Rs Aggarwal 2017 Solutions for Class 7 Math Chapter 4 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 7 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 7 Math Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.
Page No 60:
Question 1:
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
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:
Which of the following are rational numbers?
(i)
(ii)
(iii)
(iv)
(v) 6
(vi) −3
(vii) 0
(viii)
(ix)
(x)
Answer:
Page No 60:
Question 3:
Write down the numerator and the denominator of each of the following rational numbers:
(i)
(ii)
(iii)
(iv)
(v) 9
Answer:
(i)
Numerator = 8
Denominator =19
(ii)
Numerator = 5
Denominator = −8
(iii)
Numerator = −13
Denominator =15
(iv)
Numerator = −8
Denominator = −11
(v) 9
i.e
Numerator = 9
Denominator = 1
Page No 60:
Question 4:
Write each of the following integers as a rational number. Write the numerator and the denominator in each case.
(i) 5
(ii) −3
(iii) 1
(iv) 0
(v) −23
Answer:
(i) 5
The rational number will be .
Numerator = 5
Denominator = 1
(ii) -3
The rational number will be .
Numerator = -3
Denominator = 1
(iii)1
The rational number will be .
Numerator = 1
Denominator = 1
(iv) 0
The rational number will be .
Numerator =0
Denominator = 1
(v) -23
The rational number will be .
Numerator = -23
Denominator = 1
Page No 60:
Question 5:
Which of the following are positive rational numbers?
(i)
(ii)
(iii)
(iv)
(v)
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:
Which of the following are negative rational numbers?
(i)
(ii) 0
(iii)
(iv)
(v) −6
(vi)
Answer:
Negative rational numbers:
(iii)
(iv)
(v) -6
(vi)
Page No 60:
Question 7:
Find four rational numbers equivalent to each of the following.
(i)
(ii)
(iii)
(iv) 8
(v) 1
(vi) −1
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:
Write each of the following as a rational number with positive denominator.
(i)
(ii)
(iii)
(iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 61:
Question 9:
Express as a rational number with numerator
(i) 15
(ii) −10
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:
Express as a rational number with denominator
(i) 21
(ii) −35
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:
Express as a rational number with numerator
(i) −48
(ii) 60
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.
−12 should be multiplied by −5 to get 60
Multiplying its numerator and denominator by -5:
Page No 61:
Question 12:
Express as a rational number with denominator
(i) 22
(ii) −55
Answer:
(i) Denominator of is 11.
Clearly, 11×2= 22
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:
Express as a rational number with numerator
(i) 56
(ii) −70
Answer:
(i) Numerator of is 14.
Clearly, 14×4=56
Multiplying both the numerator and the denominator by 4:
=
=
(ii) −70
Numerator of is 14.
Clearly, 14×(−5)=−70
Multiplying both the numerator and the denominator by -5:
=
=
Page No 61:
Question 14:
Express as a rational number with denominator
(i) −40
(ii) 32
Answer:
(i) Denominator of is −8.
Clearly, (−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:
Express as a rational number with numerator
(i) −9
(ii) 6
Answer:
(i) Numerator of is -36.
Clearly, (−36) ÷ 4= (−9)
Dividing both the numerator and the denominator by 4:
(ii) Numerator of is −36.
Clearly, (−36) ÷ ( −6) = 6
Dividing both the numerator and the denominator by -6:
=
Page No 61:
Question 16:
Express as a rational number with denominator
(i) 7
(ii) −49
Answer:
(i) Denominator of is −147.
∴ −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:
Write each of the following rational numbers in standard form:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
(i)
H.C.F. of 35 and 49 is 7.
Dividing the numerator and the denominator by 7:
So, in the standard form.
(ii)
Denominator is -36, which is negative.
Multiplying both the numerator and the denominator by -1:
H.C.F. of 8 and 36 is 4.
Dividing its numerator and denominator by 4:
So, in the standard form.
(iii)
H.C.F. of 27 and 45 is 9.
Dividing its numerator and denominator by 9:
Hence, in the standard form.
H.C.F. of 14 and 49 is 7.
Dividing both the numerator and the denominator by 7.
H.C.F. of 91 and 78 is 13.
Dividing both the numerator and the denominator by 13:
H.C.F. of 68 and 119 is 17.
Dividing both the numerator and the denominator by 17:
H.C.F. of 87 and 116 is 29.
Dividing both the numerator and the denominator by 29:
The denominator is negative.
Multiplying both the numerator and denominator by -1:
H.C.F. of 299 and 161 is 23.
Dividing both the numerator and the denominator by 23:
Page No 61:
Question 18:
Fill in the blanks:
(i)
(ii)
Answer:
(i)
(ii)
Page No 61:
Question 19:
Which of the following are pairs of equivalent rational numbers?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
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:
Find x such that:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
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×(−5)
=> x = −30
(v)
=>
=> x= (−4)
vi)
=>
=>
=>
x= (−24)
Page No 61:
Question 21:
Which of the following rational numbers are equal?
