Class 6 Mathematics · 83 questions · 83 with answers
Write the correct answer from the given four options: Sania and Trapi visited Leh and Tawang respectively during winter. Sania reported that she had experienced –4°C on Sunday, while Trapi reported that she had experienced –2°C on that day. On that Sunday
Solution: The correct answer is (A).
State whether each of the following statements is true or false:
Solution: (a) True (b) False
Fill in the blank using <, > or = to make the statement correct 3 + (–2) ____ 3 + (–3)
Solution : 3 + (–2) > 3 + (–3) 11.4.2018
Represent the following using integers with proper sign:
Solution: (a) +3 (b) –500
Find the sum of the pairs of integers:
Solution: (a) – 6 and – 4 both have negative signs. So, – 6 + (– 4) = – (6 + 4) = –10 (b) + 3 and – 4 have opposite signs. As 4 – 3 = 1, therefore + 3 + (– 4) = –1 (c) + 4 and –2 have opposite signs. So, 4 + (–2) = 4 – 2 = 2
Find the sum of –2 and –3, using the number line.
Solution: To add –2 and –3, on the number line, we first move 2 steps to the left of 0, reaching –2. Then we move 3 steps to the left of –2 and reach –5. (Fig. 3.2) Fig. 3.2 Thus, –2 + (–3) = –5.
Subtract :
Solution: (a) The additive inverse of 3 is –3. So, – 4 – 3 = – 4 + (–3) = – (4 + 3) = –7 (b) The additive inverse of –3 is + 3. So, – 4 – (–3) = – 4 + (+3) = –1
Using the number line, subtract :
Solution: (a) To subtract 2 from –3, we move 2 steps to the left of – 3 on the number line and reach –5. (Fig. 3.3) Fig. 3.3 So, –3 – 2 = –5. (b) To subtract –2 from –3, we observe that 2 is the addtive inverse of –2. So, we add 2 to –3 using the number line and reach at –1. So, –3 – (–2) = –3 + (+ 2) = –1
How many integers are there between –9 and –2 ?
Solution: The integers –8, –7, –6, –5, –4 and –3 lie between –9 and –2. So, there are six integers between – 9 and –2. Example10: Calculate: 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 Solution: 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 = (1 + 3 + 5 + 7 + 9) – (2 + 4 + 6 + 8 + 10) = 25 – 30 = –5. Alternatively, 1 – 2 + 3 – 4 + 5 – 6 + 7 –8 + 9 – 10 = (1 – 2) + (3 – 4 ) + (5 – 6) + (7 – 8) + (9 – 10) = (–1) + ( –1) + (–1) + (–1) + (–1) = –5.
The sum of two integers is 47. If one of the integers is – 24, find the other.
Solution: As the sum is 47, the other integer is obtained by subtracting –24 from 47. So, the required integer = 47 – (–24) = 47 + 24 = 71. 11.4.2018 MATHEMATICS
Write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in this order and insert ‘+ ‘or ‘–’ between them to get the result
Solution: (a) 0 + 1 – 2 + 3 – 4 + 5 – 6 + 7 –8 + 9 = 5 (b) 0 – 1 – 2 + 3 + 4 – 5 + 6 – 7 + 8 – 9 = –3
Write five distinct integers whose sum is 5.
Solution: As the required sum is 5, keep 5 as one of the integers and write two pairs of integers which are additive inverses of each other. For example, 5 + [2+(–2)]+[3+(–3)]= 5. Thus, the required five integers are 5, 2, –2, 3, –3 There can be many combinatioins of five integers, such as 5, 3, –3, 6, –6 or 4, 2, 3, –3, –1 etc., whose sum is 5.
Every integer less than 0 has the sign
(B) –
The integer ‘5 units to the right of 0 on the number line’ is
(A) +5
The predecessor of the integer –1 is
(C) –2
Number of integers lying between –1 and 1 is
(A) 1
Number of whole numbers lying between –5 and 5 is
(D) 5
The greatest integer lying between –10 and –15 is
(B) –11
The least integer lying between –10 and –15 is
(D) –14
On the number line, the integer 5 is located
(B) to the right of 0
In which of the following pairs of integers, the first integer is not on the left of the other integer on the number line?
(B) (–3, –5)
The integer with negative sign (–) is always less than
(A) 0
An integer with positive sign (+) is always greater than
(A) 0
The successor of the predecessor of –50 is
(C) –50
The additive inverse of a negative integer
(B) is always positive
Amulya and Amar visited two places A and B respectively in Kashmir and recorded the minimum temperatures on a particular day as –4°C at A and –1°C at B. Which of the following statement is true?
(A) A is cooler than B
When a negative integer is subtracted from another negative integer, the sign of the result
(D) depends on the numerical value of the integers 11.4.2018 MATHEMATICS
The statement “When an integer is added to itself, the sum is greater than the integer” is
(C) true only when the integer is positive
Which of the following shows the maximum rise in temperature?
(B) –4°C to 8°C
The smallest natural number is zero.
F
Zero is not an integer as it is neither positive nor negative.
F
The sum of all the integers between –5 and –1 is –6.
F
The successor of the integer 1 is 0.
F
Every positive integer is larger than every negative integer.
T
The sum of any two negative integers is always greater than both the integers.
F
The sum of any two negative integers is always smaller than both the integers.
T
The sum of any two positive integers is greater than both the integers.
T
All whole numbers are integers.
T
All integers are whole numbers.
F
Since 5 > 3, therefore –5 > –3
F
Zero is less than every positive integer.
