1.Put the following numbers on a number line to represent them.
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
1.Put the following numbers on a number line to represent them.
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
Explanation:
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
2.A vertical number line representing integers is seen in the adjacent figure. Find the following points by observing it.
(a) Which point is -8 if point D is +8?
(b) Is the number G a positive or negative integer?
(c) Write integer values for positions B and E in ?
(d) Which point on this number line indicated with the lowest value?(e) Sort all of the points by decreasing value?
2.A vertical number line representing integers is seen in the adjacent figure. Find the following points by observing it.
(a) Which point is -8 if point D is +8?
(b) Is the number G a positive or negative integer?
(c) Write integer values for positions B and E in ?
(d) Which point on this number line indicated with the lowest value?(e) Sort all of the points by decreasing value?
Explanation:
(a)Point F is -8 if point D is +8 .
(b)Point G has a negative integer value.
(c) Point B is 4, while point E is – 10.
(d) Point E, which stands for -10 on this number line, has the lowest value.
(e) The points are D, C, B, A, O, H, G, F, E, in decreasing order.
3.Which number on the number line is next to the other in each of the pairings below?
(a) 2, 9
(b) – 3, – 8
(c) 0, – 1
(d) – 11, 10
(e) – 6, 6
(f) 1, – 100
3.Which number on the number line is next to the other in each of the pairings below?
(a) 2, 9
(b) – 3, – 8
(c) 0, – 1
(d) – 11, 10
(e) – 6, 6
(f) 1, – 100
Explanation:
(a) In the number line, 9 is located to the right (9 > 2).
(b)On the number line, (b) - 3 is to the right (- 3 > - 8).
(c) On the number line, 0 is to the right (0 > -1).
(d) On the number line, 10 is to the right (10 > -11).
(b)In the number line, 6 is to the right (6 > -6).
(f) On the number line, 1 is to the right (1 > -100).
4.Input each integer between the indicated pairings (write them in increasing order).
(a) 0 and – 7
(b) – 4 and 4
(c) – 8 and – 15
(d) – 30 and – 23
4.Input each integer between the indicated pairings (write them in increasing order).
(a) 0 and – 7
(b) – 4 and 4
(c) – 8 and – 15
(d) – 30 and – 23
Explanation:
(a) The integers -6, -5, -4, 3, 2, 1, and so on are in the range of 0 and -7.
(b) The numbers -3, -2, -1, 0, 1, 2, 3, and 4 are all integers between -4 and 4.
(c) The numbers -8 and -15 fall inside the range of the integers -14, -13, -12, -11, -10, and -9.
(d) Between -30 and -23, there are the integers -30, -28, -27, -26, -25, and -24.
5. (a)Write four negative numbers that are greater than – 20.
(b) Compose four integers less than or equal to 10.
5. (a)Write four negative numbers that are greater than – 20.
(b) Compose four integers less than or equal to 10.
Explanation:
(A) The integers bigger than -20 are -19, -18, -17, and -16.
(b) The integers less than -10 are -11, -12, -13, and -14.
6.Write True (T) or False (F) for each of the following statements (F). Make the assertion true if it's incorrect.
(a) In a number line, -8 is next to -10.
(b) In a number line, 100 is located to the right of (-50).
(c) The smallest negative number is one (-).
(d) 26 is greater than 25.
6.Write True (T) or False (F) for each of the following statements (F). Make the assertion true if it's incorrect.
(a) In a number line, -8 is next to -10.
(b) In a number line, 100 is located to the right of (-50).
(c) The smallest negative number is one (-).
(d) 26 is greater than 25.
Explanation:
(a) True in that (-8 > -10).
(b) False in (-50 is more than -100. Hence, on the number line, -100 is located to the left of -50.
(c) -1 is the larger negative number, hence is false.
(d) False in -25 is less than -26.
7.Don't use a number line when adding.
(a) 11 + (–7) (–7)
(b) (–13) + (+18)
(c) (–10) + (+19)
(d) (–250) + (+150)
(e) (–380) + (–270) (–270)
(f) (–217) + (–100) (–100)
7.Don't use a number line when adding.
