Lesson Worksheet: Properties of Multiplication and Addition Mathematics

In this worksheet, we will practice using the associative, commutative, and distributive properties to solve problems.


Rewrite the expression 19(34+21) using the distributive property.

  • A21(19+34)
  • B(19+34)+(19+21)
  • C19(34)+19(21)
  • D34(19+21)
  • E19(34)βˆ’19(21)


Rewrite the expression 6(46)+6(49) using the distributive property

  • A6(49βˆ’46)
  • B6(46+49)
  • C49(6+46)
  • D(6+46)+(6+49)
  • E46(6+49)


Using the distributive property, evaluate 3(43)βˆ’3(10).


Mia has not been using the elevator at her building for 8Β weeks. She climbed up and down 354 steps every day for the duration of that period. Use the distributive property to determine the number of steps she climbed during that period.


Which of the following expressions is equivalent to 2π‘Ž+2𝑏?

  • A2(π‘Ž+𝑏)
  • Bπ‘Ž+2𝑏
  • C2π‘Ž+𝑏
  • D2π‘Žπ‘
  • E4π‘Žπ‘


Use the distributive property to rewrite the expression 10(47)βˆ’10(5).

  • A47(10βˆ’5)
  • B10(47+5)
  • C5(10βˆ’47)
  • D10(47βˆ’5)
  • E(10βˆ’47)βˆ’(10βˆ’5)


Use the properties of real numbers to write an expression equivalent to 3(6π‘Ž) that does not use parentheses.

  • A18+3π‘Ž
  • B18π‘Ž
  • C3π‘Ž
  • D6+3π‘Ž
  • E9π‘Ž


Each morning, Noah runs for 12 minutes and does push-ups for 22 minutes in the park. Use the distributive property to determine the total number of minutes that Noah exercises in 2 days.


Mr. Mason and Mrs. Jones want to take their students to the zoo. The tickets cost $9 each. If Mr. Mason’s class has 16 students and Mrs. Jones’s class has 24 students, use the distributive property to write a mathematical sentence to express how to find the total cost of tickets in two ways.

  • A9(16)+9(24)=9(16+24)
  • B9(16Γ—24)=(9Γ—16)24
  • C16+24=24+16
  • D16+24(9)=16(9)+24
  • E9+(16+24)=(9+16)+24


What property is illustrated by the step π‘₯+π‘₯βˆ’12=0,π‘₯+4π‘₯βˆ’3π‘₯βˆ’12=0?

  • AThe property of opposites
  • BThe associative property of multiplication
  • CThe associative property of addition
  • DThe commutative property of addition
  • EThe distributive property of multiplication over addition


Fill in the blank: 93Γ—96Γ—43=Γ—43Γ—93.


Evaluate (100Γ—8+10Γ—80)Γ—30 using the distributive property.


Evaluate 100Γ—(46+334βˆ’36) using the distributive property.


Michael walked 3 blocks from home to the movie theatre. After the movie, he walked 7 blocks to an ice cream shop. Given that Michael walks the same way home, write a mathematical sentence to show that the distance walked from Michael’s home to the ice cream shop is the same as that of the walk back home. What number property illustrates that?

  • A3Γ—7=7Γ—3, commutative property of multiplication
  • B2(3+7)=2Γ—7+2Γ—3, distributive property of multiplication over addition
  • C3Γ—7=7Γ—3, associative property of multiplication
  • D3+7=7+3, commutative property of addition
  • E3+7=7+3, associative property of addition

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