Question

Ari watched 1 4 of a movie in the morning, and she watched some more at night. By the end of the day, she still had 1 3 of the movie left to watch. How much of the movie did Ari watch at night?

Answer 1

Ari watched 5/12 of the movie at night, which was calculated by subtracting the portion watched in the morning and the portion left from the whole.

Step-by-step explanation:

To solve how much of the movie Ari watched at night, we need to take into account the parts watched in the morning and the remaining portion left to watch. Ari watched 1/4 of the movie in the morning and had 1/3 of the movie left to watch. Since a whole movie can be represented as 1, or 100%, we can calculate the part watched at night by subtracting both these parts from the whole.

First, find the common denominator for 1/4 and 1/3, which is 12. Convert 1/4 to 3/12 and 1/3 to 4/12.

Next, add the two fractions: 3/12 (morning) + 4/12 (remaining) = 7/12. This means that 7/12 of the movie is accounted for.

To find out how much she watched at night, subtract 7/12 from the whole: 1 (whole movie) - 7/12 = 5/12. So, Ari watched 5/12 of the movie at night.

Answer 2

Answer: Ari watched 5/12 of the movie at night.

Step-by-step explanation:

Let x represent the portion of the movie that Ari watched at night.

Ari watched 1 4 of a movie in the morning, and she watched some more at night. It means that the total portion she has watched already is 1/4 + x

The portion of the movie remaining for her to watch is

1 - (1/4 + x) = 1 - (1 + 4x)/4

By the end of the day, she still had 1 3 of the movie left to watch. It means that

1/3 = 1 - (1 + 4x)/4

1/3 = (4 - 1 - 4x)/4

1/3 = (3 - 4x)/4

Cross multiplying by 3, it becomes

1 = 3(3 - 4x)/4

Multiplying through by 4, it becomes

4 = 3(3 - 4x)

4 = 9 - 12x

12x = 9 - 4

12x = 5

x = 5/12