Answer:
D) 8/9
Step-by-step explanation:
There are a couple of ways to do division by fractions. In the end, they amount to the same thing, but they look different as you go through the process. They might be summarized as ...
- "invert and multiply", or "dot swap", and
- numerators of the same denominator.
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Signs
The sign of the quotient will be negative only if there are an odd number of minus signs in the problem. Here, both the dividend and divisor have minus signs, so the number of them is even. The result will be positive. (This eliminates choices A and B.)
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Invert and Multiply
As with ordinary division by any number, it is equivalent to multiplication by the reciprocal of the number. That fact is used here to change the division problem to a multiplication problem.
[tex]\dfrac{8}{15}\div\dfrac{3}{5}=\dfrac{8}{15}\times\dfrac{5}{3}\qquad\text{multiply by the reciprocal of the divisor}[/tex]
[tex]=\dfrac{8}{15}\cdot\dfrac{5}{3}\qquad\text{"dot" for multiplication, "swap" to make reciprocal}[/tex]
The result can be reduced by cancelling common factors in this process.
[tex]\dfrac{8}{15}\times\dfrac{5}{3}=\dfrac{8}{3}\times\dfrac{5}{5}\times\dfrac{1}{3}=\dfrac{8}{3\cdot3}=\boxed{\dfrac{8}{9}}[/tex]
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Numerators of the Same Denominator
For this method, both the dividend and the divisor need to be expressed over the same denominator.
[tex]\dfrac{8}{15}\div\dfrac{3}{5}=\dfrac{8}{15}\div\dfrac{3\cdot3}{5\cdot3}=\dfrac{8}{15}\div\dfrac{9}{15}[/tex]
We can rewrite this as a compound fraction to show that we effectively cancel the same denominators.
[tex]=\dfrac{\left(\dfrac{8}{15}\right)}{\left(\dfrac{9}{15}\right)}=\boxed{\dfrac{8}{9}}[/tex]
