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Partial Products
Distributive Detectives
Property Puzzles
1 to 4 Digit Masters
2 by 2 Champs
100

Expand 23×4 into partial products.

20×4=80

3×4=12.

100

True or False: 6×(4+2)=(6×4)+(6×2)

True

100

What is the property?

6×9=9×6

Commutative Property of Multiplication

100

8×7

56

100

12×12

144

200

Solve 46×3 using partial products

40×3=120

6×3=18.

Total = 138.

200

Rewrite 7×13 with distributive property

7×(10+3)=(7×10) + (7×3).

200

(2×3)×4=2×(3×4)

Associative Property of Multiplication

200

13×6

78

200

23×45

1035

300

124×5

100×5=500

20×5=100

4×5=20. 

Total = 620.

300

8×47 by distributive property

8×40=320

8×7=56. 

Total = 376.

300

7×(1+9)=(7×1)+(7×9)

Distributive Property

300

427×3

427+427+427=1281. 

(Or 400×3=1200, 20×3=60, 7×3=21 → Total: 1281.)

300

36×27

972

400

237×6

200×6=1200

30×6=180

7×6=42. 

Total = 1422

400

Find two ways to solve for 25×16 using the distributive property


  • Break 16: 25×(10+6)=250+150=400

  • Break 25: (20+5)×16=320+80=400


  • Final = 400.


400

What is the Zero property?

Any number multiplied by 0 equals 0 

(example: 7×0=0)

400

2,314×4

=(2000×4)+(300×4)+(10×4)+(4×4)

=8000+1200+40+16

=9256

400

48×56

2688

500

Partial products for 324×8 (showing a clear break into tens & ones):

8 * (300 + 20 + 8)


(8*300) + (8*20) + (8*8)


2400 + 160 + 64

Total: 2,624

500
How can I distribute the following problem?


8*(5000+400+30+9)
(8*5000) + (8*400) + (8*30) + (8*9)


(40000) + (3200) + (240) + (72)

Total: 43,512

500

Give an example of the Associative Property.

Answers will vary but here's a possible response.

(2×3)×4=6×4=24 and

 2×(3×4)=2×12=24


500

7,652×8

=(7000×8)+(600×8)+(50×8)+(2×8)

=56000+4800+400+16

=61,216

500

75×89

6675