To determine which statement is true, we need to calculate the total fraction of the shed that Macy and Bill painted together.
Macy painted \( \frac{2}{3} \) of the shed, and Bill painted \( \frac{1}{4} \) of the shed.
To add these fractions, we first need a common denominator. The least common multiple of 3 and 4 is 12.
Now, we can convert each fraction:
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For Macy: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
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For Bill: \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]
Now we can add the two fractions: \[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \]
So together, Macy and Bill painted \( \frac{11}{12} \) of the shed.
Now, let's evaluate the statements:
- "Together they painted a little more than half the shed." - True, since \( \frac{11}{12} \) is greater than \( \frac{1}{2} \).
- "Together they painted almost the entire shed." - True, since \( \frac{11}{12} \) is very close to 1 (the whole shed).
- "Together they didn't paint half of the shed." - False, because they did paint more than half.
- "Together they painted three-fourths of the shed." - False, because \( \frac{11}{12} \) is greater than \( \frac{3}{4} \) (which is \( \frac{9}{12} \)).
Both the first and second statements can be considered true, but the first statement emphasizes the fact that they painted more than half, while the second emphasizes that they painted almost all of it. The strongest conclusion based on the calculations is that they painted almost the entire shed, so the second statement stands out as a concise culmination of their efforts:
Together they painted almost the entire shed.
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