5th Grade - Distributive Property

 
     
 
     
 
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5th
Algebra
Distributive Property
Know and use the Distributive Property in equations and expressions with variables.
Ability to understand that multiplication is a faster way to addition. Ability to break apart numbers to make them easier to multiply.
 

Sample Problems

(1)

Use the grid to find the product. 5x17 Answer:

(5x10) +(5x7)






















































































(50 + 35)

( 85)

(2)

Use the Distributive Property to restate each expression. Find the product.


14 x 8


(10 + 4 ) x 8

(10 x 8) + ( 8x4)

(80) + (32)

112

(3)

Restate the expression, using the Distributive Property. Find the value of the expression.


9 x (y+8) if y = 10


(9x10)+(9x8)=162


(4)

Use the Distributive Property to restate each expression. Find the product.


33 x 4


(30 + 3) x 4

(30 x 4 ) + ( 4 x 3)

120 + 12

132

(5)

Use the Distributive Property


5 x 3, 214 = n


(5 x 3,000) + (5 x 200) + ( 5 x 10) + (5 x 4) = n

(15,000) + (1000) + (50) + (20) = n

n= 16,070




Learning Tips

(1)

Math Vocabulary:

Distributive Property: States that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products.

Multiplication: The operation that, for positive integers, consists of adding a number to itself a certain number of times.

Factor: a number multiplied by another number to find a product.

Product: the answer of a multiplication problem.

Sum: answer for addition problem

Addend: Numbers added together to reach a sum

Area of rectangle: length time width

Perimeter of rectangle: add all sides

(2)

Have your child practice the distributive property on grid paper so they can see the grids separated to show the distribution. On the grid paper, have your child outline a rectangle that is 5 units’ high and 16 units wide. Have them think of the area as the product.

16



5x16

































5






















































(3)

The second thing your child can do is break 5 times 16 into smaller parts. Have your child break the grid into 10 columns and 6 columns.


10





















5





























5x10=50




6












5



















5x6=30

30+50=80


Explain to your child that the distributive property has been used because the problem was broken down into smaller parts. The two products were added together to get the answer of 80. This property helps your child understand what he or she is actually doing when multiplying.


(4)

Remind your child when applying the Distributive Property to apply the first factor to each part of the second factor. When children have difficulty with this concept, sometimes it is because they forget to distribute the first factor to all other factors in the problem.

Example: Incorrect Correct

7x15=7x(10+5) 7x15=7 x (10 + 5)

= 7x10+5 = (7x10) + (7x5)

= 70+5 = 70 + 35

= 75 = 105

(5)

Your child must know multiplication facts 1-12 by automaticity. This is the key skill to master this concept.

Extra Help Problems

(1)

Use the grid to find the product.

9x16

































































































































































( 9x10) + (9x6)=

(90+ 54)

(144)



(2)

Use the grid to find the product. 15x14
























































































































































































































(15 x ( 10 +4)

(15x10) + (15x4)

150 + 60

210)




(3)

Use the grid to find the product. 12x18







































































































































































































































12x18

(12x (10 +8)

(12x10 )+ (12x8)

120 + 96

216)

(4)

Use the grid to find the product. 20x14


























































































































































































































































































( 20 x ( 10 +4)

( 20 x 10 ) + (20 x4)

(200 + 80)

(280)


(5)


Use the grid to find the product. 7x15













































































































( 7x (10 + 5)

(7x10) + (7x5)

(70 + 35)

(105)


(6)

Use the distributive property to restate each expression. Find the product.


8x34


8 x ( 30 +4)

(8 x 30) + (8 x 4)

(240)+(32)

(272)


(7)

Use the distributive property to restate each expression. Find the product.


9x37


9 x (30 + 7)

(9 x 30) + (9 x 7)

(270) + (63)

(333)

(8)

Use the distributive property to restate each expression. Find the product.


6x35


6 x (30 + 5)

(6 x 30) + (6 x 5)

(180) + (30)

(210)

(9)

Use the distributive property to restate each expression. Find the product.

5x55


5 x (50 + 5)

(50 x 5) +(5 x 5)

(250) + (25)

(275)

(10)

Use the distributive property to restate each expression. Find the product.


2 x 653

2 x (600 + 50 + 3)

(2 x 600) + (2 x 50) + (2 x 3)

(1,200) + (100) + (6)

(1,306)

(11)

Restate the expression, using the Distributive Property. Find the value of the expression.


8 x (4+n) if n=20



(8 x 4) + ( 8 x 20)

(32 + 160)

(n=192)


(12)

Restate the expression, using the Distributive Property. Find the value of the expression.





3 x (6+n) if n=40


(3x6 )+(3x40)

(18 )+(120)

(n=138)




(13)

Restate the expression, using the Distributive Property. Find the value of the expression.

5 x (d+7) if d=80

( 5 x 80) + (5 x 7)

(400 + 35)

(n=435)


(14)

Restate the expression, using the Distributive Property. Find the value of the expression.


4 x ( n+8) if n=25


( 4 x 8) + (4x25)

(32 + 100)

(n=132)

(15)

Restate the expression, using the Distributive Property. Find the value of the expression.


6 x ( d + 4) if d = 9


(6 x 9) + (6 x 4)

(54 + 24)

(d=78)

(16)

Restate the expression, using the Distributive Property. Find the value of the expression.


8 x (n + 5) if n = 30


(8 x30) + (8 x 5)

(240 + 40)

(n=280)

(17)

Restate the expression, using the Distributive Property. Find the value of the expression.


n x (10 +9) if n=3



(3 x 10) + ( 3 x 9)

(30) + (27)

(n=57)

(18)

Restate the expression, using the Distributive Property. Find the value of the expression.


n x (20 +7) if n=9


( 9 x 20) + (9 x 7)

(180) +(63)

(n=243)

(19)

Restate the expression, using the Distributive Property. Find the value of the expression.


7 x (n +9) if n=50


(7x50 )+(7 x 9)

(350 + 63)

(n=413)

(20)

Restate the expression, using the Distributive Property. Find the value of the expression.


4 x ( 60 + n) if n = 7

( 4 x 60) +( 4 x 7)

(240)+(28)

(n=268 )

(21)

Use the Distributive Property


223 x 3 = n


(200 x 3) + (20 x 3) + (3 x 3)

(600) + (60) +(9)

(n=669)



(22)

Use the Distributive Property


3,476 x 5 = n


(3,000 x 5) + (400 x 5) + (70 x 5) + (6 x 5)

(15,000) + (2,000) + (350) + (30)

(n= 17,380)


(23)

Use the Distributive Property


52,113 x 2 = n


(50,000 x 2)+(2,000 x 2)+(100 x 2)+(10 x 2)+(3 x 2)

(100,000) + (4,000) + (200) + (20) + (6)

(n= 104,226)

(24)

Use the Distributive Property


88,112 x 7 = n


(80,000 x7) + (8,000 x 7) + ( 100 x 7) + (10 x 7) + ( 2 x 7)

(560,000) +(56,000) + (700) + (70) + (14)

( n = 616,784)



(25)

Use the Distributive Property

3,584 x 4 = n

( 3,000 x 4)+(500 x 4 )+(80 x 4)+(4 x 4)

(12,000)+ (2,000 )+(320)+(16)

(n=14,336)

 

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