Page No 60:
Answer:
The numbers that are in the form of , where p and q are integers and q ≠0, are called rational numbers.
For example:
Five positive rational numbers:
Five negative rational numbers:
Yes, there is a rational number that is neither positive nor negative, i.e. zero (0).
Page No 60:
Question 2:
The numbers that are in the form of , where p and q are integers and q ≠0, are called rational numbers.
For example:
Five positive rational numbers:
Five negative rational numbers:
Yes, there is a rational number that is neither positive nor negative, i.e. zero (0).
Answer:
Page No 60:
Question 3:
Answer:
(i)
Numerator = 8Denominator =19(ii)
Numerator = 5Denominator = −8(iii) Numerator = −13Denominator =15(iv)Numerator = −8Denominator = −11(v) 9i.e Numerator = 9Denominator = 1
Page No 60:
Question 4:
(i)
Numerator = 8Denominator =19(ii)
Numerator = 5Denominator = −8(iii) Numerator = −13Denominator =15(iv)Numerator = −8Denominator = −11(v) 9i.e Numerator = 9Denominator = 1
Answer:
(i) 5The rational number will be .
Numerator = 5
Denominator = 1
(ii) -3The rational number will be .
Numerator = -3Denominator = 1(iii)1The rational number will be .
Numerator = 1Denominator = 1(iv) 0The rational number will be .
Numerator =0Denominator = 1(v) -23The rational number will be .
Numerator = -23Denominator = 1
Page No 60:
Question 5:
(i) 5The rational number will be .
Numerator = 5
Denominator = 1
(ii) -3The rational number will be .
Numerator = -3Denominator = 1(iii)1The rational number will be .
Numerator = 1Denominator = 1(iv) 0The rational number will be .
Numerator =0Denominator = 1(v) -23The rational number will be .
Numerator = -23Denominator = 1
Answer:
Positive rational numbers:
(iii)
(iv)
(vi) 8 because 8 can be written as .
0 is neither positive nor negative.
Page No 60:
Question 6:
Positive rational numbers:
(iii)
(iv)
(vi) 8 because 8 can be written as .
0 is neither positive nor negative.
Answer:
Negative rational numbers:
(iii)
(iv)
(v) -6
(vi)
Page No 60:
Question 7:
Negative rational numbers:
(iii)
(iv)
(v) -6
(vi)
Answer:
(i) Following are the four rational numbers that are equivalent to .
(ii) Following are the four rational numbers that are equivalent to .
,,
and
i.e.
,
,
and
(iii) Following are the four rational numbers that are equivalent to .(iv) Following are the four rational numbers that are equivalent to 8, i.e. .
(v) Following are the four rational numbers that are equivalent to -1, i.e. .
(vi) Following are the four rational numbers that are equivalent to -1, i.e. .
Page No 61:
Question 8:
(i) Following are the four rational numbers that are equivalent to .
(ii) Following are the four rational numbers that are equivalent to .
,,
and
i.e.
,
,
and
(iii) Following are the four rational numbers that are equivalent to .(iv) Following are the four rational numbers that are equivalent to 8, i.e. .
(v) Following are the four rational numbers that are equivalent to -1, i.e. .
(vi) Following are the four rational numbers that are equivalent to -1, i.e. .
Answer:
(i)
(ii)
(iii)
(iv)
Page No 61:
Question 9:
(i)
(ii)
(iii)
(iv)
Answer:
(i) Numerator of is 5.
5 should be multiplied by 3 to get 15.
Multiplying both the numerator and the denominator by 3:
(ii) Numerator of is 5.
5 should be multiplied by −2 to get −10.
Multiplying both the numerator and the denominator by −2:
Page No 61:
Question 10:
(i) Numerator of is 5.
5 should be multiplied by 3 to get 15.
Multiplying both the numerator and the denominator by 3:
(ii) Numerator of is 5.
5 should be multiplied by −2 to get −10.
Multiplying both the numerator and the denominator by −2:
Answer:
(i) Denominator of is 7.
7 should be multiplied by 3 to get 21.
Multiplying both the numerator and the denominator by 3:
= =
(ii)
Denominator of is 7.
7 should be multiplied by -5 to get
−35.
Multiplying both the numerator and the denominator by
−5:
Page No 61:
Question 11:
(i) Denominator of is 7.
7 should be multiplied by 3 to get 21.
Multiplying both the numerator and the denominator by 3:
= =
(ii)
Denominator of is 7.
7 should be multiplied by -5 to get
−35.
Multiplying both the numerator and the denominator by
−5:
Answer:
(i) Numerator of is −12.
