Arithmetic properties: Distributive property

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/6
?
Intros
Lessons
  1. Introduction to the distributive property:
  2. Showing that a × (b + c) = (a × b) + (a × c)
  3. Common mistakes to avoid when using the distributive property
  4. Using area blocks to demonstrate the distributive property
  5. Why is it called the "distributive" property?
  6. The general formula for the distributive property
  7. Using the distributive property for other types of real numbers (decimals, fractions, integers)
0/15
?
Examples
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?
      1. 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?
      0%
      ?
      Practice
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
      • Easily See Your Progress

        We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
      • Make Use of Our Learning Aids

        Last Viewed
        Practice Accuracy
        Suggested Tasks

        Get quick access to the topic you're currently learning.

        See how well your practice sessions are going over time.

        Stay on track with our daily recommendations.

      • Earn Achievements as You Learn

        Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
      • Create and Customize Your Avatar

        Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
      Topic Notes
      ?

      Notes:

      • The distributive property is what happens when you multiply a number (called a multiplier or factor) with a sum of two or more numbers (addends inside of brackets).
        • Ex. 2 × (9 + 5) =

      • To distribute means to spread out or to hand around
        • So, the distributive property makes you distribute the multiplier
        • The multiplier/factor is distributed (given to) all the addends in brackets
        • Ex. 2 × (9 + 5) = 2×9 + 2×5
          • = 18 + 10 = 28
          • In other words, multiplying a sum of two numbers is equal to the sum of each addend multiplied by the factor

      • A common mistake that many students make with the distributive property is that they do not FULLY distribute the multiplier/factor:
        • Ex. 2 × (9 + 5) the 2 should be multiplied with both addends = 2 × 9 + 2 × 5
          • The common mistake is to only multiply the with the first addend:
            • 2 × (9 + 5) ? 2 × 9 + 5
              • 2 × 9 + 5 = 18 + 5 = 23
          • The correct answer should have been 28; not distributing will give the incorrect answer of 23

      • The distributive property can be demonstrated using area block models:
        • Area is given by two dimensions (i.e. length × width or height × length)
        • Ex. 2 × (9 + 5) means an area block with a height of 2, and a combined length of 9 and 5. The total number of area blocks is 28.
      Representing Numbers: Tally Marks

      • The general formula for the distributive property (where aa, bb and cc are variables that represent real numbers) is:

      Representing Numbers: Tally Marks

      • The distributive property works for any type of real number as the multiplier and/or addends (such as integers, fractions, and/or decimals):
        • Ex. -3 x (15+35)=(3x15)+(3x35)=35+95=125 (\frac{1}{5} + \frac{3}{5}) = (-3 \,x \, \frac{1}{5}) + (-3 \, x \, \frac{3}{5}) = \frac{-3}{5} + \frac{-9}{5} = \frac{-12}{5}
        • Ex. 5 × (0.2+ 0.05) = (5×0.2) + (5×0.05) = 1.0 + 0.25 = 1.25