NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1
- Watch the Video given above for detailed Explanation -
Chapter 9 : Rational Numbers
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1
Question 1... Class 7 Maths Ex.9.1
List five rational numbers between:
(i) –1 and 0
Explanation :
Given rational numbers are
⇒ -1/1 and 0/1
( To find 5 rational numbers, we need to multiply it by a larger number )
Step 1. So, Multiply numerator and denominator by 6 in both the rational numbers
⇒ -1x6/1x6 and 0x6/1x6
# Now, Resultant rational numbers are
⇒ -6/6 and 0/6
Step 2. Now, you can easily write 5 rational number between -6/6 and 0/6
Ans. -6/6 | -5/6 | -4/6 | -3/6 | -2/6 | -1/6 | 0/6
Write your Solution like this
Solution :
(ii) –2 and –1
Explanation :
Given rational numbers are
⇒ -2/1 and -1/1
( To find 5 rational numbers, we need to multiply it by a larger number )
Step 1. So, Multiply numerator and denominator by 6 in both the rational numbers
⇒ -2x6/1x6 and -1x6/1x6
# Now, Resultant rational numbers are
⇒ -12/6 and -6/6
Step 2. Now, you can easily write 5 rational number between -12/6 and -6/6
Ans. -12/6 | -11/6 | -10/6 | -9/6 | -8/6 | -7/6 | -6/6
Write your Solution like this
Solution :
(iii) -4/5 & -2/3
Explanation :
Given rational numbers are
⇒ -4/5 and -2/3
Step 1. First we need to make the denominators equal,
To do so, just cross multiply the denominators to each other
⇒-4x3/5x3 and -2x5/3x5
# Now, The Resultant rational numbers are
⇒ -12/15 and -10/15
Now,
( To find 5 rational numbers, we need to multiply it by a larger number )
Step 2. So, Multiply numerator and denominator by 6 in both the rational numbers
⇒ -12x6/15x6 and -10x6/15x6
# Now, Resultant rational numbers are
⇒ -72/90 and -60/90
Step 3. Now, you can easily write 5 rational number between -72/90 and -60/90
Ans. -72/90 | -71/90 | -70/90 | -69/90 | -68/90 | -77/90 | -60/90
Write your Solution like this
Solution :
(iv) -1/2 and 2/3
Explanation :
Given rational numbers are
⇒ -1/2 and 2/3
Step 1. First we need to make the denominators equal,
To do so, just cross multiply the denominators to each other
⇒-1x3/2x3 and 2x2/3x2
# Now, The Resultant rational numbers are
⇒ -3/6 and 4/6
Step 2. Now, you can easily write 5 rational number between -3/6 and 4/6
Ans. -3/6 | -2/6 | -1/6 | 1/6 | 2/6 | 3/6 | 4/6
Write your Solution like this
Solution :
Question 2... Class 7 Maths Ex.9.1
Write four more rational numbers in each of the following patterns :
(i) -3/5, -6/10, -9/15, -12/15, ......
Explanation :
In the given pattern of the Rational Numbers, we can observe that the numerator and denominator are the multiples of 3 and 5.
⇒ (-3×1)/(5×1), (-3×2)/(5×2), (-3×3)/(5×3), (-3×4)/(5×4)
Therefore, The Next Four Rational Number will be..
⇒ (-3×5)/(5×5), (-3×6)/(5×6), (-3×7)/(5×7), (-3×8)/(5×8)
= -15/25, -18/30, -21/35, -24/40
Write your Solution like this
Solution :
(ii) -1/4, -2/8, -3/12, ......
Explanation :
In the given pattern of the Rational Numbers, we can observe that the numerator and denominator are the multiples of 1 and 4.
⇒ (-1×1)/(4×1), (-1×2)/(4×2), (-1×3)/(1×3)
Therefore, The Next Four Rational Number will be..
⇒ (-1×4)/(4×4), (-1×5)/(4×5), (-1×6)/(4×6), (-1×7)/(4×7)
= -4/16, -5/20, -6/24, -7/28
Write your Solution like this
Solution :
(iii) -1/6, 2/-12, 3/-18, 4/-24, ......
Explanation :
In the given pattern of the Rational Numbers, we can observe that the numerator and denominator are the multiples of 1 and 6.
⇒ (-1×1)/(6×1), (1×2)/(-6×2), (1×3)/(-6×3), (1×4)/(-6×4)
Therefore, The Next Four Rational Number will be..
