ML Aggarwal Class 8 Chapter 1 Rational Numbers Exercise 1.3
Exercise 1.3
Question 1
Sol :
(i)⇒6−7×1430
=6×14−7×30
=−84210
=−25
(ii) 623×127
⇒203×97
⇒20×93×7
=18021
=607
(iii) 25−9×−310
=25×(−3)−9×10
=−75−90
=−5−6
=56
Question 2
Sol :
(i) To verify commutative property of multiplication, we have
to show 45×−78=−78×45
L.H.S ⇒ 4×−75×8
⇒ −2840
L.H.S ⇒ −710
R.H.S⇒ −78×45
⇒−7×48×5
⇒−2840
R.H.S⇒ −710
∴ L.H.S =R.H.S∴ Commutative property of multiplication is verified
Question 3
Sol :
35×(−47×−89)=(35×−47)×−89
L.H.S =35×(−47×−89)
=35×(−4×(−8)7×9)
=35×(3263)
=3×325×63
=96315
L.H.S⇒ 32165
R.H.S =(35×−47)×(−89)=(−3×(−4)5×7)×(−89)=−1235×−89=−12×(−8)35×9=96315R.H.S=32105
L.H.S=R.H.S, HENCE PROVED∴This law is called associative property of multiplication
(ii) 59×(−32+75)=59×−32+59×75
L.H.S =59×(−32+75)
=59×((−3×5)+(7×2)10) LCM of 2,5=10
=59×(−15+1410)
=59×(−110)
L.H.S= −118
R.H.S= (59×−32)+(59×75)
(5×(−3)18]+[5×79×5]
=[5×(−3)18]+[5×79×5]
=−1518+3545
=(−15×5)+(35×2)90
=−75+7090
=−590
R.H.S =−118
L.H.S = R.H,S, Hence provedThis law is called distributive law of multiplication over addition
Question 4
Sol :
(i) 12 reciprocal of 12 =112
∴ 112 is multiplicative inverse of 12
ii} reciprocal of 23=32∴32 is multipl:cative inverse of 23
(iii) reciprocal of −47=7−4 or −74
∴−74 is multiplicative inverse of −47
(iv) −38×(−713)=−3×(−7)8×13=21104
reciprocal of 21104 in 10421
∴ 10421 in multiplicative inverse of −38×(−713)
Question 5
Sol :
(i) 25×−37−114=37×35
=2×(−3)5×7−114−(3×3)7×5
=−635−114−935
⇒(−6×2)−(1×5)−(9×2)70 LCM OF 35,14,35=70
=−12−5−1870
=−3570
=−12
(ii) 89×45+56−95×89
=(8×4)9×5+56−(9×8)(5×9)
=3245+56−7245
=(32×2)+(5×15)−(72×2)90 L.C.M of 45,6,45= 90
=64+75−14490
⇒64+75−14490
=−590
⇒ −118
(ii) −37×1415×712×(−3035)
=−3×14×77×15×12×(−3035)
=−2941260×(−3035)
=−294×(−30)1260×35
15
Question 6
Sol :
P=−827,q=34, r=−1215
(i) P(q× r)=(p×q)× r
L.H.S⇒P x (q x r)
=−827×(34×(−1215))
=−827×(3×(−12)4×15)
=−827×(−3660)
=−8×(−36)27×60
L⋅H⋅S=845R⋅H⋅S=(P×q)× r=(−827×34)×(−1215)=(−8×327×4)×(−1215)=−24108×(−1215)=−24×−12108×15
R.H.S =845
∴ L.H.S = R.H.S, Hence verified
(ii)
P×(q− r)=P×q−P×r.L.H⋅S=P×(q− r)=−827×(34−(−1215))=−827×(34+1215)=−827×((3×15)+(12×4)60)=−827×(45+4860)=−827×9360=−827×3120
L.H.S =−62135
R.H.S =−p×q−P× r
⇒−827×34−(−827×(−1215)
⇒−8×327×4−(−8×(−12)27×15)
⇒−24108−96405
⇒−29−32135
⇒(−2×15)−(32×1)135
=−30−32135
R⋅H⋅S=−62135
∴LHS= RHS; Hence veritied.
Question 7
Sol :
(i) 23×−45 is a Rational number
(ii) 5481×−63108=−63108×5481
(iii) 45×1=45=1×45
(iv) 5−12×−125=1=−125×5−12
(v) 37×(−28×59)=(37×−28)×59
(vi) −89×[413+517]=(−89×413)+(−89×517)
(vii) −613×[89−47]=−613×89−(−613×47)
(viii) 1625×0=0
(ix) Not defined
x) 1,−1 xi ⟩x2 xii) 1 xiii) negative
Question 8
Sol :
NO,
= 45×(−114)
=45×(−54)
=−1≠1
∴−114 is not multiplicative inverse of 45
∴ multiplicative inverse of 45 should be 54
Question 9
Sol :
(i) {75×(−312)}+{75+512}
=75×{−312+512} (-i distributive property)
=75×{−3+512}
=75×212
=730
(ii) {916×412}+{916×(−39)}
916×{412+(−39)}(∵ distributive property )
916×{13+(−13)}
916{13−13}
916×0=0
Question 10
Sol :
Additive inverse of 9=-9
Multiplicative inverse of 9=19
Required Sum =−9+19=−81+19=−809=−889
Question 11
Sol :
Additive inverse of −27=27
Multiplicative inverse ot −27=−72
Required product =27×−72
=-1
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