Distributive Property

Distributive property- Is when you take the number or variable outside the brackets and distribute(multiply) towards EVERYTHING inside the brackets.

Distributive property is helpful in such a way, as in making mental math easier and is also a faster method for understanding multiplication

Let's say I have to quickly multiply:
4 x 53
(4 x 50) + (4 x 3)

200 + 12

212


Let's view a step my step by step equation using distributive law:
Example #1
3(x-2) = 21 ---> You have a pair of brackets with 2 terms inside, this means distribute.
3x -6 = 21 ---> Distribute, 3(x) - 3(2), now you have a two step equation.
3x -6+6 = 21+6 ---> You would then add 6 to both sides, what you do to one side, you must do to the other*.
3x + 27 ---> You now have a one step equation.
3x 27 ---> Now divide by 3 on both sides, what you do to one side, you must do to the other*.
--- ---
3 3
x =9 ---> Solution of 9.
Check your answers.
3(x-2) = 21
3(9-2) = 21
3(7) =21
21=21 ---> Always check your answers by substituting back into the equation. Making sure both sides are equal.

Example #2

2x-3(2x-3) +4 = 33 ---> You have a pair of brackets with 2 terms inside, this means distribute.
2x - 6x +9 +4 = 33 ---> Distribute. -3(2x) = -6x & -3(-3) = 9, (like terms have already been collected here)
-4x +13 = 33 --->( You would need to collect like terms which had already been collected in the last step) combine like terms now.
-4x +13 -13 = 33-13 ---> Now solve your 2 step equation. subtract 13 from BOTH sides.
-4x = 20 ---> Now you have a 1 step equation.
-4x = 20 ---> Divide by -4 on BOTH sides.
---- ----
-4 -4
x =5 ---> Solution of 5.

Check your answers.
2x-3(2x-3) +4 = 33 ---> Always check your answers by substituting back into the equation. Making sure both sides are equal. 2(-5) -3(2-5 -3 +4 =33
33=33


Example #3
3(2x +2) -4(x -5) =18 ---> You have 2 sets of brackets with two terms inside->This means distribute twice.6x +6 -4x +20 =18 ---> Distribute both sets of brackets.6x-4x +6 +20 =18 ---> Collect like terms( rewrite the problem with like terms together)2x +26 =18 --->Combine like terms, now you have a 2 step equation.2x +26-26 = 18-26 --->Subtract 26 from both sides.

2x = -8 ---> Now you have a 1 step equation.2x = -8 ---> Divide by 2 on both sides.--- ---2 2x =4 ---> Solution of 4Check your answer.3(2x+2) -4(x-5) =18 -->Always check your answers by substituting back into the equation. Making sure both sides are equal.
3(2(-4) +2) -4(-4 -5) =18
18=18


Video Tutorial:
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http://edubakery.com/Word-Searches/Distributive-Property-v1-Word-Search

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Practice Problems & Worksheet

1. Solve.
a). 5(x+6) =
b). 3(2x+1) =

c). 2(2x-3) =

d). 6(x-4) =

e). 8(2x-3) =

f). -3(x + 4)=

g). -2(3x - 1)=

h). -10(2x + 1/5 )=

i). -18(x - 2/3)=

j). 1/2(x -4) =


Mary has 6 jars with 240 marbles in each jar. Which of the following expressions shows the total number of marbles Mary has?



a) 240 × 7 + 240 b) 240 × 7 – 240 c) 240 × 6 − 240 d) 240 × 6 + 240