To simplify the expression 12 8/15 − 7 + 7/15 + 15, we can follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
12 8/15 can be converted to (12 * 15 + 8)/15 = 188/15.
7 can be written as 7/1.
7/15 remains the same.
15 can be written as 15/1.
Step 2: Combine the fractions.
188/15 − 7/1 + 7/15 + 15/1
To combine the fractions, we need to find a common denominator. In this case, the lowest common denominator is 15.
So, we rewrite the fractions with a common denominator of 15:
(188/15) − (7 * 15/1) + (7/15) + (15 * 15/1)
Which simplifies to:
(188/15) − (105/1) + (7/15) + (225/1)
Step 3: Perform the calculations.
To add or subtract fractions, we need a common denominator. In this case, the common denominator is still 15.
So, we have:
(188 − (105 * 15) + 7 + (225 * 15))/15
Simplifying further:
(188 − 1575 + 7 + 3375)/15
Calculating:
(188 − 1575 + 7 + 3375)/15 = (188 + 7 + 3375 - 1575)/15 = 1995/15
Step 4: Simplify the fraction.
The fraction 1995/15 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
1995/15 = (15 * 133)/15
Simplifying further:
(15 * 133)/15 = 133
Therefore, the simplified answer is 133.