Solve: 9 × 3⅘ Mixed Number Multiplication Problem

Solve the following problem:

$9\times3\frac{8}{9}=$

Apply the distributive property of multiplication in order to break down the fraction into a subtraction exercise between a whole number and a fraction. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication allows us to break down the larger term in a multiplication problem into a sum or difference of smaller numbers, which makes multiplication easier and gives us the ability to solve the problem without using a calculator

$9\times(4-\frac{1}{9})=$

Apply the distributive property formula $a(b+c)=ab+ac$

$(9\times4)-(9\times\frac{1}{9})=$

Proceed to solve what's inside of the left parentheses:

$9\times4=36$

Note that in the right parentheses we can reduce 9 by 9 as follows:

$9=\frac{9}{1}$

$\frac{9}{1}\times\frac{1}{9}=\frac{9\times1}{1\times9}=\frac{9}{9}=\frac{1}{1}=1$

We obtain the following exercise:

$36-1=35$

Shown below are the various steps of the solution:

$9\times3\frac{8}{9}=9\times(4-\frac{1}{9})=(9\times4)-(9\times\frac{1}{9})=36-1=35$