Difference between revisions of "2024 AMC 8 Problems/Problem 2"

Latest revision as of 20:48, 4 April 2024

Problem 2

What is the value of this 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 that $\frac{44}{11}$ is $4$ ; $\frac{110}{44}$ simplifies to $\frac{5}{2}$ , which is $2.5$ ;

and $\frac{44}{1100}$ simplifies to $\frac{1}{25}$ , which is $0.04$ ;

$4+2.5+0.04$ reveals $\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}$ is $\boxed{\textbf{(C)\ 6.54}}$ . ~ le_petit_chouetteur from TSMV

~Minor Formatting by GreenPlanet2050

Video Solution 1 (Quick and Easy!)

https://youtu.be/nzPT89ymlKk

~Education, the Study of Everything

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/BaE00H2SHQM?si=noTBPTosCtH31CpW&t=287

~Math-X

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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

@@ Line 1: / Line 1: @@
-==Problem==
+==Problem 2 ==
+What is the value of this expression in decimal form?
+<cmath>\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}</cmath>
+<math>\textbf{(A) } 6.4\qquad\textbf{(B) } 6.504\qquad\textbf{(C) } 6.54\qquad\textbf{(D) } 6.9\qquad\textbf{(E) } 6.94</math>
-What is the value of the expression in decimal form?
+==Solution 1==
-<cmath>\frac{44}{11}+\frac{110}{44}+\frac{44}{1100}</cmath>
+We see that <math>\frac{44}{11}</math> is <math>4</math>;
+<math>\frac{110}{44}</math> simplifies to <math>\frac{5}{2}</math>, which is <math>2.5</math>;
-<math>\textbf{(A) } 6.4 \qquad\textbf{(B) } 6.504 \qquad\textbf{(C) } 6.54 \qquad\textbf{(D) } 6.9 \qquad\textbf{(E) } 6.94</math>
+and <math>\frac{44}{1100}</math> simplifies to <math>\frac{1}{25}</math>, which is <math>0.04</math>;
-==Solution 1==
+<math>4+2.5+0.04</math> reveals <cmath>\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}</cmath> is <math>\boxed{\textbf{(C)\ 6.54}}</math>.
+~ le_petit_chouetteur from TSMV
-We see <math>\frac{44}{11}=4</math>, <math>\frac{110}{44}=2.5</math>, and <math>\frac{44}{1100}=0.04</math>. Thus, <math>4+2.5+0.04=\boxed{\textbf{(C) }6.54}</math>
+~Minor Formatting by GreenPlanet2050
-For this problem, a lot of people struggle to immediately think of this solution, and instead try to make all denominators the same which wastes a lot of time.
+==Video Solution 1 (Quick and Easy!)==
+https://youtu.be/nzPT89ymlKk
-After solving this problem why don't we consider some poetry?
+~Education, the Study of Everything
-Roses are red
-Violets are blue
+==Video Solution by Math-X (First understand the problem!!!)==
+https://youtu.be/BaE00H2SHQM?si=noTBPTosCtH31CpW&t=287
-Carrot
+~Math-X
-~MrThinker ~ Nivaar
-==Solution 2==
-We can simplify this expression into <math>4+\frac{5}{2}+\frac{1}{25}</math>. Now, taking the common denominator, we get <cmath>\frac{200}{50}+\frac{125}{50}+\frac{2}{50}</cmath>
-<cmath>= \frac{200+125+2}{50}</cmath>
-<cmath>= \frac{327}{50}</cmath>
-<cmath>= \frac{654}{100}</cmath>
-<cmath>= \boxed{\textbf{(C) }6.54}</cmath>
-~Dreamer1297
-==Solution 3==
-Convert all of them into the same demoninator of <math>1100</math>. We have <math>\frac{4400}{1100} + \frac{2750}{1100} + \frac{44}{1100} = \frac{7194}{1100} = \boxed{\textbf{(C) }6.54}</math>
-~andliu766
-==Solution 4(fastest)==
-Use 4400 as the common denominator.
-<math>\frac{17600}{4400} + \frac{11000}{4400} + \frac{176}{4400} = \frac{17600+11000+176}{4400} = \frac{28776}{4400} =
-\boxed{\textbf{(C) }6.54}</math>
--thebanker88
-==Video Solution by Math-X (First fully understand the problem!!!)==
-https://www.youtube.com/watch?v=dQw4w9WgXcQ
-~Rick Atsley
-==Video Solution 1 (easy to digest) by Power Solve==
-https://www.youtube.com/watch?v=dQw4w9WgXcQ
-Note: thiss link was made by @iamatinychildwhoisincapableofdoinganything,existentornonexistent
-==Video Solution by NiuniuMaths (Easy to understand!)==
-https://www.youtube.com/watch?v=dQw4w9WgXcQ
-~NiuniuMaths
-==Video Solution 2 by SpreadTheMathLove==
-https://www.youtube.com/watch?v=dQw4w9WgXcQ
-== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
-https://www.youtube.com/watch?v=dQw4w9WgXcQ
 ==See Also==
 {{AMC8 box|year=2024|num-b=1|num-a=3}}
 {{MAA Notice}}

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