🇺🇸 AMC 8 ⇄ switch contest
2024 AMC 8

Problem 2

Problem 2 · 2024 AMC 8 Easy
Fractions, Decimals & Percents fraction-to-decimal

What is the value of this expression in decimal form?

4411 + 11044 + 441100
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Answer: C — 6.54.
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Hint 1 of 2
Before finding a common denominator, glance at each fraction alone — do any of them just collapse to a clean number?
Still stuck? Show hint 2 →
Hint 2 of 2
Each one simplifies on its own (every part hides a factor of 11). Turn each into a decimal, then add.
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Approach: simplify each fraction, then add
  1. Don't reach for a common denominator — each fraction simplifies to a clean decimal on its own, so just turn them one at a time. 4411 = 4.
  2. 11044 = 52 = 2.5 (cancel 22).
  3. 441100 = 4100 = 0.04 (cancel 11).
  4. Add: 4 + 2.5 + 0.04 = 6.54. Sanity check: answers near 6.5 should sit just above 6.5 once the tiny 0.04 is added — rules out 6.4 and 6.9.
Another way — pull out the shared 11 first (MAA):
  1. Every numerator and denominator carries a factor of 11. Spotting that turns 44, 110, 1100 into 4×11, 10×11, 100×11 — the 11's cancel before you divide.
  2. You're left with 41 + 104 + 4100 = 4 + 2.5 + 0.04 = 6.54.
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