NCERT Solutions for Chapter 9 Rational Numbers Class 7 Maths
Book Solutions1
List five rational numbers between:
(i) −1 and 0
(ii) −2 and −1
(iii) −4/5 and −2/3
(iv) −1/2 and 2/3
Answer
(i) −1 and 0
Let us write −1 and 0 as rational numbers with denominator 6.
⇒ −1=−6/6 and 0 = 0/6
∴ −6/6<−5/6<−4/6<−3/6<−2/6<−1/6<0
⇒ −1<−5/6<−2/3<−1/2<−1/3<−1/6<0
Therefore, five rational numbers between −1 and 0 would be
−56,−23,−12,−13,−16
(ii) −2 and −1
Let us write −2 and −1 as rational numbers with denominator 6.
⇒ −2=−12/6 and −1=−6/6
∴ −12/6<−11/6<−10/6<−9/6<−8/6<−7/6<−6/6
−2<−11/6<−5/3<−3/2<−4/3<−7/6<−1
Therefore, five rational numbers between −2 and −1 would be
−11/6,−5/3,−3/2,−4/3,−7/6
(iii) −4/5and −2/3
Let us write −4/5 and −2/3 as rational numbers with the same denominators.
⇒ −4/5=−36/45 and −2/3=−30/45
∴ −36/45<−35/45<−34/45<−33/45<−32/45<−31/45<−30/4
⇒ −4/5<−7/9<−34/45<−11/15<−32/45<−31/45<−2/3
Therefore, five rational numbers between −45−45 and −23−23 would be
−7/9,−34/45,−11/15,−32/45,−31/45,−2/3
(iv) −1/2 and 2/3
Let us write −1/2and 2/3 as rational numbers with the same denominators.
⇒ −1/2=−3/6 and 2/3=4/6
∴ −3/6<−2/6<−1/6<0<1/6<2/6<3/6<4/6
⇒ −1/2<−1/3<−1/6<0<1/6<1/3<1/2<2/3
Therefore, five rational numbers between −1/2 and 2/3 would be −1/3,−1/6,0,1/6,1/3
Let us write −1 and 0 as rational numbers with denominator 6.
⇒ −1=−6/6 and 0 = 0/6
∴ −6/6<−5/6<−4/6<−3/6<−2/6<−1/6<0
⇒ −1<−5/6<−2/3<−1/2<−1/3<−1/6<0
Therefore, five rational numbers between −1 and 0 would be
−56,−23,−12,−13,−16
(ii) −2 and −1
Let us write −2 and −1 as rational numbers with denominator 6.
⇒ −2=−12/6 and −1=−6/6
∴ −12/6<−11/6<−10/6<−9/6<−8/6<−7/6<−6/6
−2<−11/6<−5/3<−3/2<−4/3<−7/6<−1
Therefore, five rational numbers between −2 and −1 would be
−11/6,−5/3,−3/2,−4/3,−7/6
(iii) −4/5and −2/3
Let us write −4/5 and −2/3 as rational numbers with the same denominators.
⇒ −4/5=−36/45 and −2/3=−30/45
∴ −36/45<−35/45<−34/45<−33/45<−32/45<−31/45<−30/4
⇒ −4/5<−7/9<−34/45<−11/15<−32/45<−31/45<−2/3
Therefore, five rational numbers between −45−45 and −23−23 would be
−7/9,−34/45,−11/15,−32/45,−31/45,−2/3
(iv) −1/2 and 2/3
Let us write −1/2and 2/3 as rational numbers with the same denominators.
⇒ −1/2=−3/6 and 2/3=4/6
∴ −3/6<−2/6<−1/6<0<1/6<2/6<3/6<4/6
⇒ −1/2<−1/3<−1/6<0<1/6<1/3<1/2<2/3
Therefore, five rational numbers between −1/2 and 2/3 would be −1/3,−1/6,0,1/6,1/3
Exercise 9.1
Page Number 182
2
Write four more rational numbers in each of the following patterns:
(i) −3/5,−6/10,−9/15,−12/20,.........
(ii) −1/4,−2/8,−3/12,.........
(iii) −1/6,2/−12,3/−18,4/−24,.........
(iv) −2/3,2/−3,4/−6,6/−9,..........