⇒ (1×5)/(-6×5), (1×6)/(-6×6), (1×7)/(-6×7), (1×8)/(-6×8)
= 5/-30, 6/-36, 7/-42, 8/-48
Write your Solution like this
Solution :
(iv) -2/3, 2/-3, 4/-6, 6/-9, ......
Explanation :
In the given pattern of the Rational Numbers, we can observe that the numerator and denominator are the multiples of 2 and 3.
⇒ (-2×1)/(3×1), (2×1)/(-3×1), (2×2)/(-3×2), (2×3)/(-3×3)
Therefore, The Next Four Rational Number will be..
⇒ (2×4)/(-3×4), (2×5)/(-3×5), (2×6)/(-3×6), (2×7)/(-3×7)
= 8/-12, 10/-15, 12/-18, 14/-21
Write your Solution like this
Solution :
Question 3... Class 7 Maths Ex.9.1
Give four rational numbers equivalent to :
(i) -2/7
Explanation :
To make equivalent rational Number,
We need to multiply both Numerator & Denominator with a Same Natural number
Therefore,
The four rational numbers equivalent to -2/7 are...
⇒ (-2×2)/(7×2), (-2×3)/(7×3), (-2×4)/(7×4), (-2×5)/(7×5)
= -4/14, -6/21, -8/28, -10/35
Write your Solution like this
Solution :
(ii) 5/-3
Explanation :
To make equivalent rational Number,
We need to multiply both Numerator & Denominator with a Same Natural number
Therefore,
The four rational numbers equivalent to 5/-3 are...
⇒ (5×2)/(-3×2), (5×3)/(-3×3), (5×4)/(-3×4), (5×5)/(-3×5)
= 10/-6, 15/-9, 20/-12, 25/-15
Write your Solution like this
Solution :
(iii) 4/9
Explanation :
To make equivalent rational Number,
We need to multiply both Numerator & Denominator with a Same Natural number
Therefore,
The four rational numbers equivalent to 4/9 are...
⇒ (4×2)/(9×2), (4×3)/(9×3), (4×4)/(9×4), (4×5)/(9×5)
= 8/18, 12/27, 16/36, 20/45
Write your Solution like this
Solution :
Question 4... Class 7 Maths Ex.9.1
Draw the number line and represent the following rational numbers on it :
(i) 3/4
Explanation :
We know that 3/4 is greater than 0 but less than 1.
Therefore, 3/4 lies between 0 and 1.
So to represent 3/4 on number line we need to...
Step 1. Divide the Number line from 0 to 1 in four equal parts (as denominator is four)
Step 2. Now mark the Rational Number 3/4 on it
Write your Solution like this
Solution :
(ii) -5/8
Explanation :
We know that -5/8 is greater than -1 but less than 0.
Therefore, -8/8 lies between 0 and -1.
So to represent -8/8 on number line we need to...
Step 1. Divide the Number line from 0 to -1 in Eight equal parts (as denominator is eight)
Step 2. Now mark the Rational Number -5/8 on it
Write your Solution like this
Solution :
(iii) -7/4
Explanation :
We know that -7/4 is greater than -1 but less than 0.
Therefore, -7/4 lies between 0 and -2.
So to represent -7/4 on number line we need to...
Step 1. Divide the Number line from 0 to -1 & from -1 to -2 in four equal parts (as denominator is four)
Step 2. Now mark the Rational Number -7/4 on it
Write your Solution like this
Solution :
(iv) 7/8
Explanation :
We know that 7/8 is greater than 0 but less than 1.
Therefore, 7/8 lies between 0 and 1.
So to represent 7/8 on number line we need to...
Step 1. Divide the Number line from 0 to 1 in Eight equal parts (as denominator is eight)
Step 2. Now mark the Rational Number 7/8 on it
Write your Solution like this
Solution :
Question 5... Class 7 Maths Ex.9.1
The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.