(a) 11 + (–7) (–7)
(b) (–13) + (+18)
(c) (–10) + (+19)
(d) (–250) + (+150)
(e) (–380) + (–270) (–270)
(f) (–217) + (–100) (–100)
Explanation:
(a) 11 + (-7) = 4
(b) (-13) + (+18) = 5
(c) (-10) + (+19) = 9
(d) (-250) + (+150) = -100
(e) (-380) + (-270) = -650
(f) (-217) + (-100) = -317
8.What is the sum of:
(a) 137 and – 354
8.What is the sum of:
(a) 137 and – 354
Explanation:
(a) 137 and -354
(137) + (-354) = (137) + (-137) + (-217) (-217)
= 0 + (-217) [(137) + (-137) = 0]
= (-217) (-217)
= -217
9.What is the sum of:
– 312, 39 and 192
9.What is the sum of:
– 312, 39 and 192
Explanation:
-312, 39 and 192
(-312) + (+39) + (+192) = (-231) + (-81) + (+39) + (+192)
= (-231) + (-81) + (+231)
= (-231) + (+231) + (-81) (-81)
= 0 + (-81) (-81) [(-a) + (+a) = 0]
= -81
10.Find
(a) 35 – (20) (20)
(b) 72 – (90) (90)
(c) (-15) – (-18) (-18)
(d) (-20) – (13) (13)
(e) 23 – (-12) (-12)
(f) (-32) – (-40) (-40)
10.Find
(a) 35 – (20) (20)
(b) 72 – (90) (90)
(c) (-15) – (-18) (-18)
(d) (-20) – (13) (13)
(e) 23 – (-12) (-12)
(f) (-32) – (-40) (-40)
Explanation:
(a) 35 – (20) (20)
= 35 – 20
= 15
(b) 72 – (90) (90)
= 72 – 90
= -18
(c) (-15) – (-18) (-18)
= -15 + 18
= 3
(d) (-20) – (13) (13)
= -20 – 13
= -33
(e) 23 – (-12) (-12)
= 23 + 12
= 35
(f) (-32) – (-40) (-40)
= -32 + 40
= 8
11.Write the integer that is: using the number line.
(a) 3 More than (5)
(b) Five more than five.
11.Write the integer that is: using the number line.
(a) 3 More than (5)
(b) Five more than five.
Explanation:
(a)
From 5, we take 3 steps to the right to get to 8. As a result, 3 plus 5 equals 8.
(b)
At -5, turning right five steps brings us to 0. In light of this, 5 + -5 Equals 0.
12.Write the integer that is: using the number line.
Less than six, two, and three
12.Write the integer that is: using the number line.
Less than six, two, and three
Explanation:
6 less than 2.
Six steps to the left from 2, we arrive at -4. So, 6 less than 2 equals -4.
(d) 3 less than -2.
3 steps to the left from -2 brings us to -5.
13.Add the following integers using a number line:
13.Add the following integers using a number line:
Explanation:
(a) 9 + (-6)
(b) 5 + (-11)
(c) (-1) + (-7)
(d) (- 5) + 10
(e) (-1) + (-2) + (-3)
14.Without using a number line, add the following:
(a) 11 + (-7)
(b) (-13) + (+18)
(c) (-10) + (+19).
14.Without using a number line, add the following:
(a) 11 + (-7)
(b) (-13) + (+18)
(c) (-10) + (+19).
Explanation:
(a) (+7) + (-7) = 0 (11 + (-7) = 4 + (+7) + (-7)
= 4 + 0 = 4 Thus, 11 + (-7) = 4.
(b) (-13) + (+18) = (-13) + (+13) + (+5)
[∵ (-13) + (+13) = 0]
= 0 + (+ 5) = 5 Thus, (- 13) + (+ 18) = 5.
(c) (-10) + (+19) = (-10) + (+10) + (+9)
[∵ (-10) + (10) = 0] = 0 + (+9) = 9 Thus, (-10) + (19) = 9.
