To determine how much of the shed Macy and Bill painted together, we need to add the fractions of the shed each of them painted.
Macy painted \( \frac{2}{3} \) of the shed, and Bill painted \( \frac{1}{4} \) of the shed. We can find a common denominator to add these fractions together. The least common denominator of 3 and 4 is 12.
Converting each fraction:
- \( \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
Now we can add them: \[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \]
This means together they painted \( \frac{11}{12} \) of the shed.
To evaluate the statements:
- "Together they painted a little more than half the shed." (True, since \( \frac{11}{12} > \frac{1}{2} \))
- "Together they painted almost the entire shed." (True, since \( \frac{11}{12} \) is very close to 1)
- "Together they didn't paint half of the shed." (False, since they painted more than half)
- "Together they painted three-fourths of the shed." (False, since \( \frac{11}{12} > \frac{3}{4} \))
The most appropriate true statement would be: "Together they painted almost the entire shed."
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