T
Zero is larger than every negative integer.
T
Zero is neither positive nor negative.
T
On the number line, an integer on the right of a given integer is always larger than the integer. INTEGERS 47 11.4.2018 UNIT-3
T
–2 is to the left of –5 on the number line.
F
The smallest integer is 0.
F
6 and –6 are at the same distance from 0 on the number line.
T
The difference between an integer and its additive inverse is always even.
T
The sum of an integer and its additive inverse is always zero.
T
The sum of two negative integers is a positive integer.
F
The sum of three different integers can never be zero. In questions 40 to 49, fill in the blanks to make the statements true:
F
On the number line, –15 is to the _______ of zero.
Left
On the number line, 10 is to the _______ of zero.
Right
The additive inverse of 14 is _______.
–14 ANSWERS 153 OOLRLPNOV _lqucpq
The additive inverse of –1 is _______.
1
The additive inverse of 0 is _______.
0
The number of integers lying between –5 and 5 is _______.
9
(–11) + (–2) + (–1) = _______.
–14
_______ + (–11) + 111 = 130
30
(–80) + 0 + (–90) = _______
–170
_______ –3456 = –8910 In questions 50 to 58, fill in the blanks using <, = or > :
–5454
(–11) + (–15) _______ 11 + 15
<
(–71) + (+9) _______ (–81) + (–9)
>
0 _______ 1
<
–60 _______ 50
<
–10 _______ –11
>
–101 _______ –102
>
(–2) + (–5) + (–6) _______ (–3) + (–4) + (–6)
=
0 _______ –2
>
1 + 2 + 3 _______ (–1) + (–2) + (–3) 11.4.2018
>
Match the items of Column I with that of Column II: Column I Column II (i) The additive inverse of +2
(A) 0 (ii) The greatest negative integer
(B) –2 (iii) The greatest negative even integer
(C) 2 (iv) The smallest integer greater than every negative integer
(D) 1 (v) Sum of predecessor and successor of –1 (E) –1
Compute each of the following:
(a) 30 + (–25) + (–10)
(b) (–20) + (–5)
(c) 70 + (–20) + (–30)
(d) –50 + (–60) + 50 (e) 1 + (–2) + (– 3) + (– 4) (f) 0 + (– 5) + (– 2) (g) 0 – (–6) – (+6) (h) 0 – 2 – (–2)
If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, write the following using integers with the appropriate signs:
(a) 200 m above sea level
(b) 100 m below sea level
(c) 10 m above sea level
(d) sea level
Write the opposite of each of the following:
(a) Decrease in size
(b) Failure
(c) Profit of Rs.10
(d) 1000 A.D. (e) Rise in water level (f) 60 km south (g) 10 m above the danger mark of river Ganga (h) 20 m below the danger mark of the river Brahmaputra (i) Winning by a margin of 2000 votes (j) Depositing Rs.100 in the Bank account (k) 20°C rise in temperature.
Temperature of a place at 12:00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1°C in the second hour. What was the temperature at 2:00 pm? 11.4.2018 UNIT-3
7°C
Write the digits 0, 1, 2, 3, ..., 9 in this order and insert ‘+’ or ‘–’ between them to get the result 3.
0 – 1 – 2 – 3 – 4 – 5 – 6 + 7 + 8 + 9 (One possible answer).
Write the integer which is its own additive inverse.
0
Write six distinct integers whose sum is 7.
1 + 2 + 3 + 6 + (– 2) + (– 3) (One possible answer).
Write the integer which is 4 more than its additive inverse.
2
Write the integer which is 2 less than its additive inverse.
– 1
Write two integers whose sum is less than both the integers.
– 2, – 3 (any two negetive integers can be takan).
Write two distinct integers whose sum is equal to one of the integers.
2, 0 ( any two integers with one of them as 0).
Using number line, how do you compare
(a) two negative integers?
(b) two positive integers?
(c) one positive and one negative integer?
Observe the following : 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = –5 Change one ‘–’ sign as ‘+’ sign to get the sum 9.
1 + 2 – 3 + 4 +5 – 6 + 7 + 8 – 9 = 9
Arrange the following integers in the ascending order : –2, 1, 0, –3, +4, –5
– 5, – 3, – 2, 0, 1, 4
Arrange the following integers in the descending order : –3, 0, –1, –4, –3, –6
0, – 1, – 3, – 3, – 4, – 6
Write two integers whose sum is 6 and difference is also 6.
0, 6
Write five integers which are less than –100 but greater than –150.
– 140, – 130, – 120, – 110, – 101 (there can be many answers).
Write four pairs of integers which are at the same distance from 2 on the number line.
( 1, 3), ( 0, 4), (– 1, 5), (– 2, 6)
The sum of two integers is 30. If one of the integers is –42, then find the other.
72
Sum of two integers is –80. If one of the integers is –90, then find the other. 11.4.2018 MATHEMATICS
10
If we are at 8 on the number line, in which direction should we move to reach the integer
(a) –5
(b) 11
(c) 0?
Using the number line, write the integer which is
(a) 4 more than –5
(b) 3 less than 2
(c) 2 less than –2
Find the value of 49 – (–40) – (–3) + 69
161
Subtract –5308 from the sum [(–2100) + (–2001)] (D) Activities Activity I : The faces of two dice are marked +1, +2, +3, +4, +5, +6 and –1, –2, –3, –4, –5, –6, respectively. Two players throw the pair of dice alternately and record the sum of the numbers that turn up each time and keep adding their scores separately. The player whose score reaches 20 or more first, wins the game.
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