−12 should be multiplied by 4 to get 48.
Multiplying both the numerator and the denominator by 4:
(ii) Numerator of is −12.â
−12 should be multiplied by
−5 to get 60
Multiplying its numerator and denominator by -5:
Page No 61:
Question 12:
(i) Numerator of is −12.
−12 should be multiplied by 4 to get 48.
Multiplying both the numerator and the denominator by 4:
(ii) Numerator of is −12.â
−12 should be multiplied by
−5 to get 60
Multiplying its numerator and denominator by -5:
Answer:
(i) Denominator of is 11.
âClearly, 11×2= â22
Multiplying both the numerator and the denominator by 2:
(ii) Denominator of is 11.
Clearly, 11×5=55
Multiplying both the numerator and the denominator by 5:
Page No 61:
Question 13:
(i) Denominator of is 11.
âClearly, 11×2= â22
Multiplying both the numerator and the denominator by 2:
(ii) Denominator of is 11.
Clearly, 11×5=55
Multiplying both the numerator and the denominator by 5:
Answer:
(i) Numerator of is 14.
Clearly, 14×4=56
Multiplying both the numerator and the denominator by 4:=
=
(ii)
−70
âNumerator of is 14.â
Clearly, 14×(−5)=−70Multiplying both the numerator and the denominator by -5:
==â
Page No 61:
Question 14:
(i) Numerator of is 14.
Clearly, 14×4=56
Multiplying both the numerator and the denominator by 4:=
=
(ii)
−70
âNumerator of is 14.â
Clearly, 14×(−5)=−70Multiplying both the numerator and the denominator by -5:
==â
Answer:
(i) Denominator of is
−8.
âClearly, (−8)
×5= −40
Multiplying both the numerator and the denominator by 5:
(ii) Denominator of is
−8.
Clearly, (−8)×(−4)= 32
Multiplying both the numerator and the denominator by −4:
=
Page No 61:
Question 15:
(i) Denominator of is
−8.
âClearly, (−8)
×5= −40
Multiplying both the numerator and the denominator by 5:
(ii) Denominator of is
−8.
Clearly, (−8)×(−4)= 32
Multiplying both the numerator and the denominator by −4:
=
Answer:
(i) Numerator of is -36.
Clearly, (−36) ÷ 4= (−9)
Dividing both the numerator and the denominator by 4:
(ii) Numerator of is −36.â
Clearly, (−36) ÷ ( −6) = 6Dividing both the numerator and the denominator by -6:
=
Page No 61:
Question 16:
(i) Numerator of is -36.
Clearly, (−36) ÷ 4= (−9)
Dividing both the numerator and the denominator by 4:
(ii) Numerator of is −36.â
Clearly, (−36) ÷ ( −6) = 6Dividing both the numerator and the denominator by -6:
=
Answer:
(i) Denominator of is
−147.
â
∴ −147 ÷(−21)=7
Dividing both the numerator and the denominator by -21:
(ii)Denominator of is
−147.
−147÷3=−49
Dividing both the numerator and the denominator by 3:
Page No 61:
Question 17:
(i) Denominator of is
−147.
â
∴ −147 ÷(−21)=7
Dividing both the numerator and the denominator by -21:
(ii)Denominator of is
−147.
−147÷3=−49
Dividing both the numerator and the denominator by 3:
Page No 61:
Answer:
(i)
(ii)
Page No 61:
Question 19:
(i)
(ii)
Answer:
(i)
We have:
(−13)×(−21) = 273
And 7×39=273
(ii)
We have:
3×16=48
And (−8) ×(−6) =48
∴ 3×16 =(−8)×(−6)
(iii)
We have:
9×(−16)= −144
And 4×(-36)= −144
9×(−16) = 4×(−36)
Therefore, they are equivalent rational numbers.
(iv)
We have:
7×60 =420
And 15×(-28)= −420
∴ 7×60 ≠15×(−28)
Therefore, the rational numbers are not equivalent.
(v)
We have:
3 ×4=12
And 12×(−1)= −12
12 ≠ −12
Therefore, the rational numbers are not equivalent.
(vi)
We have:
2×2=4
And 3×3=9
2×2≠3×3
Therefore, the rational numbers are not equivalent.
Page No 61:
Question 20:
(i)
We have:
(−13)×(−21) = 273
And 7×39=273
(ii)
We have:
3×16=48
And (−8) ×(−6) =48
∴ 3×16 =(−8)×(−6)
(iii)
We have:
9×(−16)= −144
And 4×(-36)= −144
9×(−16) = 4×(−36)
Therefore, they are equivalent rational numbers.
