What is the solution to 2 6/7 divided by 2/14
A. 7
B. 14
C. 20****
D. 40
To solve the division problem 2 6/7 divided by 2/14, you need to convert the mixed number and the fraction into improper fractions, and then divide the two fractions.
Step 1: Convert the mixed number 2 6/7 into an improper fraction.
To convert the mixed number 2 6/7 into an improper fraction, multiply the whole number (2) by the denominator (7), and add the numerator (6). The result is the numerator of the improper fraction.
2 * 7 + 6 = 14 + 6 = 20
The denominator of the improper fraction remains the same, which is 7.
So, 2 6/7 can be written as the improper fraction 20/7.
Step 2: Convert the fraction 2/14 into its simplest form.
The fraction 2/14 can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
The greatest common divisor of 2 and 14 is 2.
Dividing both the numerator (2) and denominator (14) by 2, we get:
2 ÷ 2 = 1
14 ÷ 2 = 7
So, 2/14 simplifies to 1/7.
Step 3: Divide the two fractions.
When you divide two fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, 20/7 divided by 1/7 can be calculated as:
20/7 * 7/1
To multiply fractions, you multiply the numerators together and multiply the denominators together.
(20 * 7) / (7 * 1) = 140/7 = 20
Therefore, the solution to 2 6/7 divided by 2/14 is 20 which corresponds to option C.