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

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==Problem==
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==Problem 2 ==
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What is the value of this expression in decimal form?
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<cmath>\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}</cmath>
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<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>
  
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What is the value of the expression in decimal form?
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==Solution 1==
  
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<cmath>\frac{44}{11}+\frac{110}{44}+\frac{44}{1100}</cmath>
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We see that <math>\frac{44}{11}</math> is <math>4</math>;
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<math>\frac{110}{44}</math> simplifies to <math>\frac{5}{2}</math>, which is <math>2.5</math>;
  
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<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>
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and <math>\frac{44}{1100}</math> simplifies to <math>\frac{1}{25}</math>, which is <math>0.04</math>;
  
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==Solution 1==
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<math>4+2.5+0.04</math> reveals <cmath>\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}</cmath> is <math>\boxed{\text{(C)\ 6.54}}</math>.
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~
  
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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>
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~Minor Formatting by GreenPlanet2050
  
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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.
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==Video Solution by Math-X (MATH-X)==
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https://youtu.be/BaE00H2SHQM?si=noTBPTosCtH31CpW&t=287
  
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~Math-X
  
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~MrThinker ~ Nivaar
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==Video Solution (A Clever Explanation You’ll Get Instantly)==
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https://youtu.be/5ZIFnqymdDQ?si=-FCGnA5WXQNp-JMF&t=175
  
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==Solution 2==
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~hsnacademy
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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>
 
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<cmath>= \frac{200+125+2}{50}</cmath>
 
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<cmath>= \frac{327}{50}</cmath>
 
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<cmath>= \frac{654}{100}</cmath>
 
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<cmath>= \boxed{\textbf{(C) }6.54}</cmath>
 
  
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~Dreamer1297
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==Video Solution 1 (Quick and Easy!)==
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https://youtu.be/nzPT89ymlKk
  
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==Solution 3==
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~Education, the Study of Everything
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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>
 
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~andliu766
 
  
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==Video Solution by Math-X (First understand the problem!!!)==
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https://youtu.be/BaE00H2SHQM?si=noTBPTosCtH31CpW&t=287
  
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==Solution 4(fastest)==
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~Math-X
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Use 4400 as the common denominator.
 
  
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<math>\frac{17600}{4400} + \frac{11000}{4400} + \frac{176}{4400} = \frac{17600+11000+176}{4400} = \frac{28776}{4400} =
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==Video Solution by Daily Dose of Math (Understandable, Speedy, and Easy)==
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\boxed{\textbf{(C) }6.54}</math>
 
  
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-thebanker88
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https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR
  
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==Video Solution by Math-X (First fully understand the problem!!!)==
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~Thesmartgreekmathdude
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https://www.youtube.com/watch?v=dQw4w9WgXcQ
 
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~Rick Atsley
 
  
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==Video Solution 1 (easy to digest) by Power Solve==
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==Video Solution by WhyMath==
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https://www.youtube.com/watch?v=dQw4w9WgXcQ
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https://youtu.be/MasK0Z6wxR4
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Note: thiss link was made by @iamatinychildwhoisincapableofdoinganything,existentornonexistent
 
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==Video Solution by NiuniuMaths (Easy to understand!)==
 
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https://www.youtube.com/watch?v=Ylw-kJkSpq8
 
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~NiuniuMaths
 
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==Video Solution 2 by SpreadTheMathLove==
 
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https://www.youtube.com/watch?v=L83DxusGkSY
 
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== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
 
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https://www.youtube.com/watch?v=NLoyzNyvFKU
 
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2024|num-b=1|num-a=3}}
 
{{AMC8 box|year=2024|num-b=1|num-a=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 06:14, 15 November 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 $\boxed{\text{(C)\ 6.54}}$. ~

~Minor Formatting by GreenPlanet2050

Video Solution by Math-X (MATH-X)

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

~Math-X

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/5ZIFnqymdDQ?si=-FCGnA5WXQNp-JMF&t=175

~hsnacademy

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

Video Solution by Daily Dose of Math (Understandable, Speedy, and Easy)

https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR

~Thesmartgreekmathdude

Video Solution by WhyMath

https://youtu.be/MasK0Z6wxR4

See Also

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

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