(iv)
We have:
7×60 =420
And 15×(-28)= −420
∴ 7×60 ≠15×(−28)
Therefore, the rational numbers are not equivalent.
(v)
We have:
3 ×4=12
And 12×(−1)= −12
12 ≠ −12
Therefore, the rational numbers are not equivalent.
(vi)
We have:
2×2=4
And 3×3=9
2×2≠3×3
Therefore, the rational numbers are not equivalent.
Answer:
(i)=> −x =5×8=> x= −40
(ii)
=> (−3)x=7×6
=> x==> x=−14
(iii) => 5x=3×(−25)=> x==>x = (−15)(iv)=> 13x=6×(−65)=> x==> x= 6×(−â5)=> x = −â30(v) => => x= (−4)vi)
=>
=>
=>
x= (−24)
Page No 61:
Question 21:
(i)=> −x =5×8=> x= −40
(ii)
=> (−3)x=7×6
=> x==> x=−14
(iii) => 5x=3×(−25)=> x==>x = (−15)(iv)=> 13x=6×(−65)=> x==> x= 6×(−â5)=> x = −â30(v) => => x= (−4)vi)
=>
=>
=>
x= (−24)
Answer:
(i)8×15 =120
A
nd ( −10)×(−12)=1208×15 =(−10) ×(−12)Therefore, the rational numbers are equal.ii)(−3)×(−21) =63
And 7× 9=63∴ (−3)×(−21) =7×9Therefore, the rational numbers are equal.(iii)
(−8) × 21 = −168
And 15 ×(−â14) = − â210(−8) × 21 ≠ 15 × 14Therefore, the rational numbers are not equal.
Page No 61:
Question 22:
(i)8×15 =120
A
nd ( −10)×(−12)=1208×15 =(−10) ×(−12)Therefore, the rational numbers are equal.ii)(−3)×(−21) =63
And 7× 9=63∴ (−3)×(−21) =7×9Therefore, the rational numbers are equal.(iii)
(−8) × 21 = −168
And 15 ×(−â14) = − â210(−8) × 21 ≠ 15 × 14Therefore, the rational numbers are not equal.
Answer:
(i) False
For example, −
1 is smaller than zero and is a rational number.
(ii)True
All integers can be written with the denominator 1. (iii) False
Though 0 is an integer, when the denominator is 0, it is not a rational number.
For example, is not a rational number. (iv)True(v) False
−1 is a rational number but not a fraction.
Page No 66:
Question 1:
(i) False
For example, −
1 is smaller than zero and is a rational number.
(ii)True
All integers can be written with the denominator 1. (iii) False
Though 0 is an integer, when the denominator is 0, it is not a rational number.
For example, is not a rational number. (iv)True(v) False
−1 is a rational number but not a fraction.
Answer:
(i)
(ii)
(iii) (7/3)=2+(1/3)
(iv)
can be written as . So, we need to move to the right of point 3. Then, we need to move distance more to the right.
(v) can be written as 4+. So, we need to move to the right of point 4. Then, we need to move distance more to the right.
(vi)
(vii)
(viii)
can be written as . So, we need to move to the left of point -1. Then, we need to move distance more to the left.
(ix)
can be written as . So, we need to move to the left of point -7. Then, we need to move distance more to the left.
(x) can be written as . So, we need to move to the left of point -4. Then, we need to move distance more to the left.
Page No 66:
Question 2:
(i)
(ii)
(iii) (7/3)=2+(1/3)
(iv)
can be written as . So, we need to move to the right of point 3. Then, we need to move distance more to the right.
(v) can be written as 4+. So, we need to move to the right of point 4. Then, we need to move distance more to the right.
(vi)
(vii)
(viii)
can be written as . So, we need to move to the left of point -1. Then, we need to move distance more to the left.
(ix)
can be written as . So, we need to move to the left of point -7. Then, we need to move distance more to the left.
(x) can be written as . So, we need to move to the left of point -4. Then, we need to move distance more to the left.
Answer:
Page No 66:
Question 3:
Page No 66:
Page No 66:
Answer:
Page No 66:
Question 6:
Answer:
Page No 66:
Question 7:
Answer:
Page No 67:
Question 8:
Answer:
Page No 67:
Question 9:
Answer:
Page No 67:
Question 10:
Answer:
Page No 69:
Question 1:
Answer:
(i)
(ii)
(iii)
(iv)
(v)
=
(vi)
(vii)
(viii)
Page No 70:
Question 2:
(i)
(ii)
(iii)
(iv)
(v)
=
(vi)
(vii)
(viii)
Page No 70:
Answer:
(ii)
Page No 70:
Question 4:
(ii)
Answer:
2+−12+−3
Page No 70:
Question 5:
2+−12+−3
Answer:
Page No 72:
Question 1:
Answer:
(i) Additive inverse of 5 is −5.
