9514 1404 393
Answer:
11/15
Step-by-step explanation:
There are three ways you can solve a problem involving division of fractions.
1) Remember that division is the same as multiplication by the reciprocal. (This is true for any division, not just division of fractions.) The reciprocal of 9/11 is 11/9 (turn it upside down). Then ...
[tex]\dfrac{3}{5}\div\dfrac{9}{11}=\dfrac{3}{5}\times\dfrac{11}{9}[/tex]
To multiply fractions, the products of numerators and denominators become the numerator and denominator of the product. We can factor 3 from the denominator here and use that to cancel a factor of 3 in the numerator.
[tex]=\dfrac{3\times11}{5\times9}=\dfrac{3\times11}{3\times5\times3}=\dfrac{3}{3}\times\dfrac{11}{15}=\dfrac{11}{15}[/tex]
The product fraction is 33/45, but each of these numbers has a factor of 3. Those common factors in numerator and denominator can cancel to reduce the fraction to lowest terms. The result is 11/15.
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2) Each fraction can be expressed using a common denominator. Here, that can be 5×11 = 55.
[tex]\dfrac{3}{5}\div\dfrac{9}{11}=\left(\dfrac{3}{5}\cdot\dfrac{11}{11}\right)\div\left(\dfrac{9}{11}\cdot\dfrac{5}{5}\right)=\dfrac{33}{55}\div\dfrac{45}{55}[/tex]
When the fractions have a common denominator, their quotient is the quotient of the numerators.
[tex]=\dfrac{33}{45}=\dfrac{3}{3}\times\dfrac{11}{15}=\dfrac{11}{15}[/tex]
The result is 11/15.
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3) Each fraction can be expressed using a common numerator. Then the quotient is the reciprocal of the quotient of denominators.
[tex]\dfrac{3}{5}\div\dfrac{9}{11}=\left(\dfrac{3}{5}\cdot\dfrac{3}{3}\right)\div\dfrac{9}{11}=\dfrac{9}{15}\div\dfrac{9}{11}=\dfrac{11}{15}[/tex]
The result is 11/15.
Note this method is rarely used. You can see how it works if you compare to the first method (9/15)÷(9/11) = (9/15)×(11/9) = (9×11)/(9×15) = 11/15.
