9514 1404 393
Answer:
20/3
Step-by-step explanation:
There are two ways to do this.
1) "invert and multiply" or "dot swap"
(10/9) ÷ (1/6) = (10/9) · (6/1)
The division is changed to multiplication (dot, ·) and the divisor fraction 1/6 is inverted (numerator and denominator are swapped).
The resulting product is ...
(10/9)×(6/1) = 60/9 = 20/3
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2. Use a common denominator. The denominators 9 and 6 of the respective fractions have a least common multiple of 18. This means both fractions can be expressed using 18 as a denominator:
[tex]\dfrac{\text{ }\dfrac{10}{9}\text{ }}{\dfrac{1}{6}}=\dfrac{\text{ }\dfrac{20}{18}\text{ }}{\dfrac{3}{18}}=\boxed{\dfrac{20}{3}}[/tex]
Once the fractions are expressed with a common denominator, the denominators can be ignored/removed/cancelled. They are equivalent to a factor of (a/a) = 1, where a=1/18.
