Solve this problem. Reduce to lowest terms.
Josh spent 6 1/2 hours at school, 3 2/3 hours at work, 2 3/4 hours doing homework, and 1 1/3 hours watching television. How much time did Josh spend doing these activities?
Select the correct answer.
Question 1 options:
14 hours
14 1 fourth hours
Mathml image hours
Mathml image hours
To solve this problem, we need to add up the hours spent on each activity and then reduce the resulting fraction to lowest terms.
First, let's convert all the mixed numbers into improper fractions:
6 1/2 = 13/2
3 2/3 = 11/3
2 3/4 = 11/4
1 1/3 = 4/3
Now, we can add up these fractions:
13/2 + 11/3 + 11/4 + 4/3
To add fractions, we need to find a common denominator:
The common denominator for 2, 3, and 4 is 12.
Adjusting the fractions to have a common denominator:
(13/2) * (6/6) = 78/12
(11/3) * (4/4) = 44/12
(11/4) * (3/3) = 33/12
4/3 * (4/4) = 16/12
Now, we can add the fractions:
78/12 + 44/12 + 33/12 + 16/12 = (78 + 44 + 33 + 16)/12 = 171/12
To reduce this fraction to lowest terms, we divide both the numerator and denominator by their greatest common divisor, which is 3:
(171/3)/(12/3) = 57/4
Therefore, Josh spent a total of 57/4 hours doing these activities.
To solve this problem, you need to add up all the given amounts of time.
Josh spent:
- 6 1/2 hours at school,
- 3 2/3 hours at work,
- 2 3/4 hours doing homework, and
- 1 1/3 hours watching television.
To add mixed numbers like these, first, convert the mixed numbers to improper fractions.
6 1/2 can be written as 13/2,
3 2/3 can be written as 11/3,
2 3/4 can be written as 11/4,
1 1/3 can be written as 4/3.
Now, let's add these fractions together:
13/2 + 11/3 + 11/4 + 4/3
To add the fractions, you need to find a common denominator. The least common denominator (LCD) of 2, 3, and 4 is 12.
Converting the fractions to have the same denominator:
13/2 = 39/6,
11/3 = 44/12,
11/4 = 33/12,
4/3 = 16/12.
Now, add the fractions:
39/6 + 44/12 + 33/12 + 16/12 =
(39 + 44 + 33 + 16)/12 =
132/12.
To reduce this fraction to lowest terms, find the highest common factor (HCF) of 132 and 12, which is 12.
Dividing both the numerator and denominator by 12:
132/12 = 11.
Therefore, Josh spent a total of 11 hours doing these activities.
To solve this problem, we need to add up the different amounts of time spent on each activity and then simplify the answer to its lowest terms.
First, let's convert all the mixed numbers into improper fractions.
Josh spent 6 1/2 hours at school, which can be simplified as (6 * 2 + 1)/2 = 13/2 hours.
He spent 3 2/3 hours at work, which can be simplified as (3 * 3 + 2)/3 = 11/3 hours.
He spent 2 3/4 hours doing homework, which can be simplified as (2 * 4 + 3)/4 = 11/4 hours.
He spent 1 1/3 hours watching television, which can be simplified as (1 * 3 + 1)/3 = 4/3 hours.
Now, let's add up all the fractions:
13/2 + 11/3 + 11/4 + 4/3
To add fractions with different denominators, we need to find a common denominator. In this case, the lowest common multiple of 2, 3, and 4 is 12.
So, let's convert all the fractions to have a denominator of 12:
(13/2) * (6/6) = 78/12
(11/3) * (4/4) = 44/12
(11/4) * (3/3) = 33/12
(4/3) * (4/4) = 16/12
Now we can add the fractions:
78/12 + 44/12 + 33/12 + 16/12 = 171/12
To simplify this fraction to its lowest terms, we can divide both the numerator and denominator by their greatest common divisor, which is 3 in this case:
171 ÷ 3 / 12 ÷ 3 = 57/4
Therefore, Josh spent a total of 57/4 hours doing these activities.
However, the options provided don't match this answer format. The closest option is "14 hours," but it is not in the lowest terms. So, none of the options provided are correct. The correct answer is 57/4 hours.