Answer
(i) −3/5,−6/10,−9/15,−12/20,.......
⇒ (−3×1)/(5×1),(−3×2)/(5×2),(−3×3)/(5×3),(−3×4)/(5×4),........
Therefore, the next four rational numbers of this pattern would 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
(ii) −1/4,−2/8,−3/12,..........
⇒ (−1×1)/(4×1),(−1×2)/(4×2),(−1×3)/(4×3),..........
Therefore, the next four rational numbers of this pattern would 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
(iii) −1/6,2/−12,3/−18,4/−24,.........
⇒ (−1×1)/(6×1),(1×2)/(−6×2),(1×3)/(−6×3),(1×4)/(−6×4),.........
Therefore, the next four rational numbers of this pattern would 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
(iv) −2/3,2/−3,4/−6,6/−9,........
⇒(−2×1)/(3×1),(2×1)/(−3×1),(2×2)/(−3×2),(2×3)/(−3×3),.........
Therefore, the next four rational numbers of this pattern would 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
⇒ (−3×1)/(5×1),(−3×2)/(5×2),(−3×3)/(5×3),(−3×4)/(5×4),........
Therefore, the next four rational numbers of this pattern would 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
(ii) −1/4,−2/8,−3/12,..........
⇒ (−1×1)/(4×1),(−1×2)/(4×2),(−1×3)/(4×3),..........
Therefore, the next four rational numbers of this pattern would 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
(iii) −1/6,2/−12,3/−18,4/−24,.........
⇒ (−1×1)/(6×1),(1×2)/(−6×2),(1×3)/(−6×3),(1×4)/(−6×4),.........
Therefore, the next four rational numbers of this pattern would 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
(iv) −2/3,2/−3,4/−6,6/−9,........
⇒(−2×1)/(3×1),(2×1)/(−3×1),(2×2)/(−3×2),(2×3)/(−3×3),.........
Therefore, the next four rational numbers of this pattern would 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
Exercise 9.1
Page Number 182
3
Give four rational numbers equivalent to:
(i) −2/7
(ii) 5/−3
(iii) 4/9
Answer
(i) −2/7
(−2×2)/(7×2)=−4/14,(−2×3)/(7×3)
=−6/21,(−2×4)/(7×4)
=−8/28,(−2×5)/(7×5)
=−10/35
Therefore, four equivalent rational numbers are −4/14,−6/21,−8/28,−10/35
(ii) 5/−3
(5×2)/(−3×2)
=10/−6,(5×3)/(−3×3)
=15/−9, (5×4)/(−3×4)
=20/−12,(5×5)/(−3×5)
=25/−15
Therefore, four equivalent rational numbers are 10/−6,15/−9,20/−12,25/−15
(iii) 4/9
(4×2)/(9×2)
=8/18,(4×3)/(9×3)
=12/27,(4×4)/(9×4)
16/36,(4×5)/(9×5)
=20/45
Therefore, four equivalent rational numbers are 8/18,12/27,16/36,20/45
(−2×2)/(7×2)=−4/14,(−2×3)/(7×3)
=−6/21,(−2×4)/(7×4)
=−8/28,(−2×5)/(7×5)
=−10/35
Therefore, four equivalent rational numbers are −4/14,−6/21,−8/28,−10/35
(ii) 5/−3
(5×2)/(−3×2)
=10/−6,(5×3)/(−3×3)
=15/−9, (5×4)/(−3×4)
=20/−12,(5×5)/(−3×5)
=25/−15
Therefore, four equivalent rational numbers are 10/−6,15/−9,20/−12,25/−15
(iii) 4/9
(4×2)/(9×2)
=8/18,(4×3)/(9×3)
=12/27,(4×4)/(9×4)
16/36,(4×5)/(9×5)
=20/45
Therefore, four equivalent rational numbers are 8/18,12/27,16/36,20/45
Exercise 9.1
Page Number 183
4
Draw the number line and represent the following rational numbers on it:
(i) 3/4
(ii) −5/8
(iii) −7/4
(iv) 7/8
Answer
(i) 3/4
(ii) −5/8
(iii) −7/4
(iv) 7/8
(ii) −5/8
(iii) −7/4
(iv) 7/8
Exercise 9.1
Page Number 183
5
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.
Answer
Each part which is between the two numbers is divided into 3 parts.
