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Worksheet: Properties of Addition and Multiplication

Q1:

Identify the property demonstrated by the following equation: 4 × ( 1 4 + 9 ) = 4 × 1 4 + 4 × 9 .

  • Aassociative property of addition
  • Bcommutative property of addition
  • Cidentity property of addition
  • Ddistributive property

Q2:

Chloe is working on memorizing her multiplication facts. She noticed that when she multiplies a number by 1, she gets the same number she started with. What is the name of this property?

  • Acommutative property
  • Bassociative property
  • Cdistributive property
  • Didentity property

Q3:

Does the commutative property apply to division?

  • Ano
  • Byes

Q4:

Is ( 1 0 0 2 8 4 ) 2 4 7 = 1 0 0 ( 2 8 4 2 4 7 ) o r ?

  • A
  • B =

Q5:

Noah knows that you can multiply three numbers in any order.

So, these two multiplication expressions are equal.

Does this work when dividing? Are these two division expressions equal?

  • Ano
  • Byes

Q6:

A vehicle traveled at a speed of 86 miles per hour for one hour. The distance it traveled can be represented as 8 6 × 1 = 8 6 . What property of the real numbers was used in solving this expression?

  • Aassociative property of multiplication
  • Bcommutative property of multiplication
  • Cdistributive property
  • Didentity property of multiplication

Q7:

Does the associative property apply to subtraction?

  • Ano
  • Byes

Q8:

What property of addition does this diagram show?

  • Athe distributive property
  • Bthe associative property
  • Cthe identity property
  • Dthe commutative property

Q9:

Does the commutative property apply to subtraction?

  • Ano
  • Byes

Q10:

Emma and her roommate, Scarlett, have decided to share a change jar for joint expenses. Emma put her loose change in the jar first, and then Scarlett put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?

  • Adistributive property of addition
  • Bassociative properties of addition
  • Cidentity property of addition
  • Dcommutative property of addition
  • Einverse property of addition

Q11:

What property of addition does the diagram illustrate?

  • Athe distributive property
  • Bthe commutative property
  • Cthe identity property
  • Dthe associative property

Q12:

Does the distributive property apply to multiplication over subtraction? I.e. does ?

  • Ayes
  • Bno

Q13:

If 𝑎 × 𝑏 = 𝑎 and 𝑎 0 , what is the value of 𝑏 ?