Final answer:
To solve 11/4 - 3/10 ÷ 6, divide 3/10 by 6 to get 1/20, and then subtract 1/20 from 11/4. After simplifying, the final answer is 27/10.
Step-by-step explanation:
To find the solution to 11/4 - 3/10 ÷ 6, we must first handle the division before subtraction due to the order of operations (PEMDAS/BODMAS).
Let's start by calculating 3/10 ÷ 6. To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number.
- Reciprocal of 6 is 1/6.
- Now multiply 3/10 by 1/6: (3/10) × (1/6) = 3/60 = 1/20.
Next, we proceed with the subtraction:
- 11/4 - 1/20 needs a common denominator. The common denominator of 4 and 20 is 20.
- Convert 11/4 to twentieths: (11 × 5) / (4 × 5) = 55/20.
- Subtract 1/20 from 55/20: 55/20 - 1/20 = 54/20.
- Simplify 54/20 by dividing both the numerator and denominator by their greatest common divisor, which is 2: 54/20 = 27/10.
Therefore, the final answer is 27/10, or 2.7 when converted to a decimal.