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

Question

Solve the following problem:

14(44+444)= \frac{1}{4}(44+444)=

Video Solution

Solution Steps

00:00 Solve
00:03 Always solve parentheses first
00:07 Use long addition
00:19 Multiply by numerator
00:23 Break down the numerator to 400 plus 88
00:28 Divide into two fractions
00:35 Calculate each division separately and then sum
00:43 And this is the solution to the question

Step-by-Step Solution

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

14(488)= \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

14(400+80+8)= \frac{1}{4}(400+80+8)=
We will apply the distributive property formula a(b+c+d)=ab+ac+ad a(b+c+d) = ab+ac+ad

14×400+14×80+14×8= \frac{1}{4}×400 + \frac{1}{4}× 80 + \frac{1}{4}×8=

Follow the order of operations and proceed to perform the operations

4004+804+84= \frac{400}{4}+\frac{80}{4}+\frac{8}{4}=

100+20+2=122 100+20+2=122

Therefore, the answer is option C - 122.

Below are the various steps of the solution:

14(44+444)=14(488)=14(400+80+8)=14×400+14×80+14×8=4004+804+84=100+20+2=122 \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

Answer

122 122