Question: 3 Marks: 1 Que3 for any two positive integers a ,b then choose correct formula
Answers
Step-by-step explanation:
In the beginning, a quick recap of the integers and their representation on the number line, operations like addition, subtraction etc that can be performed on them, additive inverse, negative integers are some of the topics given.
This is followed by a detailed description of the topic Properties of Addition and Subtraction of Integers is given.
Properties listed in this section are:
1. Closure under addition
2. Closure under subtraction
3. Commutative property
4. Associative property
5. Additive identity
All of these mentioned above are explained with the help of examples. The concept of Multiplication of Integers is covered in detail and contains various subsection which focuses more deeply on the operation of multiplication of integers:
Multiplication of a positive and a negative integer
Multiplication of two negative integers
Product of three or more negative integers
There are various properties associated with the multiplication of integers:
Closure under multiplication
Commutativity of multiplication
Multiplication by zero
Multiplicative identity
Associativity for multiplication
Distributive property
Making multiplication easier
Division of the Integers is the last topic of the chapter - Integers. Properties of the division of integers are discussed in this section.
Students will learn these two points:
1. When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice- versa.
2. Division of a negative integer by another negative integer gives a positive integer as quotient.
Also, we observer that
a divided by zero is undefined
a divided by 1 is a
A total of 4 unsolved exercises are given in this chapter to make the concept more clear.
Summarization of all the important points of the chapter at the end.
Page No 4:
Question 1:
Following number line shows the temperature in degree celsius (°C) at different places on a particular day.
(a) Observe this number line and write the temperature of the places marked on it.
(b) What is the temperature difference between the hottest and the coldest places among the above?
(c) What is the temperature difference between Lahulspiti and Srinagar?
(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?
ANSWER:
(a) By observing the given data, the temperatures of these cities are as follows.
Lahulspiti
:
−8°C
Srinagar
:
−2°C
Shimla
:
5°C
Ooty
:
14°C
Bangalore
:
22°C
(b) Temperature at the hottest place, i.e., Bangalore = 22°C
Temperature at the coldest place, i.e., Lahulspiti = −8°C
Temperature difference = 22°C − (−8°C)
= 30°C
Therefore, the temperature difference between the hottest and the coldest places is 30ºC.
(c) Temperature at Lahulspiti = −8°C
Temperature at Srinagar = −2°C
Temperature difference = −2°C − (−8°C)
= 6°C
Therefore, the temperature difference between Lahulspiti and Srinagar is 6ºC.
(d) Temperature at Srinagar = −2°C
Temperature at Shimla = 5°C
Temperature of Srinagar and Shimla taken together = −2°C + 5°C
= 3°C
3°C < 5°C
3°C < Temperature of Shimla
Yes, the temperature of Srinagar and Shimla taken together is less than the temperature of Shimla.
However, 3°C > −2°C
Hence, the temperature of Srinagar and Shimla taken together is not less than the temperature of Srinagar.
Page No 4:
Question 2:
In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If jack’s scores in five successive rounds were 25, − 5, − 10, 15 and 10, what was his total at the end?
ANSWER:
Jack’s scores in five successive rounds are 25, −5, −10, 15, and 10. Total score of Jack at the end will be the sum of these scores.
Therefore, Jack’s total score at the end = 25 − 5 − 10 + 15 + 10 = 35
Page No 4:
Question 3:
At Srinagar temperature was − 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
ANSWER:
Temperature on Monday = −5°C
Temperature on Tuesday = Temperature on Monday −2°C
= −5°C − 2°C = −7°C
Temperature on Wednesday = Temperature on Tuesday + 4°C
= −7°C + 4°C = −3°C
Therefore, the temperature on Tuesday and Wednesday was −7ºC and −3ºC respectively.
Page No 4:
Question 4:
A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
ANSWER:
Height of plane = 5000 m
Depth of submarine = −1200 m
Distance between plane and submarine = 5000 m − (−1200) m
= 5000 m + 1200 m = 6200 m
Video Solution for integers (Page: 4 , Q.No.: 4)
NCERT Solution for Class 7 math - integers 4 , Question 4