Problem 4 · 2012 AMC 8
Easy
Fractions, Decimals & Percents
fraction-of-whole
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
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Answer: C — 1/8.
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Hint 1 of 2
The whole pizza is already cut into 12 equal slices — that's your natural unit. Count Peter's share in slices first, before turning it into a fraction of the pizza.
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Hint 2 of 2
"Shared equally" means he got half a slice, not a whole one. So count in halves: how many half-slices did he eat?
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Approach: count the share in slices, then over 12
- Peter ate 1 whole slice plus half of another — that's 1½ slices out of the 12.
- A clean way to avoid the ½: count in half-slices. Peter ate 3 half-slices, and the pizza holds 24 half-slices, so his share is 3/24 = 1/8.
- Sanity check: one slice alone is 1/12, and he ate a bit more than one slice, so the answer should be a little bigger than 1/12 — 1/8 is.
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