Performing division with mixed numbers and fractions can be a bit tricky, but we can break it down step by step.
To divide 6 3/4 by 2 5/8, we need to follow the order of operations and convert the mixed numbers to improper fractions first.
6 3/4 can be converted to an improper fraction as follows:
6 3/4 = 27/4
Similarly, 2 5/8 can be converted to an improper fraction:
2 5/8 = 21/8
Now we can rewrite the division problem as:
(27/4) ÷ (21/8)
To divide fractions, we can invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
(27/4) × (8/21)
= (27 × 8) / (4 × 21)
= 216 / 84
To simplify the fraction, we can find the greatest common divisor (GCD) of 216 and 84, which is 12. Dividing both the numerator and denominator by 12, we get:
216 ÷ 12 = 18 84 ÷ 12 = 7
So, the final result is:
6 3/4 ÷ 2 5/8 = 18/7
To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator:
18 ÷ 7 = 2 with a remainder of 4
So, the final answer is:
2 4/7