(ii) Additive inverse of −9 is 9.
(iii) Additive inverse of .
(iv) Additive inverse of .
(v) Additive inverse of
(vi) Additive inverse of
(vii) Additive inverse ofâ 0 is 0.
(viii) Additive inverse of
Page No 72:
Question 2:
(i) Additive inverse of 5 is −5.
(ii) Additive inverse of −9 is 9.
(iii) Additive inverse of .
(iv) Additive inverse of .
(v) Additive inverse of
(vi) Additive inverse of
(vii) Additive inverse ofâ 0 is 0.
(viii) Additive inverse of
Answer:
(vi)
.
Page No 72:
Question 3:
(vi)
.
Answer:
[L.C.M. of 8 and 4 is 8.]
Page No 72:
Question 4:
[L.C.M. of 8 and 4 is 8.]
Answer:
Page No 72:
Question 5:
Answer:
Page No 72:
Question 6:
Answer:
Page No 72:
Question 7:
Answer:
Page No 72:
Question 8:
Answer:
Page No 72:
Question 9:
Answer:
Let the required number be x.
Page No 72:
Question 10:
Let the required number be x.
Answer:
Let the number that is to be added be x.
Page No 72:
Question 11:
Let the number that is to be added be x.
Answer:
Let the number that is to be added be x.
Page No 72:
Question 12:
Let the number that is to be added be x.
Answer:
Let the number that is to be added be x.
Page No 73:
Question 13:
Let the number that is to be added be x.
Answer:
Page No 73:
Question 14:
Answer:
Page No 73:
Question 15:
Answer:
Page No 73:
Question 16:
Answer:
Page No 75:
Question 1:
Answer:
Page No 75:
Question 2:
Answer:
Page No 75:
Question 3:
Answer:
Page No 75:
Question 4:
Answer:
Page No 75:
Question 5:
Answer:
Page No 75:
Question 6:
Answer:
Page No 78:
Question 1:
Answer:
Page No 78:
Question 2:
Answer:
Page No 78:
Question 3:
Answer:
Page No 78:
Question 4:
Answer:
Page No 78:
Question 5:
Answer:
Page No 78:
Question 6:
Answer:
Page No 78:
Question 7:
Answer:
Page No 78:
Question 8:
Answer:
Page No 78:
Question 9:
Answer:
Page No 78:
Question 10:
Answer:
Page No 78:
Question 11:
Answer:
Page No 78:
Question 12:
Answer:
Page No 78:
Question 13:
Answer:
Page No 79:
Question 1:
Answer:
Page No 79:
Question 2:
Answer:
Page No 79:
Question 3:
Answer:
Page No 79:
Question 4:
Answer:
Page No 79:
Question 5:
Answer:
Page No 79:
Question 6:
Answer:
Page No 79:
Question 7:
Answer:
Page No 79:
Question 8:
Answer:
Page No 79:
Question 9:
Answer:
Page No 79:
Question 10:
Answer:
Page No 79:
Question 11:
Answer:
Page No 80:
Question 12:
Answer:
Page No 80:
Question 13:
Answer:
Page No 80:
Question 14:
Answer:
The correct option is (b).
Page No 80:
Question 15:
The correct option is (b).
Answer:
Page No 80:
Question 16:
Answer:
Page No 80:
Question 17:
Answer:
Page No 80:
Question 18:
Answer:
Page No 80:
Question 19:
Answer:
Page No 80:
Question 20:
Answer:
Page No 82:
Question 1:
Page No 82:
Answer:
Page No 82:
Question 3:
Answer:
Page No 82:
Question 4:
Answer:
Hence , the other number is
Page No 82:
Question 5:
Hence , the other number is
Answer:
Page No 82:
Question 6:
Answer:
Page No 82:
Question 7:
Answer:
Page No 82:
Question 8:
Answer:
Page No 82:
Question 9:
Answer:
Page No 82:
Question 10:
Answer:
Page No 82:
Question 11:
Answer:
Page No 82:
Question 12:
Answer:
Page No 82:
Question 13:
Answer:
Page No 82:
Question 14:
Answer:
Page No 82:
Question 15:
Answer:
Page No 83:
Question 16:
Answer:
Page No 83:
Question 17:
Answer:
View NCERT Solutions for all chapters of Class 7