Solving the Expression: 2/3 + 1/4 × 2/5 - 3/4 + 5/2
To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Multiply 1/4 and 2/5
First, let's multiply 1/4 and 2/5:
(1/4) × (2/5) = 2/20 = 1/10
So, the expression becomes:
2/3 + 1/10 - 3/4 + 5/2
- Add 2/3 and 1/10
Next, let's add 2/3 and 1/10:
(2/3) + (1/10) = (20/30) + (3/30) = 23/30
The expression now becomes:
23/30 - 3/4 + 5/2
- Subtract 3/4 from 23/30
To subtract 3/4 from 23/30, we need to find a common denominator, which is 12. So, we can convert both fractions:
23/30 = 46/60
3/4 = 45/60
Now, let's subtract:
(46/60) - (45/60) = 1/60
The expression now becomes:
1/60 + 5/2
- Add 1/60 and 5/2
To add 1/60 and 5/2, we need to convert 5/2 to a fraction with a denominator of 60:
5/2 = 150/60
Now, let's add:
(1/60) + (150/60) = 151/60
Therefore, the final answer is:
151/60
This is the result of evaluating the expression 2/3 + 1/4 × 2/5 - 3/4 + 5/2.
