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Which of the following equations is not a correct use of the distributive property to simplify computation?

A. -3 (19) = -3(20) -3 (-1)
 
B.-3 (19) = (-3)(20) +(-3)(1)
 
C.-3 (19) = (-3)(20) + (-3) (-1)
 
D. -3 (19) = (-3)(10) + (-3) (9)

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Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (6 lesson ratings) (6)
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19=20 +(-1) or 19=10+9
19 does NOT equal 20+1
therefore B is not a correct use of the distributive property
Felice R. | Need Help in Math and Science - Engineer willing to helpNeed Help in Math and Science - Engineer...
4.0 4.0 (1 lesson ratings) (1)
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Marion,
 
if you remember the distributive property is easy to remember if you think 
 
multiplication distributes over addition
 
which can be written as
 
a(b+c) = ab + ac
 
If you take your all your equations it looks like you are trying to show distributive property using -3(19)
 
well in this case our a is  -3
 
but we don't have our or c
 
or do we
 
in A. you have the eqn -3(10) = -3(20) - 3(-1)
 
if we assume that 20  is b and -1 is c
then we would have -3(20 + (-1)) = -3(20) - 3(-1) and (20+(-1)) = 19
 
so A would be a correct usage of the distributive property
 
in B. you have (-3)(20) + (-3)(1) = -3(20+1)  but 20 + 1 ≠ 19
so it wouldn't be a correct usage of the  distributive property
 
for C and D you would need to do the same as I did above
 
Hope this helps
 
F
 
BTW you can find more examples for this property and others at Purple Math