(i)
(ii)
(iii)
Answer:
(i)
8×15 =120
And ( −10)×(−12)=120
8×15 =(−10) ×(−12)
Therefore, the rational numbers are equal.
ii)
(−3)×(−21) =63
And 7× 9=63
∴ (−3)×(−21) =7×9
Therefore, the rational numbers are equal.
(iii)
(−8) × 21 = −168
And 15 ×(−14) = − 210
(−8) × 21 ≠ 15 × 14
Therefore, the rational numbers are not equal.
Page No 61:
Question 22:
State whether the given statement is true of false:
(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) The quotient of two integers is always a rational number.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.
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:
Represent each of the following rational numbers on the number line:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
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:
Which of the two rational numbers is greater in each of the following pairs?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 66:
Question 3:
Which of the two rational numbers is greater in each of the following pairs?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 66:
Question 4:
Fill in the blanks with the correct symbol out of >, = and <:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 66:
Question 5:
Arrange the following rational numbers in ascending order:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 66:
Question 6:
Arrange the following rational numbers in descending order:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 66:
Question 7:
Which of the following statements are true?
(i) lies to the left of 0 on the number line.
(ii) lies to the right of 0 on the number line.
(iii) lie on opposite sides of 0 on the number line.
(iv) lies to the left of 0 on the number line.
(v) lies on the right of on the number line.
Answer:
Page No 67:
Question 8:
Find five rational numbers between −3 and −2.
Answer:
Page No 67:
Question 9:
Find five rational numbers between −1 and 1.
Answer:
Page No 67:
Question 10:
Find five rational numbers between and .
Answer:
Page No 69:
Question 1:
Add the following rational numbers:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
=
(vi)
(vii)
(viii)
Page No 70:
Question 2:
Add the following rational numbers:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
(i)
(ii)
(iii)
(iv)
The denominators of the given rational numbers are 27 and 18.
L.C.M. of 27 and 18 is 54.
(v)
The denominators of the given rational numbers are 36 and 12.
L.C.M. of 36 and 12 is 36.
(vi)
(vii)
(viii)
Page No 70:
Question 3:
Evaluate:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
(ii)
Page No 70:
Question 4:
Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 70:
Question 5:
Express each of the following rational numbers as the sum of an integer and a rational number:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 72:
Question 1:
Find the additive inverse of:
(i) 5
(ii) −9
(iii)
(iv)
(v)
(vi)
(vii) 0
(viii)
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 of 0 is 0.
(viii) Additive inverse of
Page No 72:
Question 2:
Subtract:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
Answer:
(vi)
.
Page No 72:
Question 3:
Evaluate:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
[L.C.M. of 8 and 4 is 8.]
Page No 72:
Question 4:
Subtract the sum of and from the sum of and .
Answer:
Page No 72:
Question 5:
The sum of two rational numbers is . If one of them is , find the other.
Answer:
Page No 72:
Question 6:
The sum of two rational numbers is . If one of them is , find the other.
Answer:
Page No 72:
Question 7:
The sum of two rational numbers is −3. If one of them is , find the other.
Answer:
Page No 72:
Question 8:
The sum of two rational numbers is . If one of them is −5, find the other.
Answer:
Page No 72:
Question 9:
What should be added to to get ?
Answer:
Let the required number be x.
Page No 72:
Question 10:
What should be added to to get 3?
Answer:
Let the number that is to be added be x.
Page No 72:
Question 11:
What should be added to to get ?
Answer:
Let the number that is to be added be x.
Page No 72:
Question 12:
What should be added to to get −1?
Answer:
Let the number that is to be added be x.
Page No 73:
Question 13:
What should be added to to get 1?
Answer:
Page No 73:
Question 14:
What should be subtracted from to get ?
Answer:
Page No 73:
Question 15:
What should be subtracted from to get ?
Answer:
Page No 73:
Question 16:
What should be subtracted from to get 1?
Answer:
Page No 75:
Question 1:
Multiply:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Answer:
Page No 75:
Question 2:
Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 75:
Question 3:
Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 75:
Question 4:
Simplify:
(i)
(ii)
(iii)
(iv)
Answer:
Page No 75:
Question 5:
Find the cost of metres of cloth at Rs per metre.
Answer:
Page No 75:
Question 6:
A bus is moving at an average speed of km/h. How much distance will it cover in huors?
Answer:
Page No 78:
Question 1:
Find the multiplicative inverse of reciprocal of each of the following:
(i) 18
(ii) −16
(iii)
(iv)
(v)
(vi)
(vii) −1
(viii) 0
Answer:
Page No 78:
Question 2:
Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 78:
Question 3:
Fill in the blanks:
(i) (......) ÷
(ii) (......) ÷
(iii)
(iv)
Answer:
Page No 78:
Question 4:
Divide the sum of and by their difference.
Answer:
Page No 78:
Question 5:
By what number should be divided to get ?
Answer:
Page No 78:
Question 6:
By what number should be multiplied to get 24?
