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

Revision as of 13:28, 26 January 2024

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

Video Solution 1 (easy to digest) by Power Solve

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

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 13: / Line 13: @@
 ~MrThinker
+==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
 ==Video Solution 1 (easy to digest) by Power Solve==
 https://youtu.be/HE7JjZQ6xCk?si=4I0UO5oOVrC2vJep&t=29

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