Therefore, A = 6/3, P = 7/3,Q = 8/3 and B = 9/3
Similarly T = −3/3, R = −4/3, S = −5/3 and U = −6/3
Thus, the rational numbers represented P, Q, R and S are 7/3,8/3,−4/3 and −5/3 respectively.
Therefore, A = 6/3, P = 7/3,Q = 8/3 and B = 9/3
Similarly T = −3/3, R = −4/3, S = −5/3 and U = −6/3
Thus, the rational numbers represented P, Q, R and S are 7/3,8/3,−4/3 and −5/3 respectively.
Exercise 9.1
Page Number 183
6
Which of the following pairs represent the same rational numbers:
(i) −7/21 and 3/9
(ii) −16/20 and 20/−25
(iii) −2/−3and 2/3
(iv) −3/5 and −12/20
(v) 8/−5 and −24/15
(vi) 1/3 and −1/9
(vii) −5/−9 and 5/−9
Answer
(i) −7/21 and 3/9
⇒ −7/21= −1/3 and 3/9 = 1/3 [Converting into lowest term]
∵ −1/3≠1/3
∴ −7/21≠3/9
(ii) −16/20 and 20/−25
⇒ −16/20 = −4/5 and 20/−25 = 4/−5 [Converting into lowest term]
∵ −4/5 = −4/5
∴ −16/20 = 20/−25
(iii) −2/−3 and 2/3
⇒ −2/−3 = 2/3 and 2/3 = 2/3 [Converting into lowest term]
∵ 2/3 = 2/3
∴ −2/−3 = 2/3
(iv) −3/5 and −12/20
⇒ −3/5 = −3/5 and −12/20 = −3/5 [Converting into lowest term]
∵ −3/5 = −3/5
∴ −3/5 = −12/20
(v) 8/−5 and −24/15
⇒ 8/−5 = −8/5 and −24/15 = −8/5 [Converting into lowest term]
∵ −8/5 = −8/5
∴ 8/−5 = −24/15
(vi) 1/3 and −1/9
⇒ 1/3 = 1/3 and −1/9 = −1/9 [Converting into lowest term]
∵ 1/3≠−1/9
∴ 1/3≠−1/9
(vii) −5/−9 and 5/−9
⇒ −5/−9 = 5/9 and 5/−9 = 5/9 [Converting into lowest term]
∵ 5/9≠ 5/9
∴ −5/−9 ≠ 5/−9
⇒ −7/21= −1/3 and 3/9 = 1/3 [Converting into lowest term]
∵ −1/3≠1/3
∴ −7/21≠3/9
(ii) −16/20 and 20/−25
⇒ −16/20 = −4/5 and 20/−25 = 4/−5 [Converting into lowest term]
∵ −4/5 = −4/5
∴ −16/20 = 20/−25
(iii) −2/−3 and 2/3
⇒ −2/−3 = 2/3 and 2/3 = 2/3 [Converting into lowest term]
∵ 2/3 = 2/3
∴ −2/−3 = 2/3
(iv) −3/5 and −12/20
⇒ −3/5 = −3/5 and −12/20 = −3/5 [Converting into lowest term]
∵ −3/5 = −3/5
∴ −3/5 = −12/20
(v) 8/−5 and −24/15
⇒ 8/−5 = −8/5 and −24/15 = −8/5 [Converting into lowest term]
∵ −8/5 = −8/5
∴ 8/−5 = −24/15
(vi) 1/3 and −1/9
⇒ 1/3 = 1/3 and −1/9 = −1/9 [Converting into lowest term]
∵ 1/3≠−1/9
∴ 1/3≠−1/9
(vii) −5/−9 and 5/−9
⇒ −5/−9 = 5/9 and 5/−9 = 5/9 [Converting into lowest term]
∵ 5/9≠ 5/9
∴ −5/−9 ≠ 5/−9
Exercise 9.1
Page Number 183
7
Rewrite the following rational numbers in the simplest form:
(i) −8/6
(ii) 25/45
(iii) −44/72
(iv) −8/10
Answer
(i) −8/6 = (−8÷2)/(6÷2) = −43 [H.C.F. of 8 and 6 is 2]
(ii)25/45 = (25÷5)/(45÷5) = 5/9
[H.C.F. of 25 and 45 is 5]
(iii)−44/72= (−44÷4)/(72÷4) = −11/18 [H.C.F. of 44 and 72 is 4]
(iv) −8/10= (−8÷2)/(10÷2) = −4/5 [H.C.F. of 8 and 10 is 2]
(ii)25/45 = (25÷5)/(45÷5) = 5/9
[H.C.F. of 25 and 45 is 5]
(iii)−44/72= (−44÷4)/(72÷4) = −11/18 [H.C.F. of 44 and 72 is 4]
(iv) −8/10= (−8÷2)/(10÷2) = −4/5 [H.C.F. of 8 and 10 is 2]
Exercise 9.1
Page Number 183
8
Fill in the boxes with the correct symbol out of <, > and =:
(i) −5/7 ___ 2/3
(ii) −4/5 ___ −5/7
(iii) −7/8___ 14/−16
(iv) −8/5 ___ −7/4
(v) 1/−3 ___ −1/4
(vi) 5/−11 ___ −5/11
(vii) 0 ___−7/6
Answer
(i) −5/7 < 2/3
Since, the positive number if greater than negative number.