15Find:
(a) (-7) - 8 - (-25)
(b) (-13) + 32 – 8 – 1
15Find:
(a) (-7) - 8 - (-25)
(b) (-13) + 32 – 8 – 1
Explanation:
(a) (-7) – 8 – (-25)
= (-7) – 8 + 25
Inverse additive of - 25 is 25
= -7 + 17
= -7 + 7 +10 [∵ (-a) + (+a) = 0]
= 0 + 10
= 10.
(b) (-13) + 32 – 8 – 1
= (-13) + (13) + 19 – (8 + 1)
= 0 + 19 – 9
= 19 – 9 [∵ (-13) + (13) = 0]
= 10 + 9 – 9 = 10 + 0 = 10.
[(+9) – (+9) = 0]
16Find:
(a) (-7) + (-8) + (-90)
(b) 50 – (-40) – (-2) (-2)
16Find:
(a) (-7) + (-8) + (-90)
(b) 50 – (-40) – (-2) (-2)
Explanation:
(-7) + (-8) + (-90)
= – (7 + 8) + (-90)
= -15 + (-90)
= -(15 + 90)
= -105.
(d) 50 – (-40) – (-2)
= 50 – [- 40 – 2]
= 50 – (-42)
= 50 + 42
= 92.
17.Put the following on a number line to represent:
(a) -5
(b) 4
17.Put the following on a number line to represent:
(a) -5
(b) 4
Explanation:
– 5
4
18.Find (a) 6 * 2 (b) (- 2) * (- 3) (c) (- 2) * (4) (d) (+ 3) * if * is an operation such that for two integers p and q, p * q = p + q - 2 (- 1)
18.Find (a) 6 * 2 (b) (- 2) * (- 3) (c) (- 2) * (4) (d) (+ 3) * if * is an operation such that for two integers p and q, p * q = p + q - 2 (- 1)
Explanation:
(a) In light of the fact that: p * q = p + q - 2 6 * 2 = 6 + 2 - 2 = 6 + 0 = 6
Thus, 6 * 2 = 6.
(b) Taking into account the fact that: p * q = p + q - 2 (- 2) * (- 3) = (- 2) + (- 3) - 2 = -5 - 2 = -7.
Thus, (- 2) * (- 3) = – 7.
(c) A consequence of this is that: p * q = p + q - 2 (- 2) * (4) = (- 2) + (4) - 2 = 2 - 2 = 0.
Thus, (- 2) * (4) = 0.
(d) Taking into account the fact that p*q - p + q - 2 (+ 3) * (- 1) = (+ 3) + (- 1) - 2 = 2 - 2 = 0,
Thus, (+ 3) * (- 1) = 0.
19.The following pair of numbers should be written down: (a) 0 and - 4 (B) 5 and 5 (c), 8 and 13, and (d) 3 and 6
19.The following pair of numbers should be written down: (a) 0 and - 4 (B) 5 and 5 (c), 8 and 13, and (d) 3 and 6
Explanation:
(a) These numbers range from 0 to -4: -3, -2, -1\s(B) (B) Between - 5 and 5 are the following integers: -4, -3, -2, -1, 0, 1, 2, 3, 4.
(c) The following numbers range from -8 to -13: -12, -11, -10, -9\s(d) (d) Between 3 and 6 integers are: 4 and 5.
20.The following pair of numbers should be written down: (a) 0 and - 4 (B) 5 and 5 (c), 8 and 13, and (d) 3 and 6
20.The following pair of numbers should be written down: (a) 0 and - 4 (B) 5 and 5 (c), 8 and 13, and (d) 3 and 6
Explanation:
(a) These numbers range from 0 to -4: -3, -2, -1\s(B) (B) Between - 5 and 5 are the following integers: -4, -3, -2, -1, 0, 1, 2, 3, 4.
(c) The following numbers range from -8 to -13: -12, -11, -10, -9\s(d) (d) Between 3 and 6 integers are: 4 and 5.
21.Ramesh considers a number. He deducts 12 from it, yielding a result of -6. What was the integer that came to mind?