Answer:
Page No 78:
Question 7:
The product of two rational numbers is 10. If one of the numbers is −8, find the other.
Answer:
Page No 78:
Question 8:
The product of two rational numbers is −9. If one of the numbers is −12, find the other.
Answer:
Page No 78:
Question 9:
The product of two rational numbers is . If one of the numbers is , find the other.
Answer:
Page No 78:
Question 10:
By what rational number should be multiplied to obtain ?
Answer:
Page No 78:
Question 11:
If 24 pairs of trousers of equal size can be prepared with 54 m of cloth, what length of cloth is required for each pair of trousers?
Answer:
Page No 78:
Question 12:
How many pieces, each of length m, can be cut from a rope of length 30 m?
Answer:
Page No 78:
Question 13:
The cost of metres of cloth is Rs . Find the cost of cloth per metre.
Answer:
Page No 79:
Question 1:
Mark (✓) against the correct answer
in standard form is
(a)
(b)
(c)
(d) none of these
Answer:
Page No 79:
Question 2:
Mark (✓) against the correct answer
in standard form is
(a)
(b)
(c)
(d) none of these
Answer:
Page No 79:
Question 3:
Mark (✓) against the correct answer
If then the value of x is
(a) −14
(b) 14
(c) 21
(d) −21
Answer:
Page No 79:
Question 4:
What should be added to to get 1?
(a)
(b)
(c)
(d)
Answer:
Page No 79:
Question 5:
What should be subtracted from to get ?
(a)
(b)
(c)
(d)
Answer:
Page No 79:
Question 6:
Mark (✓) against the correct answer
Which is smaller out of ?
(a)
(b)
(c) cannot be compared
Answer:
Page No 79:
Question 7:
Mark (✓) against the correct answer
Which is larger out of and ?
(a)
(b)
(c) cannot be compared
Answer:
Page No 79:
Question 8:
Mark (✓) against the correct answer
Reciprocal of −6 is
(a) 6
(b)
(c)
(d) none of these
Answer:
Page No 79:
Question 9:
Mark (✓) against the correct answer
Multiplicative inverse of is
(a)
(b)
(c)
(d) none of these
Answer:
Page No 79:
Question 10:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 79:
Question 11:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 12:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 13:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 14:
Which is greater between and ?
(a)
(b)
(c) both are equal
Answer:
The correct option is (b).
Page No 80:
Question 15:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 16:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 17:
Mark (✓) against the correct answer
(a)
(b) 2
(c)
(d)
Answer:
Page No 80:
Question 18:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 80:
Question 19:
Mark (✓) against the correct answer
(a) not defined
(b)
(c) 0
(d)
Answer:
Page No 80:
Question 20:
Mark (✓) against the correct answer
(a)
(b) 0
(c)
(d) not defined
Answer:
Page No 82:
Question 1:
Express each of the following rational numbers in standard form:
(i)
(ii)
(iii)
Answer:
Page No 82:
Question 2:
List five rational numbers between −2 and −1.
Answer:
Page No 82:
Question 3:
The sum of two rational numbers is −4. If one of them is , find the other.
Answer:
Page No 82:
Question 4:
What should be added to to get ?
Answer:
Hence , the other number is
Page No 82:
Question 5:
A car is moving at an average speed of km per hour. How much distance will it cover in hours?
Answer:
Page No 82:
Question 6:
By what number should be divided to obtain ?
Answer:
Page No 82:
Question 7:
How many pieces, each of length m, can be cut from a rope of length 45 m?
Answer:
Page No 82:
Question 8:
Find the cost of m of cloth at Rs per metre.
Answer:
Page No 82:
Question 9:
Mark (✓) against the correct answer
in standard form is
(a)
(b)
(c)
(d) none of these
Answer:
Page No 82:
Question 10:
Mark (✓) against the correct answer
What should be subtracted from to get ?
(a)
(b)
(c)
(d)
Answer:
Page No 82:
Question 11:
Mark (✓) against the correct answer
The product of two numbers is . If one of them is , the other number is
(a)
(b)
(c)
(d)
Answer:
Page No 82:
Question 12:
Mark (✓) against the correct answer
The multiplicative inverse of is
(a)
(b)
(c)
(d) none of these
Answer:
Page No 82:
Question 13:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
Page No 82:
Question 14:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d) none of these
Answer:
Page No 82:
Question 15:
Mark (✓) against the correct answer
Which is smaller between and ?
(a)
(b)
(c) cannot be compared
Answer:
Page No 83:
Question 16:
Fill in the blanks.
(i)
(ii)
(iii)
(iv) Multiplicative inverse of is ...... .
Answer:
Page No 83:
Question 17:
Write 'T' for true and 'F' for false for each of the following:
(i) lies to the left of 0 on the number line.
(ii) lie on opposite side of 0 on the number line.
(iii) lies to the left of 0 on the number line.
(iv) .
(v) is the largest among .
Answer:
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