Worksheet: Properties of Multiplication and Addition

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

Q1:

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

  • A 2 1 ( 1 9 + 3 4 )
  • B ( 1 9 + 3 4 ) + ( 1 9 + 2 1 )
  • C 1 9 ( 3 4 ) + 1 9 ( 2 1 )
  • D 3 4 ( 1 9 + 2 1 )
  • E 1 9 ( 3 4 ) βˆ’ 1 9 ( 2 1 )

Q2:

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

  • A 6 ( 4 9 βˆ’ 4 6 )
  • B 6 ( 4 6 + 4 9 )
  • C 4 9 ( 6 + 4 6 )
  • D ( 6 + 4 6 ) + ( 6 + 4 9 )
  • E 4 6 ( 6 + 4 9 )

Q3:

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

Q4:

Amelia has not been using the elevator at her building for eight 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.

Q5:

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

  • A 2 ( π‘Ž + 𝑏 )
  • B π‘Ž + 2 𝑏
  • C 2 π‘Ž + 𝑏
  • D 2 π‘Ž 𝑏
  • E 4 π‘Ž 𝑏

Q6:

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

  • A 4 7 ( 1 0 βˆ’ 5 )
  • B 1 0 ( 4 7 + 5 )
  • C 5 ( 1 0 βˆ’ 4 7 )
  • D 1 0 ( 4 7 βˆ’ 5 )
  • E ( 1 0 βˆ’ 4 7 ) βˆ’ ( 1 0 βˆ’ 5 )

Q7:

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

  • A 1 8 + 3 π‘Ž
  • B 1 8 π‘Ž
  • C 3 π‘Ž
  • D 6 + 3 π‘Ž
  • E 9 π‘Ž

Q8:

Each morning, Anthony 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 Anthony exercises in 2 days.

Q9:

Mr. Benjamin and Mrs. William want to take their students to the zoo. The tickets cost $9 each. If Mr. Benjamin’s class has 16 students and Mrs. William’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.

  • A 9 ( 1 6 ) + 9 ( 2 4 ) = 9 ( 1 6 + 2 4 )
  • B 9 ( 1 6 Γ— 2 4 ) = ( 9 Γ— 1 6 ) 2 4
  • C 1 6 + 2 4 = 2 4 + 1 6
  • D 1 6 + 2 4 ( 9 ) = 1 6 ( 9 ) + 2 4
  • E 9 + ( 1 6 + 2 4 ) = ( 9 + 1 6 ) + 2 4

Q10:

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

Q11:

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

Q12:

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

Q13:

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

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