21.Ramesh considers a number. He deducts 12 from it, yielding a result of -6. What was the integer that came to mind?
Explanation:
The total given can be expressed as follows.
(___) – (12) = – 6
The necessary number is 12 – 6 = 6.
22.At five in the morning on a specific day, the temperature is -11°C. Suppose the temperature falls by 3 degrees at 6 a.m., rises by 5 degrees at 8 a.m., and then falls by 3 degrees once more at 9 a.m. How hot is it at nine in the morning?
22.At five in the morning on a specific day, the temperature is -11°C. Suppose the temperature falls by 3 degrees at 6 a.m., rises by 5 degrees at 8 a.m., and then falls by 3 degrees once more at 9 a.m. How hot is it at nine in the morning?
Explanation:
5 a.m. temperature is -11 °C.
The temperature was 3°C (or -3°F) lower at 6 a.m.
Temperature increased by 5°C at 8 a.m.
Temperature dropped by 3°C (or -3°F) around 9 a.m.
At nine in the morning, the temperature was (-11) + (-3) + (+5) + (-3) = -11 - 3 + 5 - 3 = -17 + 5 = -12°C.
23.Using the number line, solve the following additions:
(a)(- 3) + 5
(B) (- 5) + (-2) (-2)
23.Using the number line, solve the following additions:
(a)(- 3) + 5
(B) (- 5) + (-2) (-2)
Explanation:
(a)(- 3) + 5
∴ (-3) + 5 = 2
(B) (- 5) + (-2)
∴ (-5) + (-2) = (-7)
24.Add the following numbers using the number line: 9 + (-6).
24.Add the following numbers using the number line: 9 + (-6).
Explanation:
On the number line, we first go 9 steps from 0 to 9 to the right, and then 6 steps from 9 to 3 to the left.
Thus, 9 + (-6) = 3.
25.Describe each of the following in reverse:
I Population growth
(ii) Making a bank deposit
(iii) Financial gain
iv) Traveling North
(v) Putting on 4 kg of weight.
(vi) A $1,000 loss
(vii) 25
(viii) – 15
25.Describe each of the following in reverse:
I Population growth
(ii) Making a bank deposit
(iii) Financial gain
iv) Traveling North
(v) Putting on 4 kg of weight.
(vi) A $1,000 loss
(vii) 25
(viii) – 15
Explanation:
I Population decline is the exact opposite of population growth.
(ii) Withdrawing money from a bank is the reverse of depositing money there.
Spending money is the opposite of making money (iii).
(iv) Traveling South is the polar opposite of heading north.
(v) A 4 kg weight loss is the polar opposite of a 4 kg weight gain.
(vi) A gain of Rs. 1000 is the polar opposite of a loss of Rs. 1000.
(vii) 25's polar opposite is 25.
(viii) The alternative of -15 is 15.
26.Provide the following information using integers:
(i) 25 degrees above 0
(ii) Five below zero
(iii) An 800 rupee profit
(iv) A $2500 down payment
(v) 3 kilometres above sea level.
(vi) 2 km underground
26.Provide the following information using integers:
(i) 25 degrees above 0
(ii) Five below zero
(iii) An 800 rupee profit
(iv) A $2500 down payment
(v) 3 kilometres above sea level.
(vi) 2 km underground
Explanation:
(i) 25o above zero equals +25o.
In (ii), -5o is 5o below zero.
(iii) An 800 rupee profit equals +800.
(iv) A Rs. 2,500 deposit is equal to +2,500.
(v) 3 km above sea level is equal to + 3.
(vi) 2km below ground equals -2.
27.Which of the following numbers is smaller in each of the pairs?
( i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
27.Which of the following numbers is smaller in each of the pairs?
( i) 0, -4
(ii) -3 , 12
(iii) 8, 13
(iv) – 15, -27
Explanation:
(i) Zero is greater than negative numbers.
The result is -4 0
As a result, -4 is smaller.
