Chapter 1 Integers
Very Short Answer Type
Question 1.
Fill in the blanks using < or >.
(a) -3 …… -4
(b) 6 ……. -20
(c) -8 …… -2
(d) 5 …… -7
Solution:
(a) -3 > -4
(b) 6 > -20
(c) -8 < -2
(d) 5 > -7
Question 2.
Solve the following:
(i) (-8) × (-5) + (-6)
(ii) [(-6) × (-3)] + (-4)
(iii) (-10) × [(-13) + (-10)]
(iv) (-5) × [(-6) + 5]
Solution:
(i) (-8) × (-5) + (-6)
= (-) × (-) × [8 × 5] + (-6)
= 40 – 6
= 34
(ii) [(-6) × (-3)] + (-4)
= (-) × (-) × [6 × 3] + (-4)
= 18 – 4
= 14
(iii) (-10) × [(-13) + (-10)]
= (-10) × (-23)
= (-) × (-) × [10 × 23]
= 230
(iv) (-5) × [(-6) + 5]
= (-5) × (-1)
= (-) × (-) × 5 × 1
= 5
Question 3.
Starting from (-7) × 4, find (-7) × (-3)
Solution:
(-7) × 4 = -28
(-7) × 3 = -21 = [-28 + 7]
(-7) × 2 – -14 = [-21 + 7]
(-7) × 1 = -7 = [-14 + 7]
(-7) × 0 = 0 = [-7 + 7]
(-7) × (-1) = 7 = [0 + 7]
(-7) × (-2) = 14 = [7 + 7]
(-7) × (-3) = 21 = [14 + 7]
Question 4.
Using number line, find:
(i) 3 × (-5)
(ii) 8 × (-2)
Solution:
(i) 3 × (-5)
From the number line, we have
(-5) + (-5) + (-5) = 3 × (-5) = -15
(ii) 8 × (-2)
From the number line, we have
(-2) + (-2) + (-2) + (-2) + (-2) + (-2) + (-2) + (-2) = 8 × (-2) = -16
Question 5.
Write five pair of integers (m, n ) such that m ÷ n = -3. One of such pair is (-6, 2).
Solution:
(i) (-3, 1) = (-3) ÷ 1 = -3
(ii) (9, -3) = 9 ÷ (-3) = -3
(iii) (6, -2) = 6 ÷ (-2) = -3
(iv) (-24, 8) = (-24) ÷ 8 = -3
(v) (18, -6) = 18 ÷ (-6) = -3
Short Answer Type
Question 6.
Solve the following:
(i) (-15) × 8 + (-15) × 4
(ii) [32 + 2 × 17 + (-6)] ÷ 15
Solution:
(i) (-15) × 8 + (-15) × 4
= (-15) × [8 + 4]
= (-15) × 12
= -180
(ii) [32 + 2 × 17 + (-6)] ÷ 15
= [32 + 34 – 6] ÷ 15
= [66 – 6] ÷ 15
= 60 ÷ 15
= 4
Question 7.
The sum of two integers is 116. If one of them is -79, find the other integers.
Solution:
Sum of two integers = 116
One integer = -79
Other integer = Sum of integer – One of integer = 116 – (-79) = 116 + 79 = 195
Question 8.
If a = -35, b = 10 cm and c = -5, verify that:
(i) a + (b + c) = (a + b) + c
(ii) a × (b + c) = a × b + a × c
Solution:
(i) Given that a = -35, b = 10, c = -5
LHS = a + (b + c) = (-35) + [10 + (-5)] = (-35) + 5 = -30
RHS = (a + b) + c = [(-35) + 10] + (-5) = (-25) + (-5) = -(25 + 5) = -30
LHS = RHS
Hence, verified.
(ii) a × (b + c) = a × b + a × c
LHS = a × (b + c) = (-35) × [10 + (-5)] = (-35) × 5 = -175
RHS = a × b + a × c = (-35) × 10 + (-35) × (-5) = -350 + (-) × (-) × (35 × 5) = -350 + 175 = -175
LHS = RHS
Hence, verified.
Question 9.
Write down a pair of integers whose
(i) sum is -5
(ii) difference is -7
(iii) difference is -1
(iv) sum is 0
Solution:
(i) (-2) + (-3) = -5
Hence, the required pair of integers = (-2, -3)
(ii) -10 – (-3) = -10 + 3 = -7
Hence, the required pair of integers = (-10, -3)
(iii) (-3) – (-2) = -1
Hence, the required pair of integers = (-3, -2)
(iv) (-4) + (4) = 0
Hence, the required pair of integers = (-4, 4)
Question 10.
You have ₹ 500 in your saving account at the beginning of the month. The record below shows all of your transactions during the month. How much money is in your account after these transactions?
Solution:
Amount in the beginning of the month in the account = ₹ 500
Amount deposited in the account for Jal Board = ₹ 200
Amount paid to Jal Board = ₹ 120
Amount left in the account after the above transactions = ₹ (500 + 200 – 120) = ₹ (700 – 120) = ₹ 580
Amount deposited for LIC India = ₹ 150
Amount paid to LIC India = ₹ 240
Amount left after this transactions = ₹ (580 + 150 – 240) = ₹ (730 – 240) = ₹ 490
Question 11.
The given table shows the freezing points in °F of different gases at sea level. Convert each of these into °C to the nearest integral value using the relations and complete the table
Question 12.
Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date on 3 days after tomorrow? [NCERT Exemplar]
Solution:
The date before yesterday = 17 January
The date of yesterday = 17 + 1 = 18 January
Today’s date = 18 + 1 = 19 January
Tomorrow’s date = 19 + 1 = 20 January
Date on 3 days after tomorrow = (20 + 3) = 23rd January