Q 1. Fill in the blanks.
Ans. (i) – 135 (ii) – 1 (iii) 0 (iv) – 1 (v) 51 (vi) 6
Q 2. In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer and 0 for answer not attempted. Ram gets 3 correct and 4 incorrect out of 7 questions he attempted. What is his score?
Ans. Ram score = 3 * 5 + 4 * (– 2) = 7
Q 3. Which of the following statements are true or false?
Ans. (i) false (ii) true (iii) false (iv) true (v) false
Q 4. Divide:
(i) 0 by – 135
(ii) – 85 by 5
(iii) – 161 by – 23
(iv) 21590 by – 10
(v) 17654 by – 17654
(vi) ( –729) by ( –27)
Ans.
(i) Given 0 by –135
We can write given question as 0 ÷( – 135)
0 ÷ – 135 = 0 [because anything divided by 0 we get the result as 0]
(ii) Given – 85 by 5
We can write given question as – 85 ÷ 5
– 85 ÷ 5 = |– 85/5| = |– 85|/|5| [by applying the mod]= –85/5 = –17
(iii) Given – 161 by – 23
We can write given question as -161 ÷ (– 23)
– 161 ÷ – 23 = |– 161/– 23| = |– 161|/|– 23| [by applying the mod]
= 161/23 = 7
(iv) Given 21590 by – 10
We can write given question as 21590 ÷ (–10)
21590 ÷ -10 = |21590/-10| = |21590|/|-10| [by applying the mod]= 21590/-10 = -2159
(v) Given 17654 by – 17654
We can write given question as 17654 ÷ (–17654)
17654 ÷ (–17654) = |17654/–17654| = |17654|/|–17654| [by applying the mod]= 17654/–17654 = –1
(vi) Given (–729) by (–27)
We can write given question as (–729) ÷ (–27)
(–729) ÷ (–27) = |–729/–27| = |–729|/|–27| [by applying the mod]= 729/27 = 27
Q 5. Using brackets, write a mathematical expression for each of the following:
(i) Nine multiplied by the sum of two and five.
(ii) Two multiplied by one less than the difference of nineteen and six.
(iii) Twenty divided by the difference of seven and two.
(iv) Eight subtracted from the product of two and three.
Ans. (i) 9 (2 + 5)
(ii) 12 ÷ (1 + 3)
(iii) 20 ÷ (7 – 2).
(iv) 2 × 3 – 8
Q 6. Using number line, find:
(i) 3 × (– 5)
(ii) 8 × (– 2)
Ans. (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
Q 7. 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?
Ans. 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
Q 8. 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?
Ans.
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
Q 9. Comparing the following pairs of number use > or < .
Ans.
(a) 0 > – 6
(b) – 10 < – 2
(c) – 100 < 100
(d) 2 > – 2
Q 10. Assertion: Zero is greater than every negative integer and less than every positive integer.
Reason: There is no greatest or smallest integer.
(a) Both assertion and reason are correct and reason is the correct explanation for assertion.
(b) Both assertion and reason are correct but reason is not the correct explanation for assertion.
(c) Assertion is correct but the reason is incorrect.
(d) Both assertion and reason are incorrect.
Ans. (b) Both assertion and reason are correct but reason is not the correct explanation for assertion.
Q 11. (– 1) × (– 1) × (– 1) × (2m + 1) times, where m is a natural number, is equal to
(a) 1
(b) – 1
(c) 1 or – 1
(d) none of these.
Ans. (b) – 1
Q 12. (– 20) × (– 5) is equal to
(a) 100
(b) – 100
(c) 20
(d) 5
Ans. (a) 100
Q 13. 10 × (– 20) is equal to
(a) 200
(b) – 200
(c) 30
(d) 20
Ans. (b) – 200
Q 14. 0 × (– 5) is equal to
(a) 0
(b) 5
(c) – 5
(d) 1
Ans. (a) 0
Q 15. 4 × (–1) is equal to
(a) 4
(b) – 4
(c) 1
(d) – 1
Ans. (b) – 4