Question

Alice is doing a project for her science class. She spends 3223​ hours collecting data, 3443​ hour analyzing her data, and 4554​ hour creating a poster with her results. In total, how many hours did she spend working on her science project? Express your answer as a fraction in simplest form.

a) 13/10 hours
b) 9/10 hours
c) 11/10​ hours
d) 7/10 hours

Answer 1

Alice spent a total of 61/220 hours on her science project, which is the sum of the time spent on collecting data, analyzing data, and creating a poster, each converted to a common denominator of 220 before adding together.

Step-by-step explanation:

The question asks for the total time Alice spent working on her science project, expressed as a fraction. We need to add the fractions of hours spent on different tasks together to get the total time. Alice spent 3/22 hours collecting data, 3/44 hours analyzing data, and 4/55 hours creating a poster.

To add these fractions, we first need a common denominator. The least common multiple of 22, 44, and 55 is 220. Now we convert each fraction to have a denominator of 220:

• 3/22 hours = (3×220) / (22×220) = 30/220 hours
• 3/44 hours = (3×220) / (44×220) = 15/220 hours
• 4/55 hours = (4×220) / (55×220) = 16/220 hours

Now, we add these fractions together:

30/220 + 15/220 + 16/220 = (30 + 15 + 16)/220 = 61/220 hours

The simplest form of 61/220 is found by dividing both the numerator and the denominator by their greatest common divisor, which is 1. So the fraction is already in simplest form.

Therefore, the total time spent on the science project is 61/220 hours.