Macy and Bill were painting the shed. Macy painted 2/3 of the shed, and Bill painted 1/4 of the shed. Which statement is TRUE?

Question

(1 point)
Responses

Together they painted a little more than half the shed.

Together they painted almost the entire shed.

Together they didn't paint half of the shed.

Together they painted three-fourths of the shed.

Answer 1

To find out how much of the shed Macy and Bill painted together, we need to add the fractions of the shed they each painted:

Macy painted \( \frac{2}{3} \) of the shed, and Bill painted \( \frac{1}{4} \) of the shed.

To add these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.

Convert the fractions:

• \( \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
• \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)

Now add the two fractions:

\[ \frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12} \]

Now we can analyze the statements:

1. Together they painted a little more than half the shed. (True, since \( \frac{11}{12} > \frac{1}{2} \))
2. Together they painted almost the entire shed. (True, since \( \frac{11}{12} \) is very close to 1)
3. Together they didn't paint half of the shed. (False, since they painted more than half)
4. Together they painted three-fourths of the shed. (False, since \( \frac{11}{12} > \frac{3}{4} \))

Since both the first and second statements are true, if we select the one that best expresses their contribution, "Together they painted almost the entire shed." is the most precise statement.

Thus, the correct response is: Together they painted almost the entire shed.