2024 AMC 8 Problems/Problem 2

Problem

What is the value of the expression in decimal form?

$\frac{44}{11}+\frac{110}{44}+\frac{44}{1100}$

$\textbf{(A) } 6.4 \qquad\textbf{(B) } 6.504 \qquad\textbf{(C) } 6.54 \qquad\textbf{(D) } 6.9 \qquad\textbf{(E) } 6.94$

Solution 1

We see $\frac{44}{11}=4$ , $\frac{110}{44}=2.5$ , and $\frac{44}{1100}=0.04$ . Thus, $4+2.5+0.04=\boxed{\textbf{(C) }6.54}$

~MrThinker

Solution 2

We can simplify this expression into $4+\frac{5}{2}+\frac{1}{25}$ . Now, taking the common denominator, we get $\frac{200}{50}+\frac{125}{50}+\frac{2}{50}$ $= \frac{200+125+2}{50}$ $= \frac{327}{50}$ $= \frac{654}{100}$ $= \boxed{\textbf{(C) }6.54}$

~Dreamer1297

Solution 3

Convert all of them into the same demoninator of $1100$ . We have $\frac{4400}{1100} + \frac{2750}{1100} + \frac{44}{1100} = \frac{7194}{1100} = \boxed{\textbf{(C) }6.54}$ ~andliu766

Solution 4(fastest)

Use 4400 as the common denominator.

$\frac{17600}{4400} + \frac{11000}{4400} + \frac{176}{4400} = \frac{17600+11000+176}{4400} = \frac{28776}{4400} = \boxed{\textbf{(C) }6.54}$

-thebanker88

Video Solution 1 (easy to digest) by Power Solve

https://youtu.be/HE7JjZQ6xCk?si=4I0UO5oOVrC2vJep&t=29

Video Solution by NiuniuMaths (Easy to understand!)

https://www.youtube.com/watch?v=Ylw-kJkSpq8

~NiuniuMaths

Video Solution 2 by SpreadTheMathLove

https://www.youtube.com/watch?v=L83DxusGkSY

Video Solution by CosineMethod [🔥Fast and Easy🔥]

https://www.youtube.com/watch?v=NLoyzNyvFKU

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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