Add the fractions 1/3, 5/6, and 3/8 and reduce your answer to lowest terms.
1/3 + 5/6 = 7/6
7/6 + 3/8 = 37/24
37/24 = 1 13/24 or approx 1.5417
To add fractions, you need to find a common denominator. The common denominator is the least common multiple of the denominators. In this case, the denominators are 3, 6, and 8.
The prime factorization of each of the denominators is as follows:
3 = 3
6 = 2 * 3
8 = 2 * 2 * 2
To find the least common multiple, take the highest exponent of each prime factor:
2 * 2 * 2 * 3 = 24
So, the common denominator is 24.
Next, you need to adjust the numerators to match the common denominator. To do this, multiply the numerator of each fraction by the same factor that was used to get the common denominator.
1/3 = 8/24 (multiplied numerator and denominator by 8)
5/6 = 20/24 (multiplied numerator and denominator by 4)
3/8 = 9/24 (multiplied numerator and denominator by 3)
Now that the fractions have a common denominator, you can add them:
8/24 + 20/24 + 9/24 = 37/24
To reduce the fraction to its lowest terms, you need to simplify the numerator and denominator by finding their greatest common divisor (GCD).
The GCD of 37 and 24 is 1. Since there is no common factor other than 1, the fraction 37/24 is already in its lowest terms.
Therefore, the sum of the fractions 1/3, 5/6, and 3/8, when reduced to lowest terms, is 37/24.