(ii) (−4×7)/(5×7)___ (−5×5)/(7×5)
⇒ −28/35 < −25/35
⇒ −4/5 < −5/7
(iii) (−7×2)/(8×2)___ {14×(−1)}/{−16×(−1)}
⇒ −14/16 = −14/16
⇒−7/8 = 14/−16
(iv) (−8×4)/(5×4)___ (−7×5)/(4×5)
⇒ −32/20 > −35/20
⇒ −8/5 > −7/4
(v) (1/−3) ___ (−1/4)
⇒1/−3 < −1/4
(vi) (5/−11)___ (−5/11)
⇒5/−11 = −5/11
(vii) 0 > −7/6
Since, 0 is greater than every negative number.
Since, the positive number if greater than negative number.
(ii) (−4×7)/(5×7)___ (−5×5)/(7×5)
⇒ −28/35 < −25/35
⇒ −4/5 < −5/7
(iii) (−7×2)/(8×2)___ {14×(−1)}/{−16×(−1)}
⇒ −14/16 = −14/16
⇒−7/8 = 14/−16
(iv) (−8×4)/(5×4)___ (−7×5)/(4×5)
⇒ −32/20 > −35/20
⇒ −8/5 > −7/4
(v) (1/−3) ___ (−1/4)
⇒1/−3 < −1/4
(vi) (5/−11)___ (−5/11)
⇒5/−11 = −5/11
(vii) 0 > −7/6
Since, 0 is greater than every negative number.
Exercise 9.1
Page Number 183
9
Which is greater in each of the following:
(i) 2/3,5/2
(ii) −5/6,−4/3
(iii) −3/4,2/−3
(iv) −1/4,1/4
(v) −3.2/7,−3.4/5
Answer
(i) (2×2)/(3×2)=4/6 and (5×3)/(2×3)=15/6
Since 4/6 < 15/6
Therefore 2/3 < 5/2
(ii) (−5×1)/(6×1)=−5/6 and (−4×2)/(3×2)=−8/6
Since −5/6 > −8/6 Therefore −5/6 > −4/3
(iii) (−3×3)/(4×3)=−9/12 and {2×(−4)}/{−3×(−4)}=−8/122
Since −9/12 < −8/12
Therefore −3/4 < 2/−3
(iv) −1/4 < 1/4 Since positive number is always greater than negative number.
(v) −3.2/7=−2.3/7=(−23×5)/(7×5)=−115/35 and −3.4/5=−19/5=(−19×7)/(5×7)=−133/35
Since −115/35 > −133/35
Therefore−3.2/7 > −3.4/5
Since 4/6 < 15/6
Therefore 2/3 < 5/2
(ii) (−5×1)/(6×1)=−5/6 and (−4×2)/(3×2)=−8/6
Since −5/6 > −8/6 Therefore −5/6 > −4/3
(iii) (−3×3)/(4×3)=−9/12 and {2×(−4)}/{−3×(−4)}=−8/122
Since −9/12 < −8/12
Therefore −3/4 < 2/−3
(iv) −1/4 < 1/4 Since positive number is always greater than negative number.