(ii) On a number line, 12 exceeds -3.
so we do
-3 < 12
As a result, -3 is smaller.
(iii) In a number line, 13 is greater than 8.
The result is 8 13.
Hence, 8 is smaller.
(iv) The number line shows that - 15 is greater than - 27.
The result is 27 - 15
As a result, -27 is smaller.
28.Which of the following pairs of numbers is larger?
(i) 3, -4
(ii) – 12, – 8
(iii) 0, 7
(iv) 12, – 18
28.Which of the following pairs of numbers is larger?
(i) 3, -4
(ii) – 12, – 8
(iii) 0, 7
(iv) 12, – 18
Explanation:
(i) On a number line, we are aware that 3 is larger than -4.
The result is 3 > – 4.
3 is hence bigger.
(ii) We are aware that on a number line, -8 is larger than -12.
Hence, we obtain -8 > -12.
Hence, -8 is greater.
(iii) On a number line, we know that 7 is larger than 0.
The result is 7 > 0.
7 is hence bigger.
(iv) On a number line, we know that 12 is larger than -18.
The result is 12 > - 18.
12 is hence bigger.
29.How many integers are in the interval?
(i) – 4 and 3
(ii) 5 and 12
(iii) 9 and 2
(iv) 0 and 5
29.How many integers are in the interval?
(i) – 4 and 3
(ii) 5 and 12
(iii) 9 and 2
(iv) 0 and 5
Explanation:
(i) Between -4 and 3 are the integers
-3, -2, -1, 0, 1, 2
As a result, there are 6 integers between - 4 and 3.
(ii) The numbers from 5 to 12 are
6, 7, 8, 9, 10, 11
Hence, there are six integers between five and twelve.
(iii) The numbers between - 9 and - 2 are.
-8, -7, -6, -5, -4, -3
As a result, there are 6 numbers between -9 and -2.
(iv) The numbers 0 through 5 are
1, 2, 3, 4
As a result, there are 4 numbers between.
30.Each of the following absolute values should be written:
(i)14
(ii) – 25
(iii) 0
(iv) – 125
(v) – 248
(vi) if an is bigger than 7, a – 7
30.Each of the following absolute values should be written:
(i)14
(ii) – 25
(iii) 0
(iv) – 125
(v) – 248
(vi) if an is bigger than 7, a – 7
Explanation:
(i) 14 has an absolute value of
|14| = 14
(ii) The value of -25 in absolute terms is
|-25| = 25
(iii) The absolute value of 0 is
|0| = 0
(iv) The value of -125 in absolute terms is
|-125| = 125
(v) The value of -248 in absolute terms is
|-248| = 248
(vi) If an is bigger than 7, the absolute value of a minus 7 is
Where a > 7, |a - 7| = a – 7
31.Each of the following absolute values should be written:
(i) If an is bigger than -4, a + 4
(ii) If a - 2 7, then a - 7
(iii) If an is smaller than -4, a + 4
(iv) |-3|
(v) -|-5|
(vi) |12 – 5|
31.Each of the following absolute values should be written:
(i) If an is bigger than -4, a + 4
(ii) If a - 2 7, then a - 7
(iii) If an is smaller than -4, a + 4
(iv) |-3|
(v) -|-5|
(vi) |12 – 5|
Explanation:
(i) If an is bigger than -4, the absolute value of a + 4 is
Where a > - 4, |a + 4| = a + 4
(ii) If a - 2 is less than 7, the absolute value of a - 7 is
(iii) If an is smaller than - 4, the absolute value of a + 4 is
Where a -4, |a + 4| = - (a + 4)
(iv) |-3| has an absolute value of
|-3| = 3
(v) -|-5| has a value of infinity.
-|-5| = 5
(vi) |12 - 5| has an absolute value of 0.
|12 – 5| = 7
32Each of the following should be represented on a number line that you draw:
I 5 + (-2) (-2)
(ii) (-9) + 4
(iii) (-3) + (-5) (-5)
32Each of the following should be represented on a number line that you draw:
I 5 + (-2) (-2)
(ii) (-9) + 4
(iii) (-3) + (-5) (-5)
Explanation:
(i) 5 + (-2) (-2)
Move from 0 to the right of the first five units to get +5.