Explanation :
By observing the figure, we can say that,
The distance between A and B = 1 unit
And it is divided into 3 equal parts = AP = PQ = QB = 1/3
Therefore,
P = 2 + (1/3)
= (6 + 1)/ 3
= 7/3
&
Q = 2 + (2/3)
= (6 + 2)/ 3
= 8/3
Similarly,
The distance between U and T = 1 unit
And it is divided into 3 equal parts = TR = RS = SU = 1/3
Therefore,
R = – 1 + (-1/3)
= (–3 – 1)/ 3
= – 4/3
&
S = – 1 + (– 2/3)
= (– 3 – 2)/ 3
= – 5/3
Write your Solution like this
Solution :
The distance between A and B = 1 unit
And it is divided into 3 equal parts = AP = PQ = QB = 1/3
Therefore,
P = 2 + (1/3)
P = (6 + 1)/ 3
P = 7/3
&
Q = 2 + (2/3)
Q = (6 + 2)/ 3
Q = 8/3
Similarly,
The distance between U and T = 1 unit
And it is divided into 3 equal parts = TR = RS = SU = 1/3
Therefore,
R = – 1 + (-1/3)
R = (–3 – 1)/ 3
R = – 4/3
&
S = – 1 + (– 2/3)
S = (– 3 – 2)/ 3
S = – 5/3
Question 6... Class 7 Maths Ex.9.1
Which of the following pairs represent the same rational number?
(i) -7/21 & 3/9
Explanation :
Given rational numbers are
⇒ -7/21 and 3/9
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ -1/3 and 1/3
Step 2. Now, you can easily said that the Rational Number are NOT Equal
Therefore , -7/21 ≠ 3/9
Write your Solution like this
Solution :
(ii) -16/20 & 20/-25
Explanation :
Given rational numbers are
⇒ -16/20 and 20/-25
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ -4/5 and 4/-5
Step 2. Now, you can easily said that the Rational Number are Equal
Therefore , -16/20 = 20/-25
Write your Solution like this
Solution :
(iii) -2/-3 & 2/3
Explanation :
Given rational numbers are
⇒ -2/-3 and 2/3
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ 2/3 and 2/3
Step 2. Now, you can easily said that the Rational Number are Equal
Therefore , -2/3 = 2/3
Write your Solution like this
Solution :
(iv) -3/5 & -12/20
Explanation :
Given rational numbers are
⇒ -3/5 and -12/20
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ -3/5 and -3/5
Step 2. Now, you can easily said that the Rational Number are Equal
Therefore , -3/5 = -12/20
Write your Solution like this
Solution :
(v) 8/-5 & -24/15
Explanation :
Given rational numbers are
⇒ 8/-5 and -24/15
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ 8/-5 and -8/5
Step 2. Now, you can easily said that the Rational Number are Equal
Therefore , 8/5 = -24/15
Write your Solution like this
Solution :
(vi) 1/3 & -1/9
Explanation :
Given rational numbers are
⇒ 1/3 and -1/9
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ 9/27 and -3/27
Step 2. Now, you can easily said that the Rational Number are NOT Equal
Therefore , 1/3 ≠ -1/9
Write your Solution like this
Solution :
(vii) -5/-9 & 5/-9
Explanation :
Given rational numbers are
⇒ -5/-9 and 5/9
Step 1. First we need to make the denominators equal,
To do so, just bring both the Rational Numbers in Simplest form (Standard form)
# Now, The Resultant rational numbers are
⇒ 5/9 and -5/9
Step 2. Now, you can easily said that the Rational Number are NOT Equal
Therefore , -5/-9 ≠ 5/-9
Write your Solution like this
Solution :
Question 7... Class 7 Maths Ex.9.1
Rewrite the following rational numbers in the simplest form :
(i) -8/6
Explanation :
Given rational number is
⇒ -8/6
To make the Rational Number in Standard form
We need to divide both the numerator & denominator by same number
⇒ -8 ÷ 2 / 6 ÷ 2
# Now, The Resultant rational number is
⇒ -4/3
Write your Solution like this
Solution :
(ii) 25/45
Explanation :
Given rational number is
⇒ 25/45
To make the Rational Number in Standard form
We need to divide both the numerator & denominator by same number
⇒ 25 ÷ 5 / 45 ÷ 5
# Now, The Resultant rational number is
⇒ 5/9
Write your Solution like this
Solution :
(iii) -44/72
Explanation :
Given rational number is
⇒ -44/72
To make the Rational Number in Standard form
We need to divide both the numerator & denominator by same number
⇒ -44 ÷ 4 / 72 ÷ 4
# Now, The Resultant rational number is
⇒ -11/18
Write your Solution like this
Solution :
(iv) -8/10
Explanation :
Given rational number is
⇒ -8/10
To make the Rational Number in Standard form
We need to divide both the numerator & denominator by same number
⇒ -8 ÷ 2 / 10 ÷ 2
# Now, The Resultant rational number is
⇒ -4/5
Write your Solution like this
Solution :
Question 8... Class 7 Maths Ex.9.1
Fill in the boxes with the correct symbol out of >, <, and =.
