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Arithmetic properties: Distributive property

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Intros
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Lessons
  1. Showing that a × (b + c) = (a × b) + (a × c)
  2. Common mistakes to avoid when using the distributive property
  3. Using area blocks to demonstrate the distributive property
  4. Why is it called the "distributive" property?
  5. The general formula for the distributive property
  6. Using the distributive property for other types of real numbers (decimals, fractions, integers)
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Examples
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Lessons
  1. Distributive Property Equations
    Use the distributive property to fill in the blanks.
    1. 6 × (3 + 5 + 4) = 6 × ___ + 6 × ___ + 6 × ___
      \qquad \qquad \qquad \qquad = _______+ _______+ ______
      \qquad \qquad \qquad \qquad = _______
      \qquad \qquad \qquad \qquad 6 × (___) = _______
      \qquad \qquad \qquad \qquad _______ = _______

    2. 12 × (10. 5 + 1.2) = 12 × ___ + 12 × ___
      \qquad \qquad \qquad \qquad = _______ + _______
      \qquad \qquad \qquad \qquad = _______
      \qquad \qquad \qquad \qquad 12 × (___) = _______
      \qquad \qquad \qquad \qquad _______ = _______

    3. 3 × (35+45\frac{3}{5} + \frac{4}{5}) = 3 × ___ + 3 × ___
      \qquad \qquad \qquad \qquad = _______ + _______
      \qquad \qquad \qquad \qquad = _______
      \qquad \qquad \qquad \qquad 3 × (___) = _______
      \qquad \qquad \qquad \qquad _______ = _______

    4. 8 × (6 + __) = 8 × ___ + 8 × ___
      \qquad \qquad \qquad \qquad = _______ + _______
      \qquad \qquad \qquad \qquad = 104
      \qquad \qquad \qquad \qquad 8 × (___) = 104
      \qquad \qquad \qquad \qquad _______ = 104

  2. Distributive property as a shortcut
    Use the distributive property to split up one of the factors. This can be a shortcut so that you can use your times tables knowledge. Solve and check the answer using long (normal) multiplication
    1. 6 × 15
    2. 44 × 12
    3. 18 × 2.5
    4. 60 × 54 \frac{5}{4}
  3. Distributive property using area blocks
    Use an area block to show each distributive property, then solve.
    1. 5 × (3 + 8)
    2. 4 × (11 + 2)
  4. Rewriting a sum as a distributive property
    Rewrite each sum as a distributive property expression. Recall that the general formula for the distributive property is: a × (b + c) = a × b + a × c
    • Hint: find the greatest common factor of each number first.

      1. 28 + 32
      2. 27 + 21
      3. 66 + 48
    • Distributive property word problem 1
      Eight people go to a restaurant for a buffet dinner. The cost per person for the meal is $11.50 and there is a separate drink cost of $2.10. How much did they pay all together?
    • Distributive property word problem 2
      In a movie theatre, there are 3 sections you can sit in (left, middle, right). Each row has 6 seats in the left section, 14 in the middle section, and 8 in the right section.
      • If there are 10 rows, how many seats are there in each section? And how many total seats are there in the theatre?