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Complete Question
Nico and Lorena used different methods to determine the product of three fractions.
Nico’s Method =
(one-sixth) (Negative four-fifths)(2) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over 30 EndFraction
Lorena’s Method
= Negative StartFraction 4 over 15 EndFraction (2) (one-sixth) (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over Negative 30 EndFraction = StartFraction 4 over 15 EndFraction
Whose solution is correct and why?
a) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction.
b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.
c) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction
d) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction
Answer:
b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.
Step-by-step explanation:
In the above question
We start from Nico's method
Nico’s Method =
Step 1 : (one-sixth) (Negative four-fifths)(2)=
(1/6)(-4/5)(2)
Step 2 : (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =
= (2/1)(1/6)(-4/5)
Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction
= (2)(1)(-4)/(1)(6)(5)
Step 4: Negative StartFraction 8 over 30 EndFraction
= (-8/30)
Step 5 : Negative StartFraction 4 over 15
EndFraction
= -4/15
Nico is correct
For Lorena’s Method
Step 1: Negative StartFraction 4 over 5 EndFraction (2) (one-sixth)
= -4/5(2)(1/6)
Step 2: (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =
(2/1)(1/6)(-4/-5)
Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (negative 5) EndFraction
(2)(-1)(-4)/(1)(6)(-5)
Step 4: Negative StartFraction 8 over Negative 30 EndFraction =
-8/-30
Step 5: StartFraction 4 over 15
EndFraction
= 4/15
Lorena is wrong because
that Negative four-fifths ≠StartFraction negative 4 over negative 5 EndFraction
Mathematically
-4/5 ≠ -4/-5
Therefore,option b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.
