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Multiplication
Using the Distributive Property
What’s the Distributive Property?


• When using the distributive property, you break
  down large complex numbers into numbers that are
  easier to work with.

• You often use expanded form.
What’s the Distributive Property?
Here’s an example:



                        62 x 3


               Let’s use the distributive
             property to find the product.
1. Write the multi-digit number in expanded form.


           Another way of writing 62 is:
                     60 + 2
  60 + 2


 62 x 3
2. Set up your parentheses.


             Since 62 is a two digit number, we
                need two sets of parentheses.

60   +   2

62 x 3 = (       x )+( x )
3. Multiply each part of the expanded number by the
                   one-digit factor.


             Multiply 60 by 3, and 2 by 3.

   +


62 x 3 = (60 x3 ) + ( 2 x 3)
4. Find the product to each multiplication problem.


      60 x 3 = 180            2x3=6




  62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6
5. Add the products together.


               180 + 6 = 186



62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6 = 186
6. Check your work using the traditional method of
                 multiplication.

                        62
                       x 3



   62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6 = 186   √
That wasn’t so bad! Let’s try
         another...

            87 x 5
1. Write the multi-digit number in expanded form.


           Another way of writing 87 is:
                     80 + 7
  80 + 7


 87 x 5
2. Set up your parentheses.


             Since 87 is a two digit number, we
                need two sets of parentheses.

80   +   7

87 x 5 = (       x )+( x )
3. Multiply each part of the expanded number by the
                   one-digit factor.


             Multiply 80 by 5, and 7 by 5.




87 x 5 = (80 x5 ) + ( 7 x 5)
4. Find the product to each multiplication problem.


      80 x 5 = 400            7 x 5 = 35




  87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35
5. Add the products together.


              400 + 35 = 435



87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35 = 435
6. Check your work using the traditional method of
                 multiplication.

                        87
                       x 5



   87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35 = 435   √
Ready to try a few on your own?

I thought so. Try solving the problems on the worksheet,
            “Using the Distributive Property”

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Distributive multiplication

  • 2. What’s the Distributive Property? • When using the distributive property, you break down large complex numbers into numbers that are easier to work with. • You often use expanded form.
  • 3. What’s the Distributive Property? Here’s an example: 62 x 3 Let’s use the distributive property to find the product.
  • 4. 1. Write the multi-digit number in expanded form. Another way of writing 62 is: 60 + 2 60 + 2 62 x 3
  • 5. 2. Set up your parentheses. Since 62 is a two digit number, we need two sets of parentheses. 60 + 2 62 x 3 = ( x )+( x )
  • 6. 3. Multiply each part of the expanded number by the one-digit factor. Multiply 60 by 3, and 2 by 3. + 62 x 3 = (60 x3 ) + ( 2 x 3)
  • 7. 4. Find the product to each multiplication problem. 60 x 3 = 180 2x3=6 62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6
  • 8. 5. Add the products together. 180 + 6 = 186 62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6 = 186
  • 9. 6. Check your work using the traditional method of multiplication. 62 x 3 62 x 3 = (60 x 3) + ( 2 x 3) = 180 + 6 = 186 √
  • 10. That wasn’t so bad! Let’s try another... 87 x 5
  • 11. 1. Write the multi-digit number in expanded form. Another way of writing 87 is: 80 + 7 80 + 7 87 x 5
  • 12. 2. Set up your parentheses. Since 87 is a two digit number, we need two sets of parentheses. 80 + 7 87 x 5 = ( x )+( x )
  • 13. 3. Multiply each part of the expanded number by the one-digit factor. Multiply 80 by 5, and 7 by 5. 87 x 5 = (80 x5 ) + ( 7 x 5)
  • 14. 4. Find the product to each multiplication problem. 80 x 5 = 400 7 x 5 = 35 87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35
  • 15. 5. Add the products together. 400 + 35 = 435 87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35 = 435
  • 16. 6. Check your work using the traditional method of multiplication. 87 x 5 87 x 5 = (80 x 5) + ( 7 x 5) = 400 + 35 = 435 √
  • 17. Ready to try a few on your own? I thought so. Try solving the problems on the worksheet, “Using the Distributive Property”