Solution :
(i) -5/7 & 2/3
Explanation :
Given rational number is
⇒ -5/7 & 2/3
To Compare the given Rational Number
We first need to make the denominator of both the Rational Number equal by taking LCM
The LCM of the denominators 7 and 3 is 21
⇒ (-5/7) = [(-5×3)/ (7×3)] = (-15/21)
And
⇒ (2/3) = [(2×7)/ (3×7)] = (14/21)
Now,
⇒ -15 < 14
So,
⇒ (-15/21) < (14/21)
Hence,
⇒ -5/7 [<] 2/3
Write your Solution like this
Solution :
(ii) -4/5 & -5/7
Explanation :
Given rational number is
⇒ -4/5 & -5/7
To Compare the given Rational Number
We first need to make the denominator of both the Rational Number equal by taking LCM
The LCM of the denominators 5 and 7 is 35
⇒ (-4/5) = [(-4×7)/ (5×7)] = (-28/35)
And
⇒ (-5/7) = [(-5×5)/ (7×5)] = (-25/35)
Now,
⇒ -28 < -25
So,
⇒ (-28/35) < (- 25/35)
Hence,
⇒ -4/5 [<] -5/7
Write your Solution like this
Solution :
(iii) -7/8 & 14/-16
Explanation :
Given rational number is
⇒ -7/8 & 14/-16
To Compare the given Rational Number
We first need to make the denominator of both the Rational Number equal by simplification
Divide both numerator and denominator ( 14/-16 ) by 2
So,
⇒ (-7/8) = (-7/8)
Hence,
⇒ -7/8 [=] 14/-16
Write your Solution like this
Solution :
(iv) -8/5 & -7/4
Explanation :
Given rational number is
⇒ -8/5 & -7/4
To Compare the given Rational Number
We first need to make the denominator of both the Rational Number equal by taking LCM
The LCM of the denominators 5 and 4 is 20
⇒ (-8/5) = [(-8×4)/ (5×4)] = (-32/20)
And
⇒ (-7/4) = [(-7×5)/ (4×5)] = (-35/20)
Now,
⇒ -32 > – 35
So,
⇒ (-32/20) > (- 35/20)
Hence,
⇒ -8/5 [>] -7/4
Write your Solution like this
Solution :
(v) 1/-3 & -1/4
Explanation :
Given rational number is
⇒ 1/-3 & -1/4
To Compare the given Rational Number
We first need to make the denominator of both the Rational Number equal by taking LCM
The LCM of the denominators 3 and 4 is 12
⇒ (-1/3) = [(-1×4)/ (3×4)] = (-4/12)
And
⇒ (-1/4) = [(-1×3)/ (4×3)] = (-3/12)
Now,
⇒ -4 < – 3
So,
⇒ (-4/12) < (- 3/12)
Hence,
⇒ 1/-3 [<] -1/4
Write your Solution like this
Solution :
(vi) 5/-11 & -5/11
Explanation :
Given rational number is
⇒ 5/-11 & -5/11
The given Rational Number are already have same denominator
so, we can directly compare them
Hence,
⇒ 5/-11 [=] -5/11
Write your Solution like this
Solution :
(vii) 0 & -7/6
Explanation :
Given rational number is
⇒ 0 & -7/6
Since Every Negative Rational Number is less then 0
Hence,
= 0 [>] -7/6
Write your Solution like this
Solution :
Question 9... Class 7 Maths Ex.9.1
Which is greater in each of the following :
(i) 2/3 and 5/2
Explanation :
To Compare the given Rational Numbers
We first need to make the denominator of both the Rational Numbers equal by taking LCM
Then we can easily compare the given Rational number...
So, The LCM of the denominators 3 and 2 is 6
⇒ (2/3) = [(2 × 2)/ (3 × 2)] = (4/6)
And
⇒ (5/2) = [(5 × 3)/ (2 × 3)] = (15/6)
Now,
⇒ 4 < 15
So, (4/6) < (15/6)
∴ 2/3 < 5/2
Hence, 5/2 is greater.
