Solve: Finding 1/4 of (44 + 444) Using Fraction Properties

$$ Perform the addition operation inside of the parentheses by following the order of operations.

$\frac{1}{4}(488)=$

Apply the distributive property of multiplication and proceed to break down the three-digit number that we obtained into a sum of three numbers: hundreds, tens, and ones. 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 a calculator

$\frac{1}{4}(400+80+8)=$
We will apply the distributive property formula $a(b+c+d) = ab+ac+ad$

$\frac{1}{4}×400 + \frac{1}{4}× 80 + \frac{1}{4}×8=$

Follow the order of operations and proceed to perform the operations

$\frac{400}{4}+\frac{80}{4}+\frac{8}{4}=$

$100+20+2=122$

Therefore, the answer is option C - 122.

Below are the various steps of the solution:

$\frac{1}{4}(44+444)= \frac{1}{4}(488)= \frac{1}{4}(400+80+8)= \frac{1}{4}×400 + \frac{1}{4}× 80 + \frac{1}{4}×8= \frac{400}{4}+\frac{80}{4}+\frac{8}{4}= 100+20+2=122$