Final answer:
To rewrite 2/3 divided by 1/6 using a common denominator of 6, you represent 2/3 as 4/6 and 1/6 stays the same. Then multiply the numerators and denominators separately, resulting in 4.
Step-by-step explanation:
To rewrite 2/3 divided by 1/6 using a common denominator, you first find a number that both denominators (3 and 6) can divide into without leaving a remainder. The smallest such number in this case is 6, which is the least common multiple of 3 and 6. We can then rewrite the fractions so that they both have the same denominator.
The fraction 2/3 can be adjusted to have 6 as the denominator by multiplying the numerator and denominator by 2, resulting in 4/6. The fraction 1/6 already has 6 as its denominator, so we leave it as it is.
Now that both fractions have the same denominator, you would simply multiply the numerators together and the denominators together for division:
2/3 ÷ 1/6 = (2 × 6)/(3 × 1) = 12/3 = 4.
Therefore, the division of the two fractions is 4 when we rewrite 2/3 divided by 1/6 using a common denominator of 6.