1 = a
- a ÷ 0 is not defined
Problems on Integers for Class 7
- Evaluate the following
- 13 ÷ [(–2) + 1]
- [(– 6) + 5)] ÷ [(–2) + 1]
- 13 ÷ [(–2) + 1]
- The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C
per hour until midnight, at what time would the temperature be 8°C below zero?
What would be the temperature at midnight?
- An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts
from 10 m above the ground level, how long will it take to reach – 350 m.
- Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2)
because 6 ÷ (–2) = (–3).
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