Write your Solution like this
Solution :
(ii) -5/6 and -4/3
Explanation :
To Compare the given Rational Numbers
We first need to make the denominator of both the Rational Numbers equal by taking LCM
Then we can easily compare the given Rational number...
So, The LCM of the denominators 6 and 3 is 6
⇒ (-5/6) = [(-5 × 1)/ (6 × 1)] = (-5/6)
And
⇒ (-4/3) = [(-4 × 2)/ (3 × 2)] = (-8/6)
Now,
⇒ -5 > -8
So, (-5/6) > (- 8/6)
∴ -5/6 > -4/3
Hence, – 5/6 is greater.
Write your Solution like this
Solution :
(iii) -3/4 and 2/-3
Explanation :
To Compare the given Rational Numbers
We first need to make the denominator of both the Rational Numbers equal by taking LCM
Then we can easily compare the given Rational number...
So, The LCM of the denominators 4 and 3 is 12
⇒ (-3/4) = [(-3 × 3)/ (4 × 3)] = (-9/12)
And
⇒ (-2/3) = [(2 × 4)/ (-3 × 4)] = (8/-12)
Now,
⇒ -9 < -8
So, (-9/12) < (- 8/12)
∴ -3/4 < 2/-3
Hence, 2/-3 is greater.
Write your Solution like this
Solution :
(iv) -1/4 and 1/4
Explanation :
The given Rational Numbers are already have same denominator
So, we do not need to take any LCM
Now, we can easily compare it as positive Rational Number is greater
Hence, 1/4 is greater Rational Number
Write your Solution like this
Solution :
(v)
Explanation :
To Compare the given Rational Numbers
We first need to convert this mixed fraction into improper fraction
⇒ (-7x3+2) /7 = -23/7
And
⇒ (-5x3+4)/7 = -19/5
make the denominator of both the Rational Numbers equal by taking LCM
Then we can easily compare the given Rational number...
So, The LCM of the denominators 7 and 5 is 35
⇒ (-23/7) = [(-23 × 5)/ (7 × 5)] = (-115/35)
And
⇒ (-19/5) = [(-19 × 7)/ (5 × 7)] = (-133/35)
Now,
⇒ -115 > -133
So, (-115/35) > (- 133/35)
Write your Solution like this
Solution :
Question 10... Class 7 Maths Ex.9.1
Write the following rational numbers in ascending order :-
(i) -3/5 , -2/5 , -1/5
Explanation :
The given Rational Numbers are already have same denominator
So, we do not need to take any LCM
Now, we can easily compare these Rational Number and arrange them in Ascending order
Write your Solution like this
Solution :
(ii) -1/3 , -2/9 , -4/3
Explanation :
To arrange these Rational Numbers in ascending order
We first need to make their denominator equal by taking LCM
So, The LCM of the denominators 3 , 9 and 3 is 9
⇒ (-1/3) = [(-1×3)/ (3×9)] = (-3/9)
⇒ (-2/9) = [(-2×1)/ (9×1)] = (-2/9)
⇒ (-4/3) = [(-4×3)/ (3×3)] = (-12/9)
Clearly,
⇒ (-12/9) < (-3/9) < (-2/9)
Hence,
⇒ (-4/3) < (-1/3) < (-2/9)
Write your Solution like this
Solution :
(iii) -3/7 , -3/2 , -3/4
Explanation :
To arrange these Rational Numbers in ascending order
We first need to make their denominator equal by taking LCM
So, The LCM of the denominators 7 , 2 and 4 is 28
⇒ (-3/7) = [(-3×4) /(7×4)] = (-12/28)
⇒ (-3/2) = [(-3×14)/(2×14)]= (-42/28)
⇒ (-3/4) = [(-3×7) /(4×7)] = (-21/28)
Clearly,
⇒ (-42/28) < (-21/28) < (-12/28)
Hence,
⇒ (-3/2) < (-3/4) < (-3/7)
Write your Solution like this
Solution :
Chapter 9 : Rational Numbers
Related links :-
Ø Chapter 7 : Whole Numbers
Ø Chapter 8 : Playing with Numbers
Ø Chapter 9 : Rational Numbers
Ø Chapter 10 : Basic Geometrical Ideas
Ø Chapter 11 : Understanding Elementary Shape
# Still have some Doubts?
--Feel Free to ask your Doubts here--
