Expert: Scott A Wilson - 9/14/2010

Question
How would you use the distributive property to simplify?
e.g. 9x28,7(2,009),30x105,7x10+7(-3),6(8) + 6(-2)

Answer
To use the distributive property means to divide one of the numbers into parts.

For example, in 9x28, 28 is 20 + 8.  This means that 9x28 is the same as 9(20+8).  This can then be divided into 9x20 + 9x8, which is 180 + 72, and that is 252.

In a similar fashion, 7x2,009 is the same as 7x2000 + 7x9, which is
14,000 + 63 = 14,063.

For the 30x105, note that the 30 can be left alone since multiplying by 30 is the same as multiplying by 3 and adding a 0 to the result.
Thus, 30x05 = 30x100 + 30x5 = 3,000 + 150 = 3,150.

For 7x10+7(-3), do each of the multiplications first and get
70 + (-21).  That is the same as 70 - 21, and that is 49.

For 6(8) + 6(-2), the multiplications come first, so it is
48 - 12, and that is 36.