To simplify the given expression, we need to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and also convert mixed numbers to improper fractions if necessary.
Let's start by converting the mixed numbers to improper fractions:
1 13/28 = (281 + 13)/28 = 41/28
1 1/4 = (41 + 1)/4 = 5/4
Now, let's substitute the improper fractions back into the expression and simplify:
8/15 + (2 - 41/28) : 25/49 - 5/4
= 8/15 + (56/28 - 41/28) : 25/49 - 5/4
= 8/15 + 15/28 : 25/49 - 5/4
= 8/15 + 15/28 : 25/49 - 20/4
= 8/15 + 15/28 : 25/49 - 5
Next, we perform division first:
= 8/15 + (15/28 * 49/25) - 5
= 8/15 + 735/1400 - 5
= 8/15 + 21/40 - 5
Now, we find a common denominator to combine the fractions:
= (840 + 2115 - 5*600) / 600
= (320 + 315 - 3000) / 600
= (635 - 3000) / 600
= -2365 / 600
Therefore, the simplified expression is -2365/600, which can be further reduced by dividing both the numerator and denominator by 5 to get the final answer:
-2365 ÷ 5 = -473
600 ÷ 5 = 120
So, the final answer is -473/120.
