NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.4

NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.4 (Ex. 1.4) Integers free to download in PDF file format or videos format for CBSE session 2020-2021. All the questions are done by the subject experts step by step using easy methods.

Class 7 math exercise 1.4 deals with the questions related to division of integers with practical examples based on daily life. Solution and Explanation videos help the students to understand the concept of the questions.

Class 7 Maths Chapter 1 Exercise 1.4 Solution

Class: 7Mathematics
Chapter: 1Integers
Exercise: 1.1NCERT Textbook’s Solution

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Class 7 Maths Chapter 1 Exercise 1.4 Solution
Class 7 Maths Exercise 1.4 Question 1 Explanation



Class 7 Maths Exercise 1.4 Question 2-5 Explanation
Class 7 Maths Exercise 1.4 Question 6-7 Explanation

Division of Integers

We know that division is an inverse process of multiplication.
Rule 1. For dividing one integer by the other, the two having unlike signs, we divide their values regardless of their signs and give a minus sign to the quotient.

Evaluate: (i) (- 48) ÷ 12 (ii) 144 ÷ (- 16) (iii) (- 69) ÷ 23

We have:
(i) (- 48) ÷ 12 = -48/12 = – 4.
(ii) 144 ÷ (- 16) = 144/-16 = -9
(iii) (- 69) ÷ 23 = -69/23 = – 3.

Rule 2. For dividing one integer by the other having like signs, we divide their values regardless of their signs and give a plus sign to the quotient.

Evaluate: (i) 98 ÷ 14 (ii) (- 48) ÷ (- 16) (iii) (- 90) ÷ (- 15)

We have:
(i) 98 ÷ 14 = 98/14 = 7.
(ii) (- 48) ÷ (- 16) = -48/-16 = 3.
(iii) (- 90) ÷ (- 15) = -90/-15 = 6.

Modulus of an Integer:

The modulus of an integer a, denoted by IaI and is defined as lal = a, if a is positive or zero. – a, if a is negative. Thus, l6l = 6 and l-6l = – (- 6) = 6.

Distance between the Two Points

Let A and B be two points at distances a and b respectively from the origin. Then, we define AB = Ia – bI.

An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 20 m above the ground level. How long will it take to reach – 370 m?

Let the point O denote the ground level.
Then, OA = 20 m and OB = – 370 m.
So, AB = lOA – OBl = l20 – (- 370)l = l20 + 370l = 390 m.
So, distance covered = 390 m.
Rate of descent = 6 m/min.
Time taken = 390/6 min = 65 min = 1 hr 5 min.

Properties of Division of Integers

We know that division is an inverse process of multiplication.

Rule 1. For division

I. If a and b are integers then (a ÷ b) is not necessarily an integer.

Examples(i) 16 and 5 are both integers, but (16 ÷ 5) is not an integer.



II. If a is an integer and a ≠ 0, then a ÷ a = 1.

Example:
(i) 16 ÷ 16 = 1.
(ii) (- 8) ÷ (- 8) = 1.

III. If a is an integer, then (a ÷ 1) = a.

Example: (i) 7 ÷ 1 = 7. (ii) (- 6) ÷ 1 = (- 6).

IV. If a is an integer and a ≠ 0, then (0 ÷ a) = 0 but (a ÷ 0) is not meaningful.

Example:
(i) 0 ÷ 6 = 0.
(ii) 0 ÷ (- 4) = 0.
(iii) 6 ÷ 0 is meaningless.

V. If a, b, c are integers, then (a ÷ b) ÷ c ≠ a ÷ (b ÷ c), unless c = 1. Thus, division on integers in not associative.

Example: Let a = – 8, b = 4 and c = – 2.
Then. (a ÷ b) ÷ c = {(- 8) ÷ 4} ÷ (- 2)
= (- 2) ÷ (- 2) = 1. a ÷ (b ÷ c)
= (- 8) ÷ {4 ÷ (- 2)}
= (- 8) ÷ (- 2)
= 4.

(a ÷ b) ÷ c ≠ a ÷ (b ÷ c).

However, if a = – 8, b = 4 and c = 1,
then (a ÷ b) ÷ c = {(- 8) ÷ 4)} ÷ 1
= (- 2) ÷ 1 = (- 2).
a ÷ (b ÷ c)
= (- 8) ÷ {4 ÷1} = (- 8) ÷ 4 = (- 2).
So, in this case, (a ÷ b) ÷ c = a ÷ (b ÷ c).

VI. If a, b, c are nonzero integers and a > b, then

(i) (a ÷ c) > (b ÷ c), if c is positive.
(ii) (a ÷ c) < (b ÷ c), if c is negative.

Example: (i) 27 > 18 and 9 is positive.
So, 27/9 > 18/9
So, (ii) 27 > 18 and (- 9) is negative.
So, 27/-9 < 18/-9



How do you solve division of integers?

First, find the absolute values of the two integers. Next, divide the numbers or find their quotient. Finally, determine the final sign of the answer or quotient. Because we are dividing two integers with the same sign, the quotient will have a positive sign.

What will be the sign of the product, if we multiply 90 negative a integer and 9 positive integer?

We have – 90 and + 9
Now -90/+9 = -10

In a class test containing 20 questions, 4 marks are given for every correct answer and (- 2) marks are given for every incorrect answer. Ranjita attempts all question and 12 of her answers are correct. What is her total score?

Marks given for 1 correct answer = 4.
Marks given for 12 correct answers = (4 x 12) = 48.
Marks given for 1 incorrect answer = – 2.
Marks given for (20 – 12), i.e., 8 incorrect answers = (- 2) x 8 = 16.
Ranjita’s total score = 48 + (- 16) = 32.

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