The second number is therefore -2, and by moving 2 units to the left of +5 we obtain +3.
Hence, 5 + (-2) = 3.
(ii) (-9) + 4
Go from 0 to the left of nine units to get - 9.
The second number is therefore 4, and by moving 4 units to the right of -9, we obtain -5.
So, (-9) plus 4 is (-) 5.
(iii) (-3) + (-5) (-5)
Go from 0 to the left of three units to get - 3.
The second number is therefore - 5, and by moving 5 units to the left of - 3, we obtain - 8.
Therefore, (-3) + (-5) = (-8).
33.(i) 6 + (-6) (-6)
(ii) (-1) + (-2) + 2
(iii) (-2) + 7 + (-9) (-9)
33.(i) 6 + (-6) (-6)
(ii) (-1) + (-2) + 2
(iii) (-2) + 7 + (-9) (-9)
Explanation:
(i) 6 + (-6) (-6)
Move from zero to the right of six units to get six
Therefore the second number is - 6 so move 6 units farther left of 6 we obtain 0
Hence, 6 + (-6) = 0.
(ii) (-1) + (-2) + 2
From zero, travel one unit to the left to obtain -1.
The second number is therefore -2, and if we move 2 units to the left of -1, we get -3.
The third number is 2, thus if we shift 2 spaces to the right of 3, we get the number 1.
Because of this, (-1) + (-2) + 2 = - 1.
(iii) (-2) + 7 + (-9) (-9)
Move from 0 to the left of two units to get -2
The second number is therefore 7, so by moving 7 units to the right of -2, we obtain 5.
Go 9 units to the left of 5 to get the third number, which is - 9, which is - 4.
34.From 709, deduct the total of - 5020 and -2320.
34.From 709, deduct the total of - 5020 and -2320.
Explanation:
We are aware that -5020 plus 2320 equals
-5020 + 2320
One way to spell it is as
= 2320 – 5020
hence, we do
= – 2700
By deducting from -709, we obtain
= – 709 – (-2700) (-2700)
We get
= – 709 + 2700
By removing
= 1991
35.Add the sums of 1250 and 1138 and subtract them from 1136 and 1272.
35.Add the sums of 1250 and 1138 and subtract them from 1136 and 1272.
Explanation:
We are aware of what 1250 minus 1138 is.
-1250 + 1138
One way to spell it is as
= 1138 – 1250
hence, we do
= – 112
We are aware that 1136 minus 1272 equals
1136 – 1272 = – 136
hence, we do
-136 – (-112) = – 136 + 112 = -24
36.If is an operation on integers, then all instances of a and b have the value a b = - a + b - (-2). Discover the importance of
(i) 4 △ 3
(ii) (-2) △ (-3) (-3)
(iii) 6 △ (-5) (-5)
(iv) (-5) △ 6
36.If is an operation on integers, then all instances of a and b have the value a b = - a + b - (-2). Discover the importance of
(i) 4 △ 3
(ii) (-2) △ (-3) (-3)
(iii) 6 △ (-5) (-5)
(iv) (-5) △ 6
Explanation:
(i) 4 △ 3
By changing the numbers in the formula a b = - a + b - (-2)
We get
4 △ 3 = – 4 + 3 – (-2) = 1
(ii) (-2) △ (-3) (-3)
By changing the numbers in the formula a b = - a + b - (-2)
We get
(-2) △ (-3) = – (-2) + (-3) – (-2) = 1
(iii) 6 △ (-5) (-5)
By changing the numbers in the formula a b = - a + b - (-2)
We get
6 △ (-5) = – 6 + (-5) – (-2) = – 9
(iv) (-5) △ 6
By changing the numbers in the formula a b = - a + b - (-2)
We get
(-5) △ 6 = – (-5) + 6 – (-2) = 13
Also Read: Integers Class 6 Extra Questions
Also Read: Chapter 7: Fractions
