# How do you use the distributive property to find 9 x 99?

Oct 18, 2017

$9 \times 99 = \textcolor{red}{891}$

#### Explanation:

$9 \times 99$
$\textcolor{w h i t e}{\text{XXX}} = 9 \times \left(90 + 9\right)$

$\textcolor{w h i t e}{\text{XXX")=underbrace(9xx90) + underbrace(9xx9)color(white)("xxx}}$...the distributive property

$\textcolor{w h i t e}{\text{XXX}} = 810 + 81$

$\textcolor{w h i t e}{\text{XXX}} = 810$
color(white)("XX=X")ul(+color(white)(".")81)
$\textcolor{w h i t e}{\text{XXXXX}} 891$

~~~~~~~~~~~~~~ OR ~~~~~~~~~~~~~~~~~~~~~~~~~

$9 \times 99$
$\textcolor{w h i t e}{\text{XXX}} = 9 \times \left(100 - 1\right)$

$\textcolor{w h i t e}{\text{XXX")=underbrace(9xx100)-underbrace(9xx1)color(white)("xxx}}$...the distributive property

$\textcolor{w h i t e}{\text{XXX}} = 900 - 9$

$\textcolor{w h i t e}{\text{XXX}} = 891$

~~~~~~~~~~~~~ OR ~~~~~~~~~~~~~~~~~~~~~~~~~~

$9 \times 99$
$\textcolor{w h i t e}{\text{XXX}} = \left(10 - 1\right) \times 99$

$\textcolor{w h i t e}{\text{XXX")=underbrace(10xx99)-underbrace(1xx99)color(white)("xxx}}$...distributive property

$\textcolor{w h i t e}{\text{XXX}} = 990 - 99$

$\textcolor{w h i t e}{\text{XXX}} = 891$