(v) −3.2/7=−2.3/7=(−23×5)/(7×5)=−115/35 and −3.4/5=−19/5=(−19×7)/(5×7)=−133/35
Since −115/35 > −133/35
Therefore−3.2/7 > −3.4/5
Exercise 9.1
Page Number 184
10
Write the following rational numbers in ascending order:
(i) −3/5,−2/5,−1/5
(ii) 1/3,−2/9,−4/3
(iii) −3/7,−3/2,−3/4
Answer
(i) −3/5,−2/5,−1/5⇒ −3/5<−2/5<−1/5
(ii) 1/3,−2/9,−4/3⇒3/9,−2/9,−12/9 [Converting into same denominator]
Now −12/9<−2/9<3/9⇒ −4/3<−2/9<1/3
(iii) −3/7,−3/2,−3/4
⇒ −3/2<−3/4<−3/7
(ii) 1/3,−2/9,−4/3⇒3/9,−2/9,−12/9 [Converting into same denominator]
Now −12/9<−2/9<3/9⇒ −4/3<−2/9<1/3
(iii) −3/7,−3/2,−3/4
⇒ −3/2<−3/4<−3/7
Exercise 9.1
Page Number 184
1
Find the sum:
(i) 5/4+(−11/4)
(ii) 5/3+3/5
(iii) −9/10+22/15
(iv) −3/−11+5/9
(v) −8/19+(−2)/57
(vi) −2/3+0
(vii) −2.1/3+4.3/5
Answer
(i) 5/4+(−11/4)
= (5−11)/4
= −6/4=−3/2
(ii) 5/3+3/5
= (5×5)/(3×5)+(3×3)/(5×3)
= 25/15+9/15 [L.C.M. of 3 and 5 is 15]
= (25+9)/15=34/15=2.4/15
(iii) −9/10+22/15
= (−9×3)/(10×3)+(22×2)/(15×2)
= −27/30+44/30 [L.C.M. of 10 and 15 is 30]
= (−27+44)/30=17/30
(iv) −3/−11+5/9
= (−3×9)/(−11×9)+(5×11)/(9×11)
= 27/99+55/99 [L.C.M. of 11 and 9 is 99]
= (27+55)/99=82/99
(v) −8/19+(−2)/57
= (−8×3)/(19×3)+{(−2)×15}/{7×1}
= −24/57+(−2)/57 [L.C.M. of 19 and 57 is 57]
= (−24−2)/57 = −26/57
= (5−11)/4
= −6/4=−3/2
(ii) 5/3+3/5
= (5×5)/(3×5)+(3×3)/(5×3)
= 25/15+9/15 [L.C.M. of 3 and 5 is 15]
= (25+9)/15=34/15=2.4/15
(iii) −9/10+22/15
= (−9×3)/(10×3)+(22×2)/(15×2)
= −27/30+44/30 [L.C.M. of 10 and 15 is 30]
= (−27+44)/30=17/30
(iv) −3/−11+5/9
= (−3×9)/(−11×9)+(5×11)/(9×11)
= 27/99+55/99 [L.C.M. of 11 and 9 is 99]
= (27+55)/99=82/99
(v) −8/19+(−2)/57
= (−8×3)/(19×3)+{(−2)×15}/{7×1}
= −24/57+(−2)/57 [L.C.M. of 19 and 57 is 57]
= (−24−2)/57 = −26/57
(vi) −2/3+0=−2/3
(vii) −2.1/3+4.3/5 = (−7/3+23/5) = (−7×5)/(3×5)+(23×3)/(5×3) = −35/15+69/15 [L.C.M. of 3 and 5 is 15]
= (−35+69)/15 = 34/15=2.4/15
Exercise 9.2
Page Number 190
2
Find:
(i) 7/24−17/36
(ii) 5/63−(−6/21)
(iii) −6/13−(−7/15)
(iv) −3/8−7/11
(v) −2.1/9−6
Answer
(i) 7/24−17/36
= (7×3)/(24×3)−(17×2)/(36×2)
= 21/72−34/72 [L.C.M. of 24 and 36 is 72]
= (21−34)/72
