Perform each of the following computations
(a)1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
(b) (5 2/7 + 2 3/7)/ 2 1/2
(c) 3/2 - 4 1/3
(a) To perform the computation of 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6, we need to follow the order of operations, which is typically known as PEMDAS (parentheses, exponents, multiplication and division - from left to right, addition and subtraction - from left to right).
Step 1: Simplify the fractions:
- 1/2 + 1/3 = (3 + 2)/6 = 5/6
- 1/4 + 1/5 = (5 + 4)/20 = 9/20
- -1/6 = -1/6
Step 2: Combine the fractions and perform the addition/subtraction:
1 - 5/6 + 9/20 - 1/6 = 20/20 - 5/6 + 9/20 - 3/20
= (20 - 50 + 9 - 3) / 20
= (29 - 53) / 20
= -24/20
= -6/5
Therefore, the value of 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 is -6/5.
(b) To perform the computation of (5 2/7 + 2 3/7) divided by 2 1/2, we need to first convert the mixed fractions to improper fractions.
Step 1: Convert mixed fractions to improper fractions:
5 2/7 = (7 * 5 + 2) / 7 = 37/7
2 3/7 = (7 * 2 + 3) / 7 = 17/7
2 1/2 = (2 * 2 + 1) / 2 = 5/2
Step 2: Perform the addition:
37/7 + 17/7 = (37 + 17) / 7 = 54/7
Step 3: Perform the division:
54/7 รท 5/2 = (54/7) * (2/5) = (54 * 2) / (7 * 5) = 108/35
Therefore, the value of (5 2/7 + 2 3/7) divided by 2 1/2 is 108/35.
(c) To perform the computation of 3/2 - 4 1/3, we need to first convert the mixed fraction to an improper fraction.
Step 1: Convert the mixed fraction to an improper fraction:
4 1/3 = (3 * 4 + 1) / 3 = 13/3
Step 2: Perform the subtraction:
3/2 - 13/3 = (3 * 3 - 13 * 2) / (2 * 3) = (9 - 26) / 6
Step 3: Simplify the fraction:
(9 - 26) / 6 = -17/6
Therefore, the value of 3/2 - 4 1/3 is -17/6.