Solve the using suitable properties
(a) 8326429*(-98)+(-8326429)*(-2)
(b) (-7624928)*997+(7624928)*(-3)
(c) (-98)*(-9)+98. (d) (-237)*(-99)+237
(e) (-563)*(-999)+563 (f) 253*(100-1)
(g) 567*(100-1) (h) (-34)*1002
(I) (-67)*101. (j) (-84)*99
Answers
Step-by-step explanation:
8326429*(-98)+(8326429)*(-2)
Answer:
Step-by-step explanation:
Recall the properties
The distributive property of multiplication over the addition of integers is given by
If a,b,c are any three integers, then
a(b+c) = a×b +a×c
(a) 8326429×(-98)+(-8326429)×(-2)
Applying distributive property we get
a = 8326429, b = -98 and c = -2
8326429×(-98)+(-8326429)×(-2)
= 8326429((-98)+(-2))
= 8326429 × -100
= -832642900
8326429×(-98)+(-8326429)×(-2) = -832642900
b) (-7624928)×997+(7624928)*(-3)
Applying distributive property we get
a = 7624928, b = -997 and c = -3
= 7624928×(-997)+(7624928)×(-3)
= 7624928((-997)+(-3))
= 7624928× -1000
= -7624928000
(-7624928)×997+(7624928)*(-3) = -7624928000
c) (-98)×(-9)+98.
(-98)×(-9)+98.1 = (98)×(9)+98.1
Applying distributive property we get
a= 98, b = 9 and c = 1
(98)×(9)+98.1 = 98(9+1)
= 98×10
= 980
(-98)×(-9)+98 = 980
d) (-237)×(-99)+237
(-237)×(-99)+237 = (237)×(99)+237×(1)
Applying distributive property
a = 237, b = 99 and c = 1
(237)×(99)+237×(1) = 237(99+1)
= 237 × 100
= 23700
(-237)×(-99)+237 = 23700
e) (-563)×(-999)+563
(-563)×(-999)+563 = 563×999+563×1
Applying distributive property
a = 563, b = 999 and c= 1
= 563(999+1)
= 563 ×1000
= 563000
(-563)×(-999)+563 = 563000
f) 253×(100-1) = 253×(100+(-1))
Applying distributive property
a = 253, b = 100 and c = -1
= 253×(100+(-1)) = 253×100 + 253×(-1)
= 25300 - 253
= 25047
253×(100-1) = 25047
g) 567×(100-1) = 567×(100+(-1)
Applying distributive property
a = 567, b = 100 and c = -1
= 567×(100+(-1)) = 567×100 + 567×(-1)
= 56700 - 567
= 56133
567×(100-1) = 56133
h) (-34)×1002 = (-34) ( 1000 +2)
Applying distributive property
a = (-34) , b = 1000 and c = 2
= (-34) × 1000+ (-34) × 2
= -34000 -68
= - 34068
(-34)×1002 = - 34068
i) (-67)×101 = (-67)(100+1)
Applying distributive property
a = (-67) , b = 100 and c = 1
= (-67×100) + (-67×1)
= -6700 - 67
= -6767
(-67)×101 = -6767
j)(-84)×99 = (-84)(100 + (-1))
Applying distributive property
a = (-84) , b = 100 and c = -1
(-84)(100 + (-1)) = (-84)×100 + (-84)×(-1))
= -8400 + 84
= -8316
(-84)×99 = -8316
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