Division of Fractions: Solving 4 7/12 ÷ 3/4 × 3/11
In this article, we will explore the step-by-step process of dividing fractions, specifically solving the problem 4 7/12 ÷ 3/4 × 3/11.
Understanding the Problem
The problem 4 7/12 ÷ 3/4 × 3/11 involves dividing a mixed fraction by a product of two fractions. To solve this problem, we need to follow the order of operations (PEMDAS) and execute the multiplication before the division.
Converting to Improper Fractions
First, let's convert the mixed fraction 4 7/12 to an improper fraction:
4 7/12 = (4 × 12) + 7 / 12 = 51/12
Now, we can rewrite the problem as:
51/12 ÷ 3/4 × 3/11
Multiplying Fractions
Next, we'll multiply 3/4 and 3/11:
3/4 × 3/11 = (3 × 3) / (4 × 11) = 9/44
Now, we have:
51/12 ÷ 9/44
Dividing Fractions
To divide fractions, we'll invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
51/12 ÷ 9/44 = 51/12 × 44/9
Multiplying Fractions (Again)
Now, let's multiply the fractions:
51/12 × 44/9 = (51 × 44) / (12 × 9) = 2244/108
Simplifying the Result
The result can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 12:
2244/108 = 187/9
Therefore, the final answer is:
4 7/12 ÷ 3/4 × 3/11 = 187/9
In conclusion, by following the order of operations and executing the multiplication before the division, we can solve the problem 4 7/12 ÷ 3/4 × 3/11 and arrive at the simplified answer 187/9.
