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

Question

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)

Answer 1

19=20 +(-1) or 19=10+9

19 does NOT equal 20+1

therefore B is not a correct use of the distributive property

Answer 2

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 b 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

 

http://www.purplemath.com/modules/numbprop.htm