A property is a characteristic about something that is always true. The distributive property of multiplication is a rule that is always true. There are many properties in math that you use regularly, like the commutative property (the property that says that you can multiply in any order, \(2 \times 3 = 3 \times 2\) ). The distributive property says that you can distribute a number being multiplied into parentheses. The following video will explain in more detail with some examples. Here is an example of the distributive property of multiplication.

\( 2 (1 + 3) = (2 \times 1) + (2 \times 3) = 2 + 6 = 8\)

Video Source (03:11 mins) | Transcript

Video Source (03:13 mins) | Transcript

Additional Resources

• Khan Academy: Distributive Property (Addition) (04:55 mins, Transcript)
• Khan Academy: Distributive Property (Subtraction) (02:10 mins, Transcript)

Practice Problems

1. \(4 \lgroup 3 + 4 \rgroup = ?\) (
   Solution

   x

   Solution: \(28\)
   Details:
   Although this problem can be solved using the Order of Operation, for this lesson, practice solving with the Distributive Property.
   Start by distributing the \(4\) into each number inside the parentheses. Multiply the \(4 × 3\) and \(4 × 4\).
   \(4\lgroup3 + 4\rgroup\)
   \(4\lgroup3\rgroup + 4\lgroup4\rgroup\)
   
   Solve \(4 × 3 = 12\) and \(4 × 4 = 16\)
   
   \(4\lgroup3\rgroup + 4\lgroup4\rgroup\)
   \(12+16\)
   
   Finally add \(12\;\text{plus}\;16 = 28\).
   )
2. \(\lgroup 2 + 9 \rgroup 3 = ?\) (
   Solution

   x

   Solution:
   \(33\)
   )
3. \(-8 \lgroup -2 + 5 \rgroup = ?\) (
   Video Solution

   x

   Solution: \(-24\)
   Details:
   

   
   (Video Source | Transcript)
   )
4. \(\lgroup -2 + 3 \rgroup \lgroup -6 \rgroup = ?\) (
   Solution)

   x

   Solution: \(-6\)
   Details:
   Solve by using the Distributive Property. Multiply \(-6\) by each number inside the parentheses.
   \(\lgroup-2 + 3\rgroup\lgroup-6\rgroup\)
   
   Continue to multiply \(-2 × -6\) and \(3 × -6\).
   \(\lgroup-2\rgroup\lgroup-6\rgroup + \lgroup3\rgroup\lgroup-6\rgroup\)
   
   The product, or answer are \(12\) and \(-18\).
   \(\lgroup12\rgroup + \lgroup-18\rgroup\)
   
   The final step is to add
   \(\lgroup12\rgroup + \lgroup-18\rgroup\)
   
   The answer is \(- 6\).
5. \(\lgroup -9 - 4 \rgroup \lgroup -8 \rgroup = ?\) (
   Video Solution

   x

   Solution: 104
   Details:
   

   
   (Video Source | Transcript)
   )
6. \(-5 \lgroup -7 - \lgroup -6 \rgroup \rgroup = ?\) (
   Solution

   x

   Solution:
   \(5\)
   )
7. \(\lgroup -5 - \lgroup -9 \rgroup \rgroup 6 = ?\) (
   Solution

   x

   Solution:
   \(24\)
   )

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