3 2/3 Divided by 2 1/6
In this article, we will solve a mathematical problem that involves dividing a mixed number by another mixed number. Specifically, we will find the result of 3 2/3 divided by 2 1/6.
Step-by-Step Solution
To divide mixed numbers, we need to convert them into improper fractions first. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).
Convert Mixed Numbers to Improper Fractions
Let's convert 3 2/3 and 2 1/6 to improper fractions:
3 2/3
3 × 3 = 9 (multiply the whole number part by the denominator)
9 + 2 = 11 (add the numerator to the product)
So, 3 2/3 = 11/3
2 1/6
2 × 6 = 12 (multiply the whole number part by the denominator)
12 + 1 = 13 (add the numerator to the product)
So, 2 1/6 = 13/6
Divide the Improper Fractions
Now, we can divide the improper fractions:
11/3 ÷ 13/6
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
11/3 × 6/13 = (11 × 6) / (3 × 13) = 66 / 39
Simplify the Result
Finally, we simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD):
GCD of 66 and 39 is 3
66 ÷ 3 = 22
39 ÷ 3 = 13
So, 66/39 = 22/13
The Final Answer
Therefore, 3 2/3 divided by 2 1/6 is equal to 22/13.
We can convert this improper fraction back to a mixed number if needed:
22/13
22 ÷ 13 = 1 with a remainder of 9
So, 22/13 = 1 9/13
There you have it! The solution to 3 2/3 divided by 2 1/6 is 1 9/13.