= −13/72
(ii) 5/63−(−6/21)= (5×1)/(63×1)−{(−6×3)/(21×3)}
= 5/63−(−18)/63 [L.C.M. of 63 and 21 is 63]
= {5−(−18)}/63
= 23/63
(iii) −6/13−(−7/15)
= (−6×15)/(13×15)−{(−7×13)/(15×13)}
= (−90/195)−(−91/195) [L.C.M. of 13 and 15 is 195]
= {−90−(−91)}/195
= (−90+91)/195
=1/195
(iv) −3/8−7/11
= (−3×11)/(8×11)−(7×8)/(11×8)
= −33/88−56/88
[L.C.M. of 8 and 11 is 88]
= (−33−56)/88
= −89/88
=−1.1/88
(v) −2.1/9−6
= (−19/9)(−6/1)
= (−19×1)/(9×1)−(6×9)/(1×9) [L.C.M. of 9 and 1 is 9]
= (−199−54)/9
= (−19−54)/9
= −73/9=−8.1/9
Exercise 9.2
Page Number 190
3
Find the product:
(i) 9/2×(−7/4)
(ii) 3/10×(−9)
(iii) −6/5×9/11
(iv) 3/7×(−2/5)
(v) 3/11×2/5
(vi) 3/−5×5/3
Answer
(i) 9/2×(−7/4)
= {9×(−7)}/{2×4}
= −63/8
=−7.7/8
(ii)3/10×(−9)
={3×(−9)}/10
=−27/10
−2.7/10
(iii) −6/5×9/11
={(−6)×9}/{5×11}
=−54/55
(iv) 3/7×(−2/5)
={3×(−2)}/{7×5}
=−6/35
(v) 3/11×2/5
=(3×2)/(11×5)
=6/55
(vi) 3/−5×(−5/3)
={13−5}×{(−5/3)}
=1
= {9×(−7)}/{2×4}
= −63/8
=−7.7/8
(ii)3/10×(−9)
={3×(−9)}/10
=−27/10
−2.7/10
(iii) −6/5×9/11
={(−6)×9}/{5×11}
=−54/55
(iv) 3/7×(−2/5)
={3×(−2)}/{7×5}
=−6/35
(v) 3/11×2/5
=(3×2)/(11×5)
=6/55
(vi) 3/−5×(−5/3)
={13−5}×{(−5/3)}
=1
Exercise 9.2
Page Number 190
4
Find the value of:
(i) (−4)÷2/3
(ii) −3/5÷2
(iii) −4/5÷(−3)
(iv) −1/8÷3/4
(v) −2/13÷1/7
(vi) −7/12÷(2/13)
(vii) 3/13÷(−4/65)
Answer
(i) (−4)÷2/3
= (−4)×3/2
=(−2)×3
=−6
(ii) −3/5÷2
= −3/5×1/2
={(−3)×1}/{5×2}
=−3/10
(iii) −4/5÷(−3)
= (−4)/5×1/(−3)
={(−4)×1}/{5×(−3)}
=4/15
(iv) −1/8÷3/4
= −1/8×4/3
= ((−1)×1)/(2×3)
=−1/6
(v) −2/13÷1/7
= −2/13×7/1
=((−2)×7)/(13×1)
=−14/13
=−1.1/13
(vi) −7/12÷(−2/13)
= −7/12×13/(−2)
=((−7)×13)/(12×(−2))
=−91/24
=3.19/24
(vii) 3/13÷(−4/65)
= 3/13×65/(−4)
=(3×(−5))/(1×4)
=−15/4
=−3.3/4
= (−4)×3/2
=(−2)×3
=−6
(ii) −3/5÷2
= −3/5×1/2
={(−3)×1}/{5×2}
=−3/10
(iii) −4/5÷(−3)
= (−4)/5×1/(−3)
={(−4)×1}/{5×(−3)}
=4/15
(iv) −1/8÷3/4
= −1/8×4/3
= ((−1)×1)/(2×3)
=−1/6
(v) −2/13÷1/7
= −2/13×7/1
=((−2)×7)/(13×1)
=−14/13
=−1.1/13
(vi) −7/12÷(−2/13)
= −7/12×13/(−2)
=((−7)×13)/(12×(−2))
=−91/24
=3.19/24
(vii) 3/13÷(−4/65)
= 3/13×65/(−4)
=(3×(−5))/(1×4)
=−15/4
=−3.3/4
Exercise 9.2
Page Number 190