11 - 8 ÷ (1/3 + 1/5) Please show work I am stuck. Thank you
11 - 8 ÷ (1/3 + 1/5)
3 / (5/15 + 3/15)
3 / (8/15)
3 * (15/8) = 45/8 = 5 5/8
11 - 8 ÷ (1/3 + 1/5)
= 11 - 8/(8/15)
= 11 - 8*15/8
= 11-15
= -4
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To solve the expression 11 - 8 ÷ (1/3 + 1/5), we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's break down the steps:
Step 1: Evaluate within parentheses
Inside the parentheses, we have 1/3 + 1/5. To add these fractions together, we need a common denominator, which in this case is 15. The calculation becomes:
1/3 + 1/5 = (5/15) + (3/15) = 8/15.
Step 2: Evaluate the division
Now that we have simplified the expression inside the parentheses, we can divide 8 by 8/15. When dividing by a fraction, we multiply by the reciprocal of the denominator. So the calculation becomes:
8 ÷ (8/15) = 8 × (15/8) = 120/8.
Step 3: Simplify the division
We can simplify 120/8 by dividing the numerator and denominator by their greatest common divisor, which is 8. The calculation is:
120/8 = (120 ÷ 8) / (8 ÷ 8) = 15/1 = 15.
Step 4: Subtract the remaining numbers
Finally, we subtract 15 from 11:
11 - 15 = -4.
Therefore, the answer to the expression 11 - 8 ÷ (1/3 + 1/5) is -4.