# How do you use the distributive property to rewrite and evaluate 9*99?

Mar 14, 2017

See the solution process for this problem below:

#### Explanation:

We can rewrite this expression as:

$\left(9 \cdot 1\right) \left(9 \cdot 11\right) = \left(9 \cdot 9\right) \left(1 \cdot 11\right) = 81 \cdot 11 = 891$

Mar 14, 2017

$\left(1\right) : 9 \cdot 99 = 9 \left(100 - 1\right) = 900 - 9 = 891.$

$\left(2\right) : 9 \cdot 99 = \left(10 - 1\right) 99 = 990 - 99 = 891.$

$\left(3\right) : 9 \cdot 99 = \left(10 - 1\right) \left(100 - 1\right) = 10 \left(100 - 1\right) - 1 \left(100 - 1\right)$

$= 1000 - 10 - 100 + 1 = 990 - 100 + 1 